Bible Numbers 2.0

Dark Prophecy Arrives

The previous numeric study, Two Dark Prophecies Concerning Israel, closed with two questions: 1) When will Israel be thrown into outer darkness? and 2) Which nation will receive the kingdom of God? The first question is answered here.

Jesus' prophecy of Israel being thrown into outer darkness came true. He gave this prophecy at the time he was proving himself to be the fulfillment of Isaiah's prophecy of a saviour and healer (Matthew 8:5-17). Despite being a saviour and healer, Isaiah's prophecy foreshadowed elements of darkness, and this continued in Jesus' prophecy for Israel (verse 12). The fulfillment of Jesus' prophecy is seen in Matthew 27:37-50 when darkness covered the land for three hours during the crucifixion (verse 45). The numeric features in this study show God’s hand behind the events, and confirm the validity of Jesus' prophecy. Israel has been in darkness ever since.

This is a numeric study on the prophecy and fulfillment of Israel being thrown into outer darkness. It is not a study on the prophecy and fulfillment of the crucifixion, a monumental historic event. Nor is it a numeric study on God or Jesus. In comparison with these topics, it would rank as fourth in importance. Some numeric inconsistencies should be expected. Nevertheless, it is an important spiritual lesson concerning the darkness dwelling in humanity.

Matthew's passage begins with the centurion since the theme is of Gentiles superseding Israel, and the consequences of being superseded. The passage ends with the quote of Isaiah's prophecy on the suffering servant. Jesus came as king and healer, but he was rejected by his own people. (Isaiah 53:3; John 1:11)

5 As he entered Capernaum, a centurion came forward to him, beseeching him 6 and saying, "Lord, my servant is lying paralyzed at home, in terrible distress." 7 And he said to him, "I will come and heal him." 8 But the centurion answered him, "Lord, I am not worthy to have you come under my roof; but only say the word, and my servant will be healed. 9 For I am a man under authority, with soldiers under me; and I say to one, `Go,' and he goes, and to another, `Come,' and he comes, and to my slave, `Do this,' and he does it." 10 When Jesus heard him, he marveled, and said to those who followed him, "Truly, I say to you, not even in Israel have I found such faith. 11 I tell you, many will come from east and west and sit at table with Abraham, Isaac, and Jacob in the kingdom of heaven, 12 while the sons of the kingdom will be thrown into the outer darkness; there men will weep and gnash their teeth." 13 And to the centurion Jesus said, "Go; be it done for you as you have believed." And the servant was healed at that very moment. 14 And when Jesus entered Peter's house, he saw his mother-in-law lying sick with a fever; 15 he touched her hand, and the fever left her, and she rose and served him. 16 That evening they brought to him many who were possessed with demons; and he cast out the spirits with a word, and healed all who were sick. 17 This was to fulfil what was spoken by the prophet Isaiah, "He took our infirmities and bore our diseases." (Matthew 8:5-17)¹

While fulfilling Isaiah's prophecy, Jesus gave his own prophecy in verse 12.

Matthew 8:5-17²
A:	1										2		3
B:	346										9		700
C:	1	2	3	4	5	6	7	8	9	10	11	12	13	14
D:	5	9	90	5	20	8	60	40	100	9	4	5	100	600
E:	εισελθοντι										δε		τω

A:	4					5
B:	366					104
C:	15	16	17	18	19	20	21	22
D:	9	7	90	60	200	5	9	90
E:	ιησου					εις

A:	6
B:	497
C:	23	24	25	26	27	28	29	30	31	32
D:	10	1	70	5	80	40	1	60	200	30
E:	καπερναουμ

A:	7									8
B:	380									901
C:	33	34	35	36	37	38	39	40	41	42	43	44	45
D:	70	80	60	90	7	20	8	5	40	1	200	100	600
E:	προσηλθεν									αυτω

A:	9
B:	947
C:	46	47	48	49	50	51	52	53	54	55	56	57
D:	5	10	1	100	60	40	100	1	80	400	60	90
E:	εκατονταρχος

A:	10									11
B:	823									401
C:	58	59	60	61	62	63	64	65	66	67	68	69	70	71
D:	70	1	80	1	10	1	20	600	40	1	200	100	60	40
E:	παρακαλων									αυτον

A:	12			13					14					15
B:	20			668					304					60
C:	72	73	74	75	76	77	78	79	80	81	82	83	84	85
D:	10	1	9	20	5	3	600	40	10	200	80	9	5	60
E:	και			λεγων					κυριε					ο

A:	16				17			18
B:	170				290			146
C:	86	87	88	89	90	91	92	93	94	95	96	97	98	99	100
D:	70	1	9	90	30	60	200	2	5	2	20	7	100	1	9
E:	παις				μου			βεβληται

A:	19		20		21
B:	45		107		89
C:	101	102	103	104	105	106	107	108	109
D:	5	40	100	7	60	9	10	9	1
E:	εν		τη		οικια

A:	22
B:	641
C:	110	111	112	113	114	115	116	117	118	119	120
D:	70	1	80	1	20	200	100	9	10	60	90
E:	παραλυτικος

A:	23
B:	748
C:	121	122	123	124	125	126
D:	4	5	9	40	600	90
E:	δεινως

A:	24													25
B:	434													20
C:	127	128	129	130	131	132	133	134	135	136	137	138	139	140	141	142
D:	2	1	90	1	40	9	6	60	30	5	40	60	90	10	1	9
E:	βασανιζομενος													και

A:	26					27				28	29
B:	42					901				60	456
C:	143	144	145	146	147	148	149	150	151	152	153	154	155	156	157	158
D:	20	5	3	5	9	1	200	100	600	60	9	7	90	60	200	90
E:	λεγει					αυτω				ο	ιησους

A:	30			31
B:	608			673
C:	159	160	161	162	163	164	165	166
D:	5	3	600	5	20	8	600	40
E:	εγω			ελθων

A:	32									33
B:	1059									401
C:	167	168	169	170	171	172	173	174	175	176	177	178	179	180
D:	8	5	80	1	70	5	200	90	600	1	200	100	60	40
E:	θεραπευσω									αυτον

A:	34			35										36
B:	20			342										60
C:	181	182	183	184	185	186	187	188	189	190	191	192	193	194
D:	10	1	9	1	70	60	10	80	9	8	5	9	90	60
E:	και			αποκριθεις										ο

A:	37												38
B:	947												312
C:	195	196	197	198	199	200	201	202	203	204	205	206	207	208	209
D:	5	10	1	100	60	40	100	1	80	400	60	90	5	300	7
E:	εκατονταρχος												εφη

A:	39					40			41
B:	304					270			53
C:	210	211	212	213	214	215	216	217	218	219	220	221
D:	10	200	80	9	5	60	200	10	5	9	30	9
E:	κυριε					ουκ			ειμι

A:	42						43			44			45
B:	210						50			290			330
C:	222	223	224	225	226	227	228	229	230	231	232	233	234	235	236
D:	9	10	1	40	60	90	9	40	1	30	60	200	200	70	60
E:	ικανος						ινα			μου			υπο

A:	46			47
B:	147			245
C:	237	238	239	240	241	242	243	244	245
D:	100	7	40	90	100	5	3	7	40
E:	την			στεγην

A:	48								49
B:	234								42
C:	246	247	248	249	250	251	252	253	254	255	256	257
D:	5	9	90	5	20	8	7	90	1	20	20	1
E:	εισελθης								αλλα

A:	50					51				52
B:	230					89				183
C:	258	259	260	261	262	263	264	265	266	267	268	269	270	271
D:	30	60	40	60	40	5	9	70	5	20	60	3	60	40
E:	μονον					ειπε				λογον

A:	53			54									55
B:	20			230									60
C:	272	273	274	275	276	277	278	279	280	281	282	283	284
D:	10	1	9	9	1	8	7	90	5	100	1	9	60
E:	και			ιαθησεται									ο

A:	56				57			58			59			60
B:	170				290			20			84			608
C:	285	286	287	288	289	290	291	292	293	294	295	296	297	298	299	300
D:	70	1	9	90	30	60	200	10	1	9	3	1	80	5	3	600
E:	παις				μου			και			γαρ			εγω

A:	61								62				63
B:	949								53				330
C:	301	302	303	304	305	306	307	308	309	310	311	312	313	314	315
D:	1	40	8	80	600	70	60	90	5	9	30	9	200	70	60
E:	ανθρωπος								ειμι				υπο

A:	64								65				66
B:	455								1045				270
C:	316	317	318	319	320	321	322	323	324	325	326	327	328	329
D:	5	50	60	200	90	9	1	40	5	400	600	40	200	70
E:	εξουσιαν								εχων				υπ

A:	67
B:	436
C:	330	331	332	333	334	335	336
D:	5	30	1	200	100	60	40
E:	εμαυτον

A:	68										69
B:	1171										20
C:	337	338	339	340	341	342	343	344	345	346	347	348	349
D:	90	100	80	1	100	9	600	100	1	90	10	1	9
E:	στρατιωτας										και

A:	70				71
B:	628				1060
C:	350	351	352	353	354	355	356	357	358
D:	20	5	3	600	100	60	200	100	600
E:	λεγω				τουτω

A:	72									73
B:	539									20
C:	359	360	361	362	363	364	365	366	367	368	369	370
D:	70	60	80	5	200	8	7	100	9	10	1	9
E:	πορευθητι									και

A:	74									75			76
B:	530									20			641
C:	371	372	373	374	375	376	377	378	379	380	381	382	383	384	385	386
D:	70	60	80	5	200	5	100	1	9	10	1	9	1	20	20	600
E:	πορευεται									και			αλλω

A:	77					78			79
B:	745					20			600
C:	387	388	389	390	391	392	393	394	395	396	397	398	399	400	401
D:	5	80	400	60	200	10	1	9	5	80	400	5	100	1	9
E:	ερχου					και			ερχεται

A:	80			81		82					83
B:	20			700		884					290
C:	402	403	404	405	406	407	408	409	410	411	412	413	414
D:	10	1	9	100	600	4	60	200	20	600	30	60	200
E:	και			τω		δουλω					μου

A:	84							85					86
B:	336							520					20
C:	415	416	417	418	419	420	421	422	423	424	425	426	427	428	429
D:	70	60	9	7	90	60	40	100	60	200	100	60	10	1	9
E:	ποιησον							τουτο					και

A:	87					88							89		90
B:	153					452							9		60
C:	430	431	432	433	434	435	436	437	438	439	440	441	442	443	444
D:	70	60	9	5	9	1	10	60	200	90	1	90	4	5	60
E:	ποιει					ακουσας							δε		ο

A:	91						92
B:	456						340
C:	445	446	447	448	449	450	451	452	453	454	455	456	457	458
D:	9	7	90	60	200	90	5	8	1	200	30	1	90	5
E:	ιησους						εθαυμασε

A:	93			94				95
B:	20			89				259
C:	459	460	461	462	463	464	465	466	467	468	469
D:	10	1	9	5	9	70	5	100	60	9	90
E:	και			ειπε				τοις

A:	96												97
B:	758												78
C:	470	471	472	473	474	475	476	477	478	479	480	481	482	483	484	485
D:	1	10	60	20	60	200	8	60	200	90	9	40	1	30	7	40
E:	ακολουθουσιν												αμην

A:	98				99				100				101		102
B:	628				279				269				45		700
C:	486	487	488	489	490	491	492	493	494	495	496	497	498	499	500	501
D:	20	5	3	600	200	30	9	40	60	200	4	5	5	40	100	600
E:	λεγω				υμιν				ουδε				εν		τω

A:	103						104
B:	207						598
C:	502	503	504	505	506	507	508	509	510	511	512	513	514	515
D:	9	90	80	1	7	20	100	60	90	1	200	100	7	40
E:	ισραηλ						τοσαυτην

A:	105						106					107
B:	318						385					628
C:	516	517	518	519	520	521	522	523	524	525	526	527	528	529	530
D:	70	9	90	100	9	40	5	200	80	60	40	20	5	3	600
E:	πιστιν						ευρον					λεγω

A:	108		109				110			111
B:	9		279				169			239
C:	531	532	533	534	535	536	537	538	539	540	541	542	543	544	545
D:	4	5	200	30	9	40	60	100	9	70	60	20	20	60	9
E:	δε		υμιν				οτι			πολλοι

A:	112			113								114
B:	131			862								20
C:	546	547	548	549	550	551	552	553	554	555	556	557	558	559
D:	1	70	60	1	40	1	100	60	20	600	40	10	1	9
E:	απο			ανατολων								και

A:	115						116						117
B:	964						416						20
C:	560	561	562	563	564	565	566	567	568	569	570	571	572	573	574
D:	4	200	90	30	600	40	7	50	60	200	90	9	10	1	9
E:	δυσμων						ηξουσι						και

A:	118
B:	396
C:	575	576	577	578	579	580	581	582	583	584	585	586	587	588
D:	1	40	1	10	20	9	8	7	90	60	40	100	1	9
E:	ανακλιθησονται

A:	119				120						121
B:	136				115						20
C:	589	590	591	592	593	594	595	596	597	598	599	600	601
D:	30	5	100	1	1	2	80	1	1	30	10	1	9
E:	μετα				αβρααμ						και

A:	122					123			124					125
B:	111					20			622					45
C:	602	603	604	605	606	607	608	609	610	611	612	613	614	615	616
D:	9	90	1	1	10	10	1	9	9	1	10	600	2	5	40
E:	ισαακ					και			ιακωβ					εν

A:	126		127								128
B:	107		137								740
C:	617	618	619	620	621	622	623	624	625	626	627	628	629
D:	100	7	2	1	90	9	20	5	9	1	100	600	40
E:	τη		βασιλεια								των

A:	129							130		131		132
B:	1021							69		9		278
C:	630	631	632	633	634	635	636	637	638	639	640	641	642	643	644
D:	60	200	80	1	40	600	40	60	9	4	5	200	9	60	9
E:	ουρανων							οι		δε		υιοι

A:	133			134
B:	197			227
C:	645	646	647	648	649	650	651	652	653	654	655	656
D:	100	7	90	2	1	90	9	20	5	9	1	90
E:	της			βασιλειας

A:	135													136
B:	359													104
C:	657	658	659	660	661	662	663	664	665	666	667	668	669	670	671	672
D:	5	10	2	20	7	8	7	90	60	40	100	1	9	5	9	90
E:	εκβληθησονται													εις

A:	137		138						139
B:	160		410						160
C:	673	674	675	676	677	678	679	680	681	682
D:	100	60	90	10	60	100	60	90	100	60
E:	το		σκοτος						το

A:	140								141
B:	940								29
C:	683	684	685	686	687	688	689	690	691	692	693	694
D:	5	50	600	100	5	80	60	40	5	10	5	9
E:	εξωτερον								εκει

A:	142					143	144
B:	205					60	419
C:	695	696	697	698	699	700	701	702	703	704	705	706	707	708
D:	5	90	100	1	9	60	10	20	1	200	8	30	60	90
E:	εσται					ο	κλαυθμος

A:	145			146	147							148
B:	20			60	465							740
C:	709	710	711	712	713	714	715	716	717	718	719	720	721	722
D:	10	1	9	60	2	80	200	3	30	60	90	100	600	40
E:	και			ο	βρυγμος							των

A:	149							150			151					152
B:	904							20			129					60
C:	723	724	725	726	727	728	729	730	731	732	733	734	735	736	737	738
D:	60	4	60	40	100	600	40	10	1	9	5	9	70	5	40	60
E:	οδοντων							και			ειπεν					ο

A:	153						154
B:	456						700
C:	739	740	741	742	743	744	745	746
D:	9	7	90	60	200	90	100	600
E:	ιησους						τω

A:	155											156
B:	1397											279
C:	747	748	749	750	751	752	753	754	755	756	757	758	759	760	761	762
D:	5	10	1	100	60	40	100	1	80	400	600	200	70	1	3	5
E:	εκατονταρχω											υπαγε

A:	157			158		159
B:	20			690		660
C:	763	764	765	766	767	768	769	770	771	772	773	774	775	776	777
D:	10	1	9	600	90	5	70	9	90	100	5	200	90	1	90
E:	και			ως		επιστευσας

A:	160								161			162
B:	770								159			20
C:	778	779	780	781	782	783	784	785	786	787	788	789	790	791
D:	3	5	40	7	8	7	100	600	90	60	9	10	1	9
E:	γενηθητω								σοι			και

A:	163				164	165				166					167
B:	25				60	170				561					45
C:	792	793	794	795	796	797	798	799	800	801	802	803	804	805	806	807
D:	9	1	8	7	60	70	1	9	90	1	200	100	60	200	5	40
E:	ιαθη				ο	παις				αυτου					εν

A:	168		169			170						171
B:	107		681			76						20
C:	808	809	810	811	812	813	814	815	816	817	818	819	820	821
D:	100	7	600	80	1	5	10	5	9	40	7	10	1	9
E:	τη		ωρα			εκεινη						και

A:	172					173	174						175
B:	673					60	456						104
C:	822	823	824	825	826	827	828	829	830	831	832	833	834	835	836
D:	5	20	8	600	40	60	9	7	90	60	200	90	5	9	90
E:	ελθων					ο	ιησους						εις

A:	176			177						178
B:	147			129						515
C:	837	838	839	840	841	842	843	844	845	846	847	848	849	850	851
D:	100	7	40	60	9	10	9	1	40	70	5	100	80	60	200
E:	την			οικιαν						πετρου

A:	179				180			181
B:	23				147			249
C:	852	853	854	855	856	857	858	859	860	861	862	863	864	865	866
D:	5	9	4	5	100	7	40	70	5	40	8	5	80	1	40
E:	ειδε				την			πενθεραν

A:	182					183
B:	561					158
C:	867	868	869	870	871	872	873	874	875	876	877	878	879	880	881
D:	1	200	100	60	200	2	5	2	20	7	30	5	40	7	40
E:	αυτου					βεβλημενην

A:	184			185
B:	20			926
C:	882	883	884	885	886	887	888	889	890	891	892	893	894	895
D:	10	1	9	70	200	80	5	90	90	60	200	90	1	40
E:	και			πυρεσσουσαν

A:	186			187					188
B:	20			668					197
C:	896	897	898	899	900	901	902	903	904	905	906
D:	10	1	9	7	500	1	100	60	100	7	90
E:	και			ηψατο					της

A:	189						190					191
B:	644						398					20
C:	907	908	909	910	911	912	913	914	915	916	917	918	919	920
D:	400	5	9	80	60	90	1	200	100	7	90	10	1	9
E:	χειρος						αυτης					και

A:	192						193					194
B:	363						348					60
C:	921	922	923	924	925	926	927	928	929	930	931	932
D:	1	300	7	10	5	40	1	200	100	7	40	60
E:	αφηκεν						αυτην					ο

A:	195							196			197
B:	605							20			110
C:	933	934	935	936	937	938	939	940	941	942	943	944	945	946	947	948
D:	70	200	80	5	100	60	90	10	1	9	7	3	5	80	8	7
E:	πυρετος							και			ηγερθη

A:	198			199
B:	20			144
C:	949	950	951	952	953	954	955	956	957	958	959
D:	10	1	9	4	9	7	10	60	40	5	9
E:	και			διηκονει

A:	200						201					202
B:	460						660					9
C:	960	961	962	963	964	965	966	967	968	969	970	971	972
D:	1	200	100	60	9	90	60	500	9	1	90	4	5
E:	αυτοις						οψιας					δε

A:	203
B:	280
C:	973	974	975	976	977	978	979	980	981
D:	3	5	40	60	30	5	40	7	90
E:	γενομενης

A:	204											205
B:	406											901
C:	982	983	984	985	986	987	988	989	990	991	992	993	994	995	996
D:	70	80	60	90	7	40	5	3	10	1	40	1	200	100	600
E:	προσηνεγκαν											αυτω

A:	206
B:	644
C:	997	998	999	1000	1001	1002	1003	1004	1005	1006	1007	1008	1009	1010	1011
D:	4	1	9	30	60	40	9	6	60	30	5	40	60	200	90
E:	δαιμονιζομενους

A:	207							208
B:	520							20
C:	1012	1013	1014	1015	1016	1017	1018	1019	1020	1021
D:	70	60	20	20	60	200	90	10	1	9
E:	πολλους							και

A:	209							210
B:	88							101
C:	1022	1023	1024	1025	1026	1027	1028	1029	1030
D:	5	50	5	2	1	20	5	100	1
E:	εξεβαλε							τα

A:	211								212				213
B:	447								683				20
C:	1031	1032	1033	1034	1035	1036	1037	1038	1039	1040	1041	1042	1043	1044	1045
D:	70	40	5	200	30	1	100	1	20	60	3	600	10	1	9
E:	πνευματα								λογω				και

A:	214						215				216
B:	302						450				711
C:	1046	1047	1048	1049	1050	1051	1052	1053	1054	1055	1056	1057	1058	1059	1060
D:	70	1	40	100	1	90	100	60	200	90	10	1	10	600	90
E:	παντας						τους				κακως

A:	217
B:	696
C:	1061	1062	1063	1064	1065	1066	1067
D:	5	400	60	40	100	1	90
E:	εχοντας

A:	218											219
B:	509											820
C:	1068	1069	1070	1071	1072	1073	1074	1075	1076	1077	1078	1079	1080	1081	1082
D:	5	8	5	80	1	70	5	200	90	5	40	60	70	600	90
E:	εθεραπευσεν											οπως

A:	220							221		222
B:	792							160		140
C:	1083	1084	1085	1086	1087	1088	1089	1090	1091	1092	1093	1094	1095	1096
D:	70	20	7	80	600	8	7	100	60	80	7	8	5	40
E:	πληρωθη							το		ρηθεν

A:	223			224						225
B:	14			367						360
C:	1097	1098	1099	1100	1101	1102	1103	1104	1105	1106	1107	1108
D:	4	9	1	7	90	1	9	60	200	100	60	200
E:	δια			ησαιου						του

A:	226								227
B:	877								378
C:	1109	1110	1111	1112	1113	1114	1115	1116	1117	1118	1119	1120	1121	1122	1123	1124
D:	70	80	60	300	7	100	60	200	20	5	3	60	40	100	60	90
E:	προφητου								λεγοντος

A:	228					229
B:	451					191
C:	1125	1126	1127	1128	1129	1130	1131	1132
D:	1	200	100	60	90	100	1	90
E:	αυτος					τας

A:	230									231
B:	249									677
C:	1133	1134	1135	1136	1137	1138	1139	1140	1141	1142	1143	1144	1145
D:	1	90	8	5	40	5	9	1	90	7	30	600	40
E:	ασθενειας									ημων

A:	232					233			234
B:	33					20			191
C:	1146	1147	1148	1149	1150	1151	1152	1153	1154	1155	1156
D:	5	20	1	2	5	10	1	9	100	1	90
E:	ελαβε					και			τας

A:	235						236
B:	540						334
C:	1157	1158	1159	1160	1161	1162	1163	1164	1165	1166	1167	1168	1169	1170	1171
D:	40	60	90	60	200	90	5	2	1	90	100	1	90	5	40
E:	νοσους						εβαστασεν

A: Word position. B: Word sum. C: Letter position. D: Letter value.
E: Greek.

The passage on the fulfillment of Jesus' prophecy begins with the charge against him. He is stated to be king, yet is rejected and to be crucified. This parallels Israel rejecting God and asking Samuel for a king. (1 Samuel 8:7) Samuel warned Israel this was great wickedness. Here, Israel rejects Jesus, God’s chosen. This section ends with Jesus' death, where it is then impossible for Israel to reverse the deed.

37 And over his head they put the charge against him, which read, "This is Jesus the King of the Jews." 38 Then two robbers were crucified with him, one on the right and one on the left. 39 And those who passed by derided him, wagging their heads 40 and saying, "You who would destroy the temple and build it in three days, save yourself! If you are the Son of God, come down from the cross." 41 So also the chief priests, with the scribes and elders, mocked him, saying, 42 "He saved others; he cannot save himself. He is the King of Israel; let him come down now from the cross, and we will believe in him. 43 He trusts in God; let God deliver him now, if he desires him; for he said, `I am the Son of God.'" 44 And the robbers who were crucified with him also reviled him in the same way. 45 Now from the sixth hour there was darkness over all the land until the ninth hour. 46 And about the ninth hour Jesus cried with a loud voice, "Eli, Eli, lama sabachthani?" that is, "My God, my God, why hast thou forsaken me?" 47 And some of the bystanders hearing it said, "This man is calling Elijah." 48 And one of them at once ran and took a sponge, filled it with vinegar, and put it on a reed, and gave it to him to drink. 49 But the others said, "Wait, let us see whether Elijah will come to save him." 50 And Jesus cried again with a loud voice and yielded up his spirit. (Matthew 27:37-50)

The fulfillment of Jesus' prophecy is seen in Israel's rejection of him. They mocked what they did not understand. As their mockery grew, Jesus' prophecy came true. The entire land became dark for three hours. This was no normal darkness caused by clouds. It was outer darkness.

The darkness was an outward manifestation of what happened within the rabble roused mob when they insisted Pilate have Jesus executed. They claimed to accept responsibility for Jesus' death. His blood be on us and on our children! (Matthew 27:25) These were extremely dark and dangerous words.

Matthew 27:37-50
A:	1			2								3
B:	20			146								716
C:	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
D:	10	1	9	5	70	5	8	7	10	1	40	5	70	1	40	600
E:	και			επεθηκαν								επανω

A:	4			5							6
B:	197			433							561
C:	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
D:	100	7	90	10	5	300	1	20	7	90	1	200	100	60	200
E:	της			κεφαλης							αυτου

A:	7			8						9
B:	147			160						561
C:	32	33	34	35	36	37	38	39	40	41	42	43	44	45
D:	100	7	40	1	9	100	9	1	40	1	200	100	60	200
E:	την			αιτιαν						αυτου

A:	10											11
B:	244											510
C:	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61
D:	3	5	3	80	1	30	30	5	40	7	40	60	200	100	60	90
E:	γεγραμμενην											ουτος

A:	12					13						14
B:	244					456						60
C:	62	63	64	65	66	67	68	69	70	71	72	73
D:	5	90	100	9	40	9	7	90	60	200	90	60
E:	εστιν					ιησους						ο

A:	15								16
B:	417								740
C:	74	75	76	77	78	79	80	81	82	83	84
D:	2	1	90	9	20	5	200	90	100	600	40
E:	βασιλευς								των

A:	17								18
B:	923								265
C:	85	86	87	88	89	90	91	92	93	94	95	96
D:	9	60	200	4	1	9	600	40	100	60	100	5
E:	ιουδαιων								τοτε

A:	19											20
B:	881											330
C:	97	98	99	100	101	102	103	104	105	106	107	108	109	110
D:	90	100	1	200	80	60	200	40	100	1	9	90	200	40
E:	σταυρουνται											συν

A:	21				22			23						24
B:	901				264			227						104
C:	111	112	113	114	115	116	117	118	119	120	121	122	123	124	125	126
D:	1	200	100	600	4	200	60	20	7	90	100	1	9	5	9	90
E:	αυτω				δυο			λησται						εις

A:	25		26						27			28			29
B:	15		708						20			104			55
C:	127	128	129	130	131	132	133	134	135	136	137	138	139	140	141	142
D:	5	10	4	5	50	9	600	40	10	1	9	5	9	90	5	50
E:	εκ		δεξιων						και			εις			εξ

A:	30								31		32
B:	1715								69		9
C:	143	144	145	146	147	148	149	150	151	152	153	154
D:	5	200	600	40	200	30	600	40	60	9	4	5
E:	ευωνυμων								οι		δε

A:	33
B:	771
C:	155	156	157	158	159	160	161	162	163	164	165	166	167	168	169
D:	70	1	80	1	70	60	80	5	200	60	30	5	40	60	9
E:	παραπορευομενοι

A:	34											35
B:	755											401
C:	170	171	172	173	174	175	176	177	178	179	180	181	182	183	184	185
D:	5	2	20	1	90	300	7	30	60	200	40	1	200	100	60	40
E:	εβλασφημουν											αυτον

A:	36									37
B:	554									191
C:	186	187	188	189	190	191	192	193	194	195	196	197
D:	10	9	40	60	200	40	100	5	90	100	1	90
E:	κινουντες									τας

A:	38							39					40
B:	427							941					20
C:	198	199	200	201	202	203	204	205	206	207	208	209	210	211	212
D:	10	5	300	1	20	1	90	1	200	100	600	40	10	1	9
E:	κεφαλας							αυτων					και

A:	41								42
B:	323								60
C:	213	214	215	216	217	218	219	220	221
D:	20	5	3	60	40	100	5	90	60
E:	λεγοντες								ο

A:	43								44			45
B:	972								200			141
C:	222	223	224	225	226	227	228	229	230	231	232	233	234	235	236
D:	10	1	100	1	20	200	600	40	100	60	40	40	1	60	40
E:	καταλυων								τον			ναον

A:	46			47		48
B:	20			45		328
C:	237	238	239	240	241	242	243	244	245	246	247
D:	10	1	9	5	40	100	80	9	90	9	40
E:	και			εν		τρισιν

A:	49							50
B:	222							873
C:	248	249	250	251	252	253	254	255	256	257	258	259	260	261	262	263
D:	7	30	5	80	1	9	90	60	9	10	60	4	60	30	600	40
E:	ημεραις							οικοδομων

A:	51					52							53
B:	880					496							14
C:	264	265	266	267	268	269	270	271	272	273	274	275	276	277
D:	90	600	90	60	40	90	5	1	200	100	60	40	5	9
E:	σωσον					σεαυτον							ει

A:	54				55		56			57
B:	359				14		360			273
C:	278	279	280	281	282	283	284	285	286	287	288	289	290
D:	200	9	60	90	5	9	100	60	200	8	5	60	200
E:	υιος				ει		του			θεου

A:	58								59			60
B:	138								131			360
C:	291	292	293	294	295	296	297	298	299	300	301	302	303	304
D:	10	1	100	1	2	7	8	9	1	70	60	100	60	200
E:	καταβηθι								απο			του

A:	61							62						63
B:	731							849						9
C:	305	306	307	308	309	310	311	312	313	314	315	316	317	318	319
D:	90	100	1	200	80	60	200	60	30	60	9	600	90	4	5
E:	σταυρου							ομοιως						δε

A:	64			65		66
B:	20			69		679
C:	320	321	322	323	324	325	326	327	328	329	330	331	332	333
D:	10	1	9	60	9	1	80	400	9	5	80	5	9	90
E:	και			οι		αρχιερεις

A:	67											68
B:	416											136
C:	334	335	336	337	338	339	340	341	342	343	344	345	346	347	348
D:	5	30	70	1	9	6	60	40	100	5	90	30	5	100	1
E:	εμπαιζοντες											μετα

A:	69			70										71
B:	740			890										20
C:	349	350	351	352	353	354	355	356	357	358	359	360	361	362	363	364
D:	100	600	40	3	80	1	30	30	1	100	5	600	40	10	1	9
E:	των			γραμματεων										και

A:	72
B:	1272
C:	365	366	367	368	369	370	371	372	373	374	375
D:	70	80	5	90	2	200	100	5	80	600	40
E:	πρεσβυτερων

A:	73						74
B:	133						391
C:	376	377	378	379	380	381	382	383	384	385	386	387
D:	5	20	5	3	60	40	1	20	20	60	200	90
E:	ελεγον						αλλους

A:	75						76						77
B:	830						406						260
C:	388	389	390	391	392	393	394	395	396	397	398	399	400	401
D:	5	90	600	90	5	40	5	1	200	100	60	40	60	200
E:	εσωσεν						εαυτον						ου

A:	78							79					80
B:	355							790					14
C:	402	403	404	405	406	407	408	409	410	411	412	413	414	415
D:	4	200	40	1	100	1	9	90	600	90	1	9	5	9
E:	δυναται							σωσαι					ει

A:	81								82
B:	417								207
C:	416	417	418	419	420	421	422	423	424	425	426	427	428	429
D:	2	1	90	9	20	5	200	90	9	90	80	1	7	20
E:	βασιλευς								ισραηλ

A:	83				84								85
B:	204				815								280
C:	430	431	432	433	434	435	436	437	438	439	440	441	442	443	444
D:	5	90	100	9	10	1	100	1	2	1	100	600	40	200	40
E:	εστι				καταβατω								νυν

A:	86			87			88							89
B:	131			360			731							20
C:	445	446	447	448	449	450	451	452	453	454	455	456	457	458	459	460
D:	1	70	60	100	60	200	90	100	1	200	80	60	200	10	1	9
E:	απο			του			σταυρου							και

A:	90											91
B:	699											561
C:	461	462	463	464	465	466	467	468	469	470	471	472	473	474	475	476
D:	70	9	90	100	5	200	90	60	30	5	40	1	200	100	60	200
E:	πιστευσομεν											αυτου

A:	92								93			94
B:	267								84			200
C:	477	478	479	480	481	482	483	484	485	486	487	488	489	490
D:	70	5	70	60	9	8	5	40	5	70	9	100	60	40
E:	πεποιθεν								επι			τον

A:	95				96							97
B:	113				1069							280
C:	491	492	493	494	495	496	497	498	499	500	501	502	503	504
D:	8	5	60	40	80	200	90	1	90	8	600	40	200	40
E:	θεον				ρυσασθω							νυν

A:	98					99		100
B:	401					14		47
C:	505	506	507	508	509	510	511	512	513	514	515	516
D:	1	200	100	60	40	5	9	8	5	20	5	9
E:	αυτον					ει		θελει

A:	101					102				103			104
B:	401					89				84			169
C:	517	518	519	520	521	522	523	524	525	526	527	528	529	530	531
D:	1	200	100	60	40	5	9	70	5	3	1	80	60	100	9
E:	αυτον					ειπε				γαρ			οτι

A:	105				106				107				108		109
B:	273				53				359				160		4
C:	532	533	534	535	536	537	538	539	540	541	542	543	544	545	546
D:	8	5	60	200	5	9	30	9	200	9	60	90	100	60	4
E:	θεου				ειμι				υιος				το		δ

A:	110				111			112		113
B:	361				20			69		227
C:	547	548	549	550	551	552	553	554	555	556	557	558	559	560	561
D:	1	200	100	60	10	1	9	60	9	20	7	90	100	1	9
E:	αυτο				και			οι		λησται

A:	114		115
B:	69		1609
C:	562	563	564	565	566	567	568	569	570	571	572	573	574	575	576	577
D:	60	9	90	200	90	100	1	200	80	600	8	5	40	100	5	90
E:	οι		συσταυρωθεντες

A:	116				117
B:	901				773
C:	578	579	580	581	582	583	584	585	586	587	588	589	590
D:	1	200	100	600	600	40	5	9	4	9	6	60	40
E:	αυτω				ωνειδιζον

A:	118				119			120		121
B:	901				131			9		212
C:	591	592	593	594	595	596	597	598	599	600	601	602	603	604
D:	1	200	100	600	1	70	60	4	5	5	10	100	7	90
E:	αυτω				απο			δε		εκτης

A:	122				123
B:	771				410
C:	605	606	607	608	609	610	611	612	613	614
D:	600	80	1	90	90	10	60	100	60	90
E:	ωρας				σκοτος

A:	124							125			126
B:	218							84			202
C:	615	616	617	618	619	620	621	622	623	624	625	626	627	628	629
D:	5	3	5	40	5	100	60	5	70	9	70	1	90	1	40
E:	εγενετο							επι			πασαν

A:	127			128			129			130
B:	147			50			695			771
C:	630	631	632	633	634	635	636	637	638	639	640	641	642
D:	100	7	40	3	7	40	5	600	90	600	80	1	90
E:	την			γην			εως			ωρας

A:	131						132				133		134
B:	243						164				9		147
C:	643	644	645	646	647	648	649	650	651	652	653	654	655	656	657
D:	5	40	1	100	7	90	70	5	80	9	4	5	100	7	40
E:	ενατης						περι				δε		την

A:	135						136
B:	193						721
C:	658	659	660	661	662	663	664	665	666	667
D:	5	40	1	100	7	40	600	80	1	40
E:	ενατην						ωραν

A:	137									138	139
B:	250									60	456
C:	668	669	670	671	672	673	674	675	676	677	678	679	680	681	682	683
D:	1	40	5	2	60	7	90	5	40	60	9	7	90	60	200	90
E:	ανεβοησεν									ο	ιησους

A:	140				141						142
B:	947				66						668
C:	684	685	686	687	688	689	690	691	692	693	694	695	696	697	698
D:	300	600	40	7	30	5	3	1	20	7	20	5	3	600	40
E:	φωνη				μεγαλη						λεγων

A:	143			144			145
B:	36			36			52
C:	699	700	701	702	703	704	705	706	707	708
D:	7	20	9	7	20	9	20	1	30	1
E:	ηλι			ηλι			λαμα

A:	146									147
B:	552									460
C:	709	710	711	712	713	714	715	716	717	718	719	720	721
D:	90	1	2	1	400	8	1	40	9	100	60	200	100
E:	σαβαχθανι									τουτ

A:	148				149			150			151			152
B:	204				18			290			18			290
C:	722	723	724	725	726	727	728	729	730	731	732	733	734	735	736	737
D:	5	90	100	9	8	5	5	30	60	200	8	5	5	30	60	200
E:	εστι				θεε			μου			θεε			μου

A:	153					154
B:	159					35
C:	738	739	740	741	742	743	744
D:	9	40	1	100	9	30	5
E:	ινατι					με

A:	155											156
B:	318											244
C:	745	746	747	748	749	750	751	752	753	754	755	756	757	758	759	760
D:	5	3	10	1	100	5	20	9	70	5	90	100	9	40	5	90
E:	εγκατελιπες											τινες

A:	157		158			159				160
B:	9		740			29				1535
C:	761	762	763	764	765	766	767	768	769	770	771	772	773	774	775	776
D:	4	5	100	600	40	5	10	5	9	5	90	100	600	100	600	40
E:	δε		των			εκει				εστωτων

A:	161										162
B:	597										133
C:	777	778	779	780	781	782	783	784	785	786	787	788	789	790	791	792
D:	1	10	60	200	90	1	40	100	5	90	5	20	5	3	60	40
E:	ακουσαντες										ελεγον

A:	163			164					165
B:	169			77					954
C:	793	794	795	796	797	798	799	800	801	802	803	804	805
D:	60	100	9	7	20	9	1	40	300	600	40	5	9
E:	οτι			ηλιαν					φωνει

A:	166					167			168
B:	510					20			908
C:	806	807	808	809	810	811	812	813	814	815	816	817	818	819
D:	60	200	100	60	90	10	1	9	5	200	8	5	600	90
E:	ουτος					και			ευθεως

A:	169						170			171		172
B:	755						104			55		941
C:	820	821	822	823	824	825	826	827	828	829	830	831	832	833	834	835
D:	4	80	1	30	600	40	5	9	90	5	50	1	200	100	600	40
E:	δραμων						εις			εξ		αυτων

A:	173			174					175
B:	20			663					326
C:	836	837	838	839	840	841	842	843	844	845	846	847	848	849	850
D:	10	1	9	20	1	2	600	40	90	70	60	3	3	60	40
E:	και			λαβων					σπογγον

A:	176						177		178					179
B:	278						105		460					20
C:	851	852	853	854	855	856	857	858	859	860	861	862	863	864	865	866
D:	70	20	7	90	1	90	100	5	60	50	60	200	90	10	1	9
E:	πλησας						τε		οξους					και

A:	180								181
B:	276								662
C:	867	868	869	870	871	872	873	874	875	876	877	878	879	880
D:	70	5	80	9	8	5	9	90	10	1	20	1	30	600
E:	περιθεις								καλαμω

A:	182								183					184
B:	295								401					69
C:	881	882	883	884	885	886	887	888	889	890	891	892	893	894	895
D:	5	70	60	100	9	6	5	40	1	200	100	60	40	60	9
E:	εποτιζεν								αυτον					οι

A:	185		186						187
B:	9		228						133
C:	896	897	898	899	900	901	902	903	904	905	906	907	908	909
D:	4	5	20	60	9	70	60	9	5	20	5	3	60	40
E:	δε		λοιποι						ελεγον

A:	188				189						190
B:	396				688						14
C:	910	911	912	913	914	915	916	917	918	919	920	921
D:	1	300	5	90	9	4	600	30	5	40	5	9
E:	αφες				ιδωμεν						ει

A:	191							192
B:	600							127
C:	922	923	924	925	926	927	928	929	930	931	932	933
D:	5	80	400	5	100	1	9	7	20	9	1	90
E:	ερχεται							ηλιας

A:	193					194					195	196
B:	1420					401					60	9
C:	934	935	936	937	938	939	940	941	942	943	944	945	946
D:	90	600	90	600	40	1	200	100	60	40	60	4	5
E:	σωσων					αυτον					ο	δε

A:	197						198
B:	456						140
C:	947	948	949	950	951	952	953	954	955	956	957
D:	9	7	90	60	200	90	70	1	20	9	40
E:	ιησους						παλιν

A:	199						200				201
B:	232						947				66
C:	958	959	960	961	962	963	964	965	966	967	968	969	970	971	972	973
D:	10	80	1	50	1	90	300	600	40	7	30	5	3	1	20	7
E:	κραξας						φωνη				μεγαλη

A:	202					203		204
B:	323					160		346
C:	974	975	976	977	978	979	980	981	982	983	984	985	986
D:	1	300	7	10	5	100	60	70	40	5	200	30	1
E:	αφηκε					το		πνευμα

A: Word position. B: Word sum. C: Letter position. D: Letter value.
E: Greek.

When Jesus' prophecy and its fulfillment are combined, there are 440 words, 2157 letters, and a numeric total of 153179.

Primary Features

(Derived from Revelation 1:8 and grouped for easy reference.)

I Am (Present tense - living through it) Add up everything.

A.1Numeric total: 153179 = 13 x 11783. (See feature 1.)

Is, Was, Is To Come (Second present tense - skipping sequentially through it) Add up every other occurrance.

B.3Every other word (odd): 74204 = 2² x 13 x 1427. (See feature 2.4.1.)

B.3.2Every other word (even): 78975 = 3⁵ x 5² x 13. (See feature 2.4.2.)

B.4Every other letter (odd): 80873 = 13 x 6221. (See feature 7.2.1.)

B.4.2Every other letter (even): 72306 = 2 x 3³ x 13 x 103. (See feature 7.2.2.)

Alpha & Omega (The first and last) Add up the first item with the last item.

C.3.2First and last letter of each word: 56021 = 7 x 53 x 151. (See feature 3.)

Alpha (The first) Add up the first item.

D.3.3First letter of each word: 19649 = 7² x 401. (See feature 4.)

Omega (The last) Add up the last item.

E.3.3Last letter of each word: 36372 = 2² x 3 x 7 x 433. (See feature 5.)

The Verses

There are 13 verses in Matthew 8:5-17, and 14 verses in Matthew 27:37-50.

List of verses:
5474 3722 4220 5128 13167 5950 7207 5815 7085 4188 4077 7447 6594 6535 5589 4118 6960 5233 7471 3903 5094 3943 6149 4997 6289 4085 2739

The highlighted verses (Matthew 8:5-17) total 80074, while the remainder (Matthew 27:37-50) totals 73105. The difference is 6969 (3 x 23 x 101). There are no factors of 7 or 13 with this breakdown of the verses because this is a prophecy and fulfillment concerning people, as seen in the number 23. In this case, 101 could be interpreted as the one God who is beginning and end, with the emptiness (zero) or darkness of man in the middle.

(Providentially, the repeating of the digits 6969 reminds the reader of the many times Israel returned to God only to stray again. Eerily, 6 and 9 visually demonstrate the reversal when the digits are turned upside down.)

1The total of the two passages: 153179 = 13 x 11783. (God’s name in Hebrew has a numeric value of 26. 13 is half of 26, and almost twice as difficult to obtain as 7.)

1.1God has hidden His name in the prophecy and its fulfillment. The letter values of God’s name in Hebrew (10-5-6-5) are applied to the list of verses.

1.1.1The letters are applied 7 times.

a) 10   5    6    5    10   5    6    5    10   5    6    5    10   5
b) 10   15   21   26   36   14   20   25   35   13   19   24   34   12
c) 10   15   21   26   9    14   20   25   8    13   19   24   7    12
d) 4188 5589 5094 4085 7085 6535 3903 6289 5815 6594 7471 4997 7207 7447

a) 6    5    10   5    6    5    10    5    6    5    10   5    6
b) 18   23   33   11   17   22   32    10   16   21   31   9    15
c) 18   23   6    11   17   22   5     10   16   21   4    9    15
d) 5233 6149 5950 4077 6960 3943 13167 4188 4118 5094 5128 7085 5589

a) 5     (Value from the Name.)
b) 20    (Count.)
c) 20    (Count adjusted to 27.)
d) 3903  (Verse total found.)

Total of the verses (d): 162883 = 7 x 23269.

1.1.1.1The first half of the results from feature 1.1.1 (d):

4188 5589 5094 4085 7085 6535 3903 6289 5815 6594 7471 4997 7207 7447

Total: 82299 = 3 x 7 x 3919.

1.1.1.2The last half of the results from feature 1.1.1 (d):

5233 6149 5950 4077 6960 3943 13167 4188 4118 5094 5128 7085 5589 3903

Total: 80584 = 2³ x 7 x 1439.

1.1.1.2.1The first half of 1.1.1.2:

5233 6149 5950 4077 6960 3943 13167

Total: 45479 = 7 x 73 x 89. SF: 169 = 13². SF: 26 = 2 x 13.

1.1.1.2.2The last half of 1.1.1.2:

4188 4118 5094 5128 7085 5589 3903

Total: 35105 = 5 x 7 x 17 x 59. (The first half does not divide perfectly like the last half. One might reason that the first half is the prophecy. It was not inevitable, but a warning. The last half is the fulfillment. At that point, it was fixed and could no longer be changed.)

1.1.1.3The difference between the first and last halves (1.1.1.1 and 1.1.1.2): 1715 = 5 x 7³. SF: 26 = 2 x 13.

1.1.2The letters are applied 13 times.

a) 10   5    6    5    10   5    6    5    10   5    6    5    10   5
b) 10   15   21   26   36   14   20   25   35   13   19   24   34   12
c) 10   15   21   26   9    14   20   25   8    13   19   24   7    12
d) 4188 5589 5094 4085 7085 6535 3903 6289 5815 6594 7471 4997 7207 7447

a) 6    5    10   5    6    5    10    5    6    5    10   5    6
b) 18   23   33   11   17   22   32    10   16   21   31   9    15
c) 18   23   6    11   17   22   5     10   16   21   4    9    15
d) 5233 6149 5950 4077 6960 3943 13167 4188 4118 5094 5128 7085 5589

a) 5    10   5    6    5    10   5    6    5    10   5    6    5    10
b) 20   30   8    14   19   29   7    13   18   28   6    12   17   27
c) 20   3    8    14   19   2    7    13   18   1    6    12   17   27
d) 3903 4220 5815 6535 7471 3722 7207 6594 5233 5474 5950 7447 6960 2739

a) 5     6    5    10   5    6    5    10   5    6    5
b) 32    11   16   26   31   10   15   25   30   9    14
c) 5     11   16   26   4    10   15   25   3    9    14
d) 13167 4077 4118 4085 5128 4188 5589 6289 4220 7085 6535

a) Value from the Name.
b) Count.
c) Count adjusted to 27.
d) Verse total found.

Total of the verses (d): 302731 = 11 x 13 x 29 x 73. SF: 126 = 2 x 3² x 7.

1.2Divide the verses into groups of three, and take every other group.

1.2.1Odd positioned groups 3 verses:

5128 13167 5950 4188 4077 7447 4118 6960 5233 3943 6149 4997

Total: 71357 = 11 x 13 x 499.

1.2.2Even positioned groups of 3 verses:

5474 3722 4220 7207 5815 7085 6594 6535 5589 7471 3903 5094 6289 4085 2739

Total: 81822 = 2 x 3 x 13 x 1049.

1.2.3The difference between the odd and even positioned groups of 3: 10465 = 5 x 7 x 13 x 23.

1.317 of the verse totals are odd valued.

a) 24   25   26   27   (Verse position.)
b) 4997 6289 4085 2739 (Verse total.)

Total of the odd valued verses: 101731 = 7 x 14533. (There is no correlating feature from the even valued verses.)

1.4When the verses are added one by one, only 3 times the accumulated total will be divisible by 13.

a) Verse position: 3     6     27
b) Verse total:    4220  5950  2739
c) Running total:  13416 37661 153179

Total of the three verses (b): 12909 = 3 x 13 x 331.

1.5The first 9 and last 9 verses: 102438 = 2 x 3³ x 7 x 271. (When the 27 verses are loaded into a 3 x 3 x 3 object, the first 9 verses would be those with a third dimension coordinate minimum of 1. The last 9 verses would be those with a third dimension coordinate maximum of 3.)

The Words

Although the number of words, 440, does not factor into 7 or 13, when the sum of its factors are factored in turn, it does lead to 13: 440 = 2³ x 5 x 11. SF: 22 = 2 x 11. SF: 13. When the innocent suffer, when catastrophe strikes, it is extremely difficult to see God working. Nevertheless, He is there.

Providentially, the first and last words have the exact same value.

2The letter values of God’s name in Hebrew are applied 7 times to the words. (This covers a little less than half of the words.)

a) 10  5  6  5  10 5  6   5   10 5   6  5  10  5  6   5   10  5   6
b) 10  15 21 26 36 41 47  52  62 67  73 78 88  93 99  104 114 119 125
c) 823 60 89 42 60 53 245 183 53 436 20 20 452 20 279 598 20  136 45

a) 5   10  5   6   5   10  5   6   5   (Value from the Name.)
b) 130 140 145 151 156 166 171 177 182 (Count.)
c) 69  940 20  129 279 561 20  129 561 (Word found.)

Total of the words found (c): 6342 = 2 x 3 x 7 x 151.

2.1Pairing first & last, 2nd & 2nd last... (together divisible by 13)

a) 134 169 192 205  = 1420 = 2² x 5 x 71.
b) 227 681  363 901
c) 307 272  249 236   = 6077 = 59 x 103.
d) 20  554  456 334
e) 247 1235 819 1235

a) # found: 17 =  17.

Sum of positions: 7497 = 3² x 7² x 17.

2.2Since there are 440 words, this means any two words positioned Nth and Nth last would have the sum of their positions adding to a multiple of 49.

2.2.1Two word pairs, Nth and Nth last, are together and individually multiples of 7.

a) Nth word:   102 106
b) Value:      700 385
c) Nth last:   339 335
d) Value:      84  14
e) Sum:        784 399

The extra feature is in the sum of these words (e): 1183 = 7 x 13². These word pairs were chosen to be divisible by 7, but their sum is divisible by 13 twice.

2.2.217 word pairs together are divisible by 13.

a) Nth word:   2   7   16  19  32   41  49  57  69  80  89  126 133
b) Value:      9   380 170 45  1059 53  42  290 20  20  9   107 197
c) Nth last:   439 434 425 422 409  400 392 384 372 361 352 315 308
d) Value:      160 140 688 228 20   77  244 204 721 84  901 790 1272
e) Sum:        169 520 858 273 1079 130 286 494 741 104 910 897 1469

a) 134 169  192 205
b) 227 681  363 901
c) 307 272  249 236
d) 20  554  456 334
e) 247 1235 819 1235

Once again the extra feature is in the sum of the words (e): 11466 = 2 x 3² x 7² x 13. SF: 35 = 5 x 7. These word pairs were chosen to be divisible by 13, but their sum is also divisible by 7 twice.

2.3Exactly 462 paired groups of words, positioned symmetrically as Nth and Nth last, can be found that together and individually are multiples of 7. (462 = 2 x 3 x 7 x 11.)

a) 1     1     1     1     1      2      2      3    3     3     3
b) 47    59    66    112   216    180    217    10   14    23    38
c) 34853 39102 45073 76048 149681 122948 150052 6951 10892 15421 27349

a) 3     3      4     4     4     4     4      5     5     5     6
b) 56    163    40    82    91    144   183    31    77    98    18
c) 36631 111727 28364 55587 63259 97244 123319 19950 51870 66199 10283

a) 6     6     6     7     7     7      8     8     8     8     8
b) 22    30    95    54    124   185    52    74    105   106   137
c) 11872 17563 63161 32858 80346 123284 31780 46648 67431 67830 89516

a) 8      9    9     9     9     10    10    10     10     10     10
b) 214    12   60    99    131   93    96    162    167    173    182
c) 142667 4081 33789 62874 83643 58870 60361 105574 108206 112504 117852

a) 11   11   11    11    11     12    12    12    13    13    13    14
b) 14   23   38    56    163    29    51    119   60    99    131   42
c) 3941 8470 20398 29680 104776 11382 27440 73017 29708 58793 79562 19908

a) 14    14    14    14     14     15   15    15    15     16    16
b) 50    67    97    174    189    23   38    56    163    103   125
c) 25081 34720 56679 109109 120869 4529 16457 25739 100835 58856 72674

a) 16    16    16     17    17    17     17     17     18    18    19
b) 148   158   209    90    130   199    201    211    45    58    22
c) 89488 97734 131957 51933 76531 124481 126231 132573 20321 25095 1589

a) 19   19    20   20    20    22   22    22    22    22    22    22
b) 30   95    32   142   150   27   35    86    92    136   161   188
c) 7280 52878 9422 83146 88690 4900 11011 45563 51513 79639 97314 116137

a) 23   23    24    24    24    25    26    26    26    26    26
b) 30   95    38    56    163   157   68    147   160   165   177
c) 5691 51289 11928 21210 96306 91448 29316 82628 93478 95487 104538

a) 26     27   27    27    27    27     28   28    28    28    28
b) 205    33   72    126   159   184    35   86    92    136   161
c) 124054 6951 32571 67662 92505 108388 6111 40663 46613 74739 92414

a) 28     29    29    29     29     30    30    31    32    32    33
b) 188    44    78    192    202    51    119   95    77    98    142
c) 111237 12565 35091 114170 120379 16058 61635 45598 31920 46249 73724

a) 33    34    34    34    34     35    36    36    36    36    36
b) 150   72    126   159   184    168   86    92    136   161   188
c) 79268 25620 60711 85554 101437 90671 34552 40502 68628 86303 105126

a) 37     37     38    38    38    38     38     39   39    40    40
b) 203    207    57    110   176   197    218    56   163   63    113
c) 114044 117600 10108 47516 94101 108416 123389 9282 84378 12810 48153

a) 40    40    40     41    41    41    41    42    42    42     42
b) 122   178   190    82    91    144   183   100   164   200    219
c) 54152 93723 103509 27223 34895 68880 94955 39011 82593 107681 121849

a) 43   43    43    43    43     44   44    44    44    44     44
b) 50   67    97    174   189    61   73    120   154   196    215
c) 5173 14812 36771 89201 100961 9807 19551 51086 74767 105084 117670

a) 45    45     45     46   47    47    47    47    47     48   48
b) 78    192    202    58   109   114   155   181   213    59   66
c) 22526 101605 107814 4774 41244 43890 74109 90125 112735 4249 10220

a) 48    48     49    49    49    49     50    50    51   51    51
b) 112   216    69    171   179   220    85    135   67   97    174
c) 41195 114828 12635 82824 88382 118083 24227 57610 9639 31598 84028

a) 51    52    53    53    53    53    53     54   54    54    54
b) 189   119   74    105   106   137   214    62   89    123   191
c) 95788 45577 14868 35651 36050 57736 110887 4130 26243 46697 95907

a) 55    55    56    56    57    58    58    58    58     60   60
b) 124   185   80    149   163   110   176   197   218    66   112
c) 47488 90426 17955 65275 75096 37408 83993 98308 113281 5971 36946

a) 60     61    61    62   62    62    62    62     63    63    63
b) 216    99    131   73   120   154   196   215    89    123   191
c) 110579 29085 49854 9744 41279 64960 95277 107863 22113 42567 91777

a) 64    64    64    64    65    65    65    65    65    65    66
b) 113   122   178   190   83    87    108   146   175   194   81
c) 35343 41342 80913 90699 16177 18459 31409 57344 79422 92239 11830

a) 66    67    67     68    68    68    69    69    69    69    69
b) 153   112   216    97    174   189   147   160   165   177   205
c) 59780 30975 104608 21959 74389 86149 53312 64162 66171 75222 94738

a) 70    70    70     71    71    71    72    72    73    73    73
b) 171   179   220    84    127   212   118   145   126   159   184
c) 70189 75747 105448 10528 37338 97580 31605 49749 35091 59934 75817

a) 74    74    74    74    75    75    75    75    76    76    76
b) 120   154   196   215   105   106   137   214   117   141   198
c) 31535 55216 85533 98119 20783 21182 42868 96019 28553 44800 84406

a) 77   77    77    78    79    79    80    80    81    82    83   83
b) 79   139   193   98    192   202   139   193   149   153   91   144
c) 1764 42406 80633 14329 79079 85288 40642 78869 47320 47950 7672 41657

a) 83    84   84    84    84    84    85    85    86    87   87    87
b) 183   87   108   146   175   194   127   212   135   92   136   161
c) 67732 2282 15232 41167 63245 76062 26810 87052 33383 5950 34076 51751

a) 87    88    88    88    88    89    89    89    90    90    91
b) 188   108   146   175   194   129   151   210   123   191   130
c) 70574 12950 38885 60963 73780 26278 41062 82523 20454 69664 24598

a) 91    91    91    92    92    93    93    93    94   94    94    94
b) 199   201   211   144   183   136   161   188   96   162   167   173
c) 72548 74298 80640 33985 60060 28126 45801 64624 1491 46704 49336 53634

a) 94    95   95    95    97    97    97    97    98    98    100   101
b) 182   107  140   204   162   167   173   182   174   189   131   164
c) 58982 7567 30898 74585 45213 47845 52143 57491 52430 64190 20769 43582

a) 101   101   102  102   103  103   104   104   104   104   105   106
b) 200   219   104  208   104  208   125   148   158   209   208   137
c) 68670 82838 2079 74060 1295 73276 13818 30632 38878 73101 71981 22085

a) 106   107   107   108   108   109   109   109   110  110   110   110
b) 214   137   214   140   204   146   175   194   114  155   181   213
c) 75236 21686 74837 23331 67018 25935 48013 60830 2646 32865 48881 71491

a) 111   111   111   112  112   113   114  114   114   115   115   115
b) 176   197   218   121  152   216   122  178   190   155   181   213
c) 46585 60900 75873 7028 27342 73633 5999 45570 55356 30219 46235 68845

a) 116   116   116   117   117   118   118   119   121   121   121
b) 133   169   186   134   187   141   198   145   154   196   215
c) 12075 37247 48860 11886 49357 16247 55853 18144 23681 53998 66584

a) 122   123   123   124   125   126   126   126   127   127   128
b) 152   178   190   191   185   148   158   209   159   184   212
c) 20314 39571 49357 49210 42938 16814 25060 59283 24843 40726 60242

a) 129   129   130   130   131   131   131   133   133   133   133
b) 143   156   151   210   199   201   211   170   172   195   206
c) 11088 21588 14784 56245 47950 49700 56042 27118 29337 45416 52885

a) 134   134   135   137   137   138   139   140   141   142   143  144
b) 169   186   187   161   188   214   166   193   204   198   150  156
c) 25172 36785 37471 17675 36498 53151 19705 38227 43687 39606 5544 10500

a) 145   147   147   148   148   148   148   149  149   152   155   155
b) 183   175   194   160   165   177   205   158  209   210   196   215
c) 26075 22078 34895 10850 12859 21910 41426 8246 42469 41461 30317 42903

a) 156   156   159   160   161  161   161   162   163  163  163   165
b) 181   213   209   184   165  177   205   188   167  173  182   200
c) 16016 38626 34223 15883 2009 11060 30576 18823 2632 6930 12278 25088

a) 165   166  166   168  168  170   171  171   171   172  172   173
b) 219   177  205   173  182  186   172  195   206   179  220   195
c) 39256 9051 28567 4298 9646 11613 2219 18298 25767 5558 35259 16079

a) 173   174  175   176   177   177   178   179  180   181   182   193
b) 206   182  189   194   197   218   205   190  220   217   213   202
c) 23548 5348 11760 12817 14315 29288 19516 9786 29701 27104 22610 6209

a) 196  197   198   200  200  201   202  204
b) 206  215   218   201  211  219   211  207
c) 7469 12586 14973 1750 8092 14168 6342 3556

a) Start position of 1st group is from the beginning, and of the 2nd group is from the end.
b) End position of the 1st group is from the beginning, and of the 2nd group is from the end.
c) Total of both groups.

Total of the starting positions (a): 34073 = 13 x 2621. (There is no corresponding feature with the end positions.)
Total of the start and end positions (a + b): 101633 = 7 x 14519.

2.4Take every other word.

2.4.1The odd positioned words: 74204 = 2² x 13 x 1427.

2.4.2The even positioned words: 78975 = 3⁵ x 5² x 13.

2.5Besides taking every other word, one can also take every Nth word. One could also start with the first word before taking every Nth word. Only three numbers work both ways in producing a total divisible by 7: 62 168 and 218. Providentially, the sum of these three numbers is a multiple of 7: 448 = 2⁶ x 7.

2.6To show the hidden order within prophecy and fulfillment, the 440 words can be divided into many different equal sized groups, with every other group added up to find multiples of 7 or 13. This technique could applied again on the resulting lists of words over and over. Just over 80 sub-features can be found this way.

2.7249 words are even valued. Their total: 78302 = 2 x 7² x 17 x 47. (There is no equivalent feature with the odd valued words. The total of the positions of the odd valued words is 44390, which factors as 2 x 5 x 23 x 193. Factor 23 is the number for man. This prophecy and its fulfillment are all about people.)

2.8Divide the words into four groups depending on their positions and values.

Odd positioned and odd valued.
Odd positioned and even valued.
Even positioned and odd valued.
Even positioned and even valued.

Groups A and D are either odd in position and value, or even in position and value. In other studies, these were termed pure groups. Groups B and C were mixed. In this study, the feature is in groups B and C because this is a prophecy of darkness. No feature is found in the pure groups. The total of the words in these two groups: 80521 = 7 x 11503.

2.9219 words have a first digit that is odd valued. The total of the positions of these words: 50570 = 2 x 5 x 13 x 389. The total of these words: 88837 = 7⁴ x 37. SF: 65 = 5 x 13. (There are four factors of 7, and a second level of factors with 13.)

2.10Precisely 26 (2 x 13) words are multiples of 13. They are also strategically positioned.

a) 5   38  48  61  64  82  85  97 104 110 116 136 175 207 253 260 264
b) 104 312 234 949 455 884 520 78 598 169 416 104 104 520 923 104 104

a) 293 303 313 340 341 381 399 406 410 (Word position.)
b) 273 416 260 169 273 52  169 104 663 (Word value.)

Total of the positions: 5291 = 11 x 13 x 37.
Total of the words: 8957 = 13² x 53. These words were chosen because they were divisible by 13. This explains one of the factors of 13, but it doesn't explain the second factor of 13.

2.10.1The first and last words that are divisible by 13 together form a symmetrical 767, where the first two digits and the last two digits also add up to 13.

2.11The middle N-number of words add up to a multiple of 13 when N is one of the following:

430 422 404 402 386 380 374 364 354 346 328 326 314 288 284 266 258 232 162 88 74 58 56 44 24

Total of the N values: 6664 = 2³ x 7² x 17.

2.12When the words are added one by one, 59 times the running total will be a multiple of 7.

a)  b)   c)          a)  b)   c)          a)  b)   c)          a)  b)   c)
4   366  1421        77  745  28168       216 711  72275       317 417  111972
11  401  5474        89  9    32172       233 20   79009       344 160  120043
17  290  6986        98  628  34860       237 20   80094       347 20   120428
29  456  10675       109 279  38577       247 510  83769       351 1609 122402
31  673  11956       112 131  39116       249 456  84469       360 218  126728
45  330  16604       114 20   39998       258 264  89250       361 84   126812
46  147  16751       117 20   41398       267 69   92267       364 50   127211
47  245  16996       119 136  41930       273 191  94948       378 668  132601
51  89   17591       123 20   42196       274 427  95375       385 18   133959
53  20   17794       141 29   47810       278 60   96719       387 18   134267
58  20   18564       155 1397 53445       290 359  101269      404 908  140994
59  84   18648       181 249  60291       291 14   101283      408 941  142849
62  53   20258       191 20   63903       298 849  104125      421 9    146433
66  270  22358       198 20   65429       301 69   104223      431 60   150500
75  20   26782       213 20   70812       302 679  104902
a) Word position.    b) Word value.    c) Running total.

Total of the positions (a) where this happens: 11963 = 7 x 1709. SF: 1716 = 2² x 3 x 11 x 13.

2.12.173 times the word position, word value, and running total will all be even valued.

a)  b)   c)          a)  b)   c)          a)  b)   c)          a)  b)   c)
12  20   5494        82  884  30392       184 20   61030       306 890  107084
14  304  6466        84  336  31018       186 20   61976       308 1272 108376
16  170  6696        86  20   31558       194 60   64674       312 406  110136
18  146  7132        90  60   32232       204 406  67388       360 218  126728
24  434  9196        92  340  33028       214 302  71114       362 202  127014
26  42   9258        96  758  34154       220 792  75092       368 164  129084
34  20   13436       98  628  34860       222 140  75392       374 60   130464
36  60   13838       104 598  36958       236 334  80074       394 740  136062
42  210  15934       114 20   39998       238 146  80240       402 510  140066
44  290  16274       116 416  41378       244 160  82454       404 908  140994
48  234  17230       118 396  41794       252 740  85686       412 278  144136
50  230  17502       124 622  42818       258 264  89250       424 396  147190
54  230  18024       132 278  45224       262 708  90304       426 14   147892
56  170  18254       146 60   48574       264 104  90428
58  20   18564       152 60   50892       276 20   96336
60  608  19256       154 700  52048       282 20   98052
66  270  22358       158 690  54434       288 496  100896
74  530  26762       160 770  55864       294 138  102054
78  20   28188       164 60   56128       300 20   104154
80  20   28808       170 76   57768       304 136  105454
a) Word position.    b) Word value.    c) Running total.

Total of the positions (a) where this occurs: 13104 = 2⁴ x 3² x 7 x 13.

2.12.249 times the word position, word value, and running total will all be odd valued.

a)  b)   c)          a)  b)   c)          a)  b)   c)          a)  b)   c)
19  45   7177        135 359  46007       265 55   90483       395 29   136091
21  89   7373        147 465  49039       267 69   92267       397 597  138223
27  901  10159       155 1397 53445       269 771  93047       399 169  138525
37  947  14785       161 159  56023       271 401  94203       405 755  141749
51  89   17591       177 129  59357       277 323  96659       413 105  144241
61  949  20205       179 23   59895       283 45   98097       419 401  146355
87  153  31711       181 249  60291       295 131  102185      421 9    146433
99  279  35139       195 605  65279       301 69   104223
101 45   35453       205 901  68289       309 133  108509
109 279  38577       211 447  70109       341 273  119471
111 239  38985       245 561  83015       343 359  119883
125 45   42863       253 923  86609       363 147  127161
127 137  43107       255 881  87755       369 9    129093
133 197  45421       259 227  89477       371 193  129433
a) Word position.    b) Word value.    c) Running total.

Total of the positions (a) where this occurs: 11039 = 7 x 19 x 83.

2.13There are 225 unique word values. Exactly 147 of them occurred only once.

2.14.1Divide the words into groups of 10, and add up each group. Gather all groups with odd valued totals, and all groups with even valued totals.

2.14.1.1Total of the odd valued groups of 10: 76531 = 7 x 13 x 29² SF: 78 = 2 x 3 x 13.

2.14.1.2Total of the even valued groups of 10: 76648 = 2³ x 11 x 13 x 67.

2.14.2Divide the words into groups of 55, and add up each group. Gather all groups with odd valued totals, and all groups with even valued totals.

2.14.2.1Total of the odd valued groups of 55: 20215 = 5 x 13 x 311. SF: 329 = 7 x 47.

2.14.2.2Total of the even valued groups of 55: 132964 = 2² x 13 x 2557. SF: 2574 = 2 x 3² x 11 x 13.

2.14.2.3Difference between the odd/even valued groups of 55: 112749 = 3 x 7² x 13 x 59.

2.14.3Why is it that only groups of 10 and groups of 55 produced multiples of 13? Perhaps because 10 + 55 = 65 (5 x 13).

2.15Place the 440 words into a 5 x 8 x 11 block.

2.15.1The outside (surface area) of the block: 97903 = 13 x 17 x 443.

2.15.2The inside of the block: 55276 = 2² x 13 x 1063.

2.15.3Wire frame (edges): 27235 = 5 x 13 x 419.

2.15.4The middle layer: 15120 = 2⁴ x 3³ x 5 x 7.

First And Last

While the total for the prophecy and fulfillment passages is divisible by 13, the total for the first and last letters of each word is a multiple of 7. When this happens in other numeric studies, there isn't always a reason for this difference. In this study, there is a reason. Jesus is the living Word (John 1:1). The prophecy is from God through him, just as God made all things through him. (John 1:3) The numbers show this by having the combined passages marked by 13 to identify God as the source of the full message. The first and last letters are marked by 7 because Jesus is the messenger, and he also claimed to be first and last. (Revelation 2:8)

3Total of the first and last letters of each word: 56021 = 7 x 53 x 151.

3.1The letter values of God’s name in Hebrew (10-5-6-5) are applied 17 times to count through the whole list in feature 3.

a) 10  5   6  5  10  5  6   5  10 5  6  5  10 5  6   5   10  5   6
b) 10  15  21 26 36  41 47  52 62 67 73 78 88 93 99  104 114 119 125
c) 10  15  21 26 36  41 47  52 62 67 73 78 88 93 99  104 114 119 125
d) 110 120 61 29 120 14 130 60 14 45 19 19 91 19 240 140 19  31  45

a) 5   10  5   6   5   10  5   6   5   10  5   6   5   10  5   6   5
b) 130 140 145 151 156 166 171 177 182 192 197 203 208 218 223 229 234
c) 130 140 145 151 156 166 171 177 182 192 197 203 208 218 223 229 234
d) 69  45  19  45  205 201 19  100 201 41  14  93  19  45  5   190 190

a) 10  5   6   5   10  5   6   5   10  5   6   5   10  5   6   5   10
b) 244 249 255 260 270 275 281 286 296 301 307 312 322 327 333 338 348
c) 244 249 255 260 270 275 281 286 296 301 307 312 322 327 333 338 348
d) 41  99  99  95  45  41  80  100 300 69  19  45  61  201 80  10  69

a) 5   6   5   10  5   6   5   10  5   6   5   10  5   6   5
b) 353 359 364 374 379 385 390 400 405 411 416 426 431 437 442
c) 353 359 364 374 379 385 390 400 405 411 416 426 431 437 2
d) 640 180 43  120 16  13  35  47  44  130 160 14  120 37  9

a) Value from the Name.
b) Count.
c) Count adjusted to 440.
d) First/last total found.

Total of the first/last sums (d): 5889 = 3 x 13 x 151.

3.1.1.1The first and last totals found: 119 = 7 x 17.

3.1.1.2Divide the results (d) in 3.1.1 into groups of 17. (The first group of 17 has no feature.)

3.1.1.2.1The second group of 17:

31 45 69 45 19 45 205 201 19 100 201 41 14 93 19 45 5

Total: 1197 = 3 x 3 x 7 x 19.

3.1.1.2.2The third group of 17:

190 190 41 99 99 95 45 41 80 100 300 69 19 45 61 201 80

Total: 1755 = 3 x 3 x 3 x 5 x 13.

3.1.1.2.3The fourth group of 17:

10 69 640 180 43 120 16 13 35 47 44 130 160 14 120 37 9

Total: 1687 = 7 x 241.

3.1.2The Name is applied 13 times.

a) 10  5   6  5  10  5  6   5  10 5  6  5  10 5  6   5   10  5   6
b) 10  15  21 26 36  41 47  52 62 67 73 78 88 93 99  104 114 119 125
c) 10  15  21 26 36  41 47  52 62 67 73 78 88 93 99  104 114 119 125
d) 110 120 61 29 120 14 130 60 14 45 19 19 91 19 240 140 19  31  45

a) 5   10  5   6   5   10  5   6   5   10  5   6   5   10  5   6   5
b) 130 140 145 151 156 166 171 177 182 192 197 203 208 218 223 229 234
c) 130 140 145 151 156 166 171 177 182 192 197 203 208 218 223 229 234
d) 69  45  19  45  205 201 19  100 201 41  14  93  19  45  5   190 190

a) 10  5   6   5   10  5   6   5   10  5   6   5   10  5   6   5
b) 244 249 255 260 270 275 281 286 296 301 307 312 322 327 333 338
c) 244 249 255 260 270 275 281 286 296 301 307 312 322 327 333 338
d) 41  99  99  95  45  41  80  100 300 69  19  45  61  201 80  10

a) Value from the Name.
b) Count.
c) Count adjusted to 440.
d) First/last total found.

Total of the first/last sums (d): 4212 = 2² x 3⁴ x 13.

3.2From the above list of sums, exactly 28 pairs (2² x 7) can be found, Nth and Nth last that together are divisible by 7.

a) Nth sum:   6   8   18  29  30  31  42  46  55  59  70  71  73  82
b) Value:     40  601 11  99  605 45  99  140 120 83  620 700 19  604
c) Nth last:  435 433 423 412 411 410 399 395 386 382 371 370 368 359
d) Value:     100 99  45  160 130 60  69  14  230 99  45  140 79  180
e) Sum:       140 700 56  259 735 105 168 154 350 182 665 840 98  784

a) 91  96  98  100 115 116 158 174 175 189 192 195 206 207
b) 99  41  620 65  44  16  690 99  95  490 41  160 94  160
c) 350 345 343 341 326 325 283 267 266 252 249 246 235 234
d) 69  8   290 208 110 19  45  69  45  140 99  43  130 190
e) 168 49  910 273 154 35  735 168 140 630 140 203 224 350

The total of the positions is naturally divisible by 49 since there are 440 sums in the list. However, in this case there is an extra factor of 7: 12348 = 2² x 3² x 7³.

3.3Not only do individual sums, Nth and Nth last, have this relationship, but also groups of sums positioned Nth and Nth last.

3.3.1527 together and individually are divisible by 7.

a) 1     1     1     2    2     2     3     3     4     4     4     4
b) 77    137   181   8    141   165   118   132   84    111   146   200
c) 19516 35105 46088 2583 35693 42847 31647 33957 21546 29687 36001 49343

a) 4     4     5    5     5     5     5     5     5     6    6    6
b) 203   209   44   85    88    120   145   153   194   28   31   39
c) 50435 51842 9100 21469 22960 30898 35574 37345 48055 5096 6195 7714

a) 6    6     6     6     6     6     6     6     7     7     7     8
b) 49   78    101   159   166   171   196   201   59    144   148   35
c) 9723 18067 25844 39788 41566 42826 48076 49035 11319 34713 35672 6804

a) 8     8     8     9     9     10    10    11   11   11    11    11
b) 97    109   215   141   165   107   134   45   46   125   173   199
c) 23933 28343 52794 33110 40264 26530 31850 7609 7763 29974 41685 47110

a) 11    12   12    13   13    13    13    14  14   14    14    14
b) 206   34   164   24   115   178   205   17  48   187   198   216
c) 49392 5502 39669 2268 28014 42441 48937 693 7749 44184 46508 51772

a) 15  15   15    15    15    16   16   16    16    16    17   17
b) 16  25   157   188   189   23   41   76    102   197   25   157
c) 343 2261 37128 44394 45024 1246 6209 15715 24682 46186 1918 36785

a) 17    17    18   18    18    18    19    20    20    21    21    21
b) 188   189   48   187   198   216   195   168   174   79    82    119
c) 44051 44681 7056 43491 45815 51079 45325 39403 40642 15470 17052 27664

a) 22   22    22    23   23    23    24   24    24    24    25    25
b) 33   131   147   30   123   180   41   76    102   197   115   178
c) 4053 29498 32613 3038 28154 41223 4963 14469 23436 44940 25746 40173

a) 25    26    26    26    27   27    27    27    27    28    28    29
b) 205   157   188   189   50   91    138   162   210   155   190   31
c) 46669 34867 42133 42763 5768 19516 29652 36659 47222 33607 42147 1099

a) 29   29   29    29    29    29    29    29    29    30   30   30
b) 39   49   78    101   159   166   171   196   201   37   62   67
c) 2618 4627 12971 20748 34692 36470 37730 42980 43939 2163 6867 8155

a) 30    30    30    30    31    31    32   32   32    32    32    32
b) 86    108   156   186   123   180   39   49   78    101   159   166
c) 15792 22428 33425 40439 25116 38185 1519 3528 11872 19649 33593 35371

a) 32    32    32    33   33    33    34    34    35    36    36    36
b) 171   196   201   68   90    126   131   147   164   97    109   215
c) 36631 41881 42840 6909 16646 24752 25445 28560 34167 17129 21539 45990

a) 37    37    37    38   38   38    38    38    38    39    39    39
b) 94    177   179   62   67   86    108   156   186   105   135   139
c) 16464 36449 36792 4704 5992 13629 20265 31262 38276 19425 25522 26474

a) 40   40    40    40    40    40    40    40    41   41    41    42
b) 49   78    101   159   166   171   196   201   52   149   182   76
c) 2009 10353 18130 32074 33852 35112 40362 41321 1918 28119 36617 9506

a) 42    42    44   44    44    44    44    45    45    45    45    45
b) 102   197   69   96    100   129   191   85    88    120   145   153
c) 18473 39977 6013 15715 17353 23758 38780 12369 13860 21798 26474 28245

a) 45    46    46    46    46    47    47    47    47    48   48   48
b) 194   125   173   199   206   125   173   199   206   57   61   65
c) 38955 22365 34076 39501 41783 22211 33922 39347 41629 1631 2765 3549

a) 48   48   48    48    48    48    48    49    49    49    50   50
b) 70   71   93    113   124   151   211   187   198   216   78   101
c) 5628 6468 14336 19838 21882 27153 42077 36435 38759 44023 8344 16121

a) 50    50    50    50    50    51    51    51    51    52    52
b) 159   166   171   196   201   91    138   162   210   130   136
c) 30065 31843 33103 38353 39312 13748 23884 30891 41454 22316 23373

a) 53    53    54   54    54    55    55    55    56   56    56    56
b) 149   182   81   89    95    110   112   175   74   87    92    116
c) 26201 34699 8729 12908 13783 18529 18823 33096 5614 11186 13034 19033

a) 56    56    56    56    57    57    57    57    57    58   58   58
b) 154   185   207   213   106   127   152   170   204   61   65   70
c) 27132 35035 40495 41783 16219 20776 25900 31948 39102 1134 1918 3997

a) 58   58    58    58    58    58    60    60    61   61    61    61
b) 71   93    113   124   151   211   144   148   75   103   121   219
c) 4837 12705 18207 20251 25522 40446 23394 24353 4879 14581 19040 42091

a) 62  62   62   62    62    62    62    62    63   63   63    63
b) 65  70   71   93    113   124   151   211   67   86   108   156
c) 784 2863 3703 11571 17073 19117 24388 39312 1288 8925 15561 26558

a) 63    64    64    64    64    64    64    64    65  65   65    65
b) 186   99    140   142   161   202   214   217   66  80   133   212
c) 33572 12915 21595 21651 28168 37107 40152 41314 721 5600 20279 39690

a) 66   66   66    66    66    66    66    67   67    67    68   68
b) 70   71   93    113   124   151   211   80   133   212   86   108
c) 2079 2919 10787 16289 18333 23604 38528 4879 19558 38969 7637 14273

a) 68    68    69   69    70   70    70    70    71   71    71    71
b) 156   186   90   126   96   100   129   191   93   113   124   151
c) 25270 32284 9737 17843 9702 11340 17745 32767 8708 14210 16254 21525

a) 71    72   72    72    72    72    73    74    74    74    75   75
b) 211   93   113   124   151   211   143   104   117   220   87   92
c) 36449 7868 13370 15414 20685 35609 18480 10766 13902 38332 5572 7420

a) 75    75    75    75    75    76   76    76    77   77    78    78
b) 116   154   185   207   213   103  121   219   102  197   137   181
c) 13419 21518 29421 34881 36169 9702 14161 37212 8967 30471 15589 26572

a) 79   79    79    79    79    79    80   80    81    81    82   82
b) 101  159   166   171   196   201   82   119   133   212   89   95
c) 7777 21721 23499 24759 30009 30968 1582 12194 14679 34090 4179 5054

a) 83    84   84    85   85    85    85    85    86   86   86    86
b) 119   114  122   111  146   200   203   209   88   120  145   153
c) 10612 8792 10465 8141 14455 27797 28889 30296 1491 9429 14105 15876

a) 86    87   87    87    88   88   88    88    88    88    89   89
b) 194   108  156   186   92   116  154   185   207   213   120  145
c) 26586 6636 17633 24647 1848 7847 15946 23849 29309 30597 7938 12614

a) 89    89    90  91   92    92    92    93   93    93    93    93
b) 153   194   95  126  138   162   210   116  154   185   207   213
c) 14385 25095 875 8106 10136 17143 27706 5999 14098 22001 27461 28749

a) 94   94   94    94    95    95    97   97   97    98   98    100
b) 113  124  151   211   177   179   100  129  191   109  215   140
c) 5502 7546 12817 27741 19985 20328 1638 8043 23065 4410 28861 8680

a) 100  100   100   100   100   101  101   102   102   102   102   102
b) 142  161   202   214   217   129  191   159   166   171   196   201
c) 8736 15253 24192 27237 28399 6405 21427 13944 15722 16982 22232 23191

a) 103   104  104   105  105   106  106  107  107  107   107   108  109
b) 197   121  219   117  220   135  139  127  152  170   204   134  156
c) 21504 4459 27510 3136 27566 6097 7049 4557 9681 15729 22883 5320 10997

a) 109   110   111 111   112  112   112   112   113   114  114  114
b) 186   215   112 175   146  200   203   209   175   124  151  211
c) 18011 24451 294 14567 6314 19656 20748 22155 14273 2044 7315 22239

a) 115  116   116   117  117   117   117   118   119  121  121  121
b) 122  178   205   154  185   207   213   220   132  145  153  194
c) 1673 14427 20923 8099 16002 21462 22750 24430 2310 4676 6447 17157

a) 122   124   125  125   126   126   126   128  128   128   129  129
b) 219   180   151  211   173   199   206   152  170   204   163  176
c) 23051 13069 5271 20195 11711 17136 19418 5124 11172 18326 8925 11592

a) 129   130   131  132  134   136 138   139  139   141 141  141   141
b) 193   191   136  147  212   139 181   162  210   142 161  202   214
c) 15393 15022 1057 3115 19411 952 10983 7007 17570 56  6573 15512 18557

a) 141   142  143  143   143   143   145 146  146   147   147   147
b) 217   165  161  202   214   217   148 153  194   200   203   209
c) 19719 7154 6517 15456 18501 19663 959 1771 12481 13342 14434 15841

a) 150  151  151   152   153  153   154   155  155   155   156  157
b) 182  184  218   211   170  204   194   185  207   213   190  186
c) 8498 9191 17661 14924 6048 13202 10710 7903 13363 14651 8540 7014

a) 158  158  159  159  159  160  160  160  160  161   162  162   162
b) 188  189  167  172  192  166  171  196  201  208   202  214   217
c) 7266 7896 2037 3276 7623 1778 3038 8288 9247 10703 8939 11984 13146

a) 163   164  164  167  167  167  168  168  169  171  172  172  173
b) 210   176  193  171  196  201  172  192  174  204  196  201  192
c) 10563 2667 6468 1260 6510 7469 1239 5586 1239 7154 5250 6209 4347

a) 174  174  177  178 179  185  186  186  188  188  197 199  200  201
b) 199  206  193  179 205  218  207  213  198  216  201 216  206  203
c) 5425 7707 3801 343 6496 8470 5460 6748 2324 7588 959 5264 2282 1092

a) 201  203  203  204  208  215
b) 209  214  217  209  213  217
c) 2499 3045 4207 1407 1288 1162

a) Start position of first group. Start of second group from the end.
b) End position of first group. End of second group from the end.
c) Total of both groups.

Total of the positions (a + b): 116424 = 2³ x 3³ x 7² x 11.

3.3.2127 together and individually are divisible by 13.

a) 1     2     3     3     5    5     5     5     6     6     7     8
b) 171   187   61    211   33   51    150   199   136   144   203   204
c) 44434 47489 13546 52858 7306 10335 36647 48906 33306 34853 49647 49556

a) 9    11    12    13   16   20    20    21   21    23    23    24
b) 31   96    85    28   54   74    124   37   163   173   200   72
c) 5135 22698 19591 3471 8346 13650 28704 4797 38194 40027 45643 12792

a) 25    26    27    33    34   34    34    35    35    35    36    37
b) 141   118   135   148   51   150   199   122   126   128   156   98
c) 30277 26221 28951 28990 3029 29341 41600 24180 24596 25012 31616 17875

a) 37    38    40    41    42    43   45   45   46    49    49    51
b) 189   163   205   167   88    62   52   64   207   152   160   186
c) 39507 33397 42848 33618 14404 3900 1313 3926 42133 27183 30940 35906

a) 51    52    52    53   56    57    58    59    61    62    64    64
b) 213   150   199   64   84    158   194   191   220   211   215   217
c) 42536 26312 38571 2613 10257 28860 36595 35880 42328 39312 40612 41314

a) 66    66    67    68    69    69    71    72    74    75    76
b) 91    94    216   192   99    100   184   178   127   124   109
c) 10660 10816 40209 33787 11726 11999 30381 28171 15509 15054 11739

a) 76    76    76    79    79    83   87    90    91   92  94   96
b) 125   132   140   180   190   87   130   202   102  94  115  176
c) 14404 15639 17173 26208 28951 2054 11102 26481 3159 156 5876 19539

a) 99    102  105  105   107   109  109   110  110  110  111   113
b) 189   143  113  196   177   139  212   125  132  140  201   161
c) 21632 8619 2418 21229 16744 6240 24531 2665 3900 5434 20215 11596

a) 114   118   122   122   123 123 124   126  126  127 132   133  134
b) 196   166   188   195   126 128 175   132  140  128 219   140  209
c) 18811 11583 15080 16731 416 832 12181 1235 2769 416 21827 1534 18291

a) 137  138  139  139   140   146   151   152   153  158  160   163
b) 144  174  151  193   212   185   199   193   160  169  206   172
c) 1547 9750 2808 13611 18291 10504 12259 10803 3757 3770 10998 2171

a) 171  174  181  187  189  198  216
b) 183  200  190  213  195  214  217
c) 2054 5616 2743 6630 1651 4563 702

a) Start position of first group. Start of second group from the end.
b) End position of first group. End of second group from the end.
c) Total of both groups.

Total of the positions (a + b): 28770 = 2 x 3 x 5 x 7 x 137. SF: 154 = 2 x 7 x 11.

3.4Over 80 sub-features are revealed when alternating groups of the sums are extracted, and the principle is re-applied to the resulting lists.

3.5There are 89 unique sums in the list in feature 3.

3.5.146 of these unique sums appeared an odd number of times in the list.

a)  b) c)        a)  b) c)        a)  b) c)
2   1  2         48  1  48        190 9  1710
3   1  3         50  1  50        200 1  200
5   1  5         64  1  64        201 5  1005
6   1  6         67  1  67        207 1  207
8   1  8         69  9  621       260 3  780
10  9  90        77  1  77        270 3  810
15  3  45        80  3  240       309 1  309
17  1  17        91  11 1001      490 1  490
21  1  21        92  5  460       603 1  603
31  3  93        93  1  93        604 1  604
35  1  35        95  17 1615      608 1  608
40  1  40        101 1  101       680 1  680
42  1  42        107 3  321       690 3  2070
43  3  129       130 7  910       700 5  3500
44  3  132       140 15 2100
45  27 1215      160 15 2400
a) Sum from feature 3.
b) Number of occurrences in the list.
c) Total value in passage (a x b).

Total of these sums (c): 25627 = 7² x 523.

3.5.243 of these unique sums appeared an even number of times in the list.

a)  b) c)        a)  b) c)        a)  b) c)
9   12 108       61  6  366       205 2  410
11  2  22        65  2  130       208 2  416
12  2  24        70  2  140       209 2  418
13  4  52        71  2  142       230 6  1380
14  20 280       79  6  474       240 2  480
16  4  64        83  2  166       290 4  1160
18  2  36        94  2  188       300 4  1200
19  42 798       97  2  194       307 2  614
29  6  174       99  12 1188      601 8  4808
37  2  74        100 10 1000      605 4  2420
41  16 656       105 2  210       610 2  1220
47  2  94        110 14 1540      620 4  2480
49  2  98        120 16 1920      640 2  1280
55  2  110       150 6  900
60  4  240       180 4  720
a) Sum from feature 3.
b) Number of occurrences in the list.
c) Total value in passage (a x b).

Total of these sums (c): 30394 = 2 x 7 x 13 x 167. SF: 189 = 3³ x 7.

3.6Divide the list of unique sums into two groups according to the total of their positions being prime numbers or not prime numbers.

3.6.115 of the unique sums have the total of their positions as prime numbers.

a)  b) c)   d)
3   1  3    127
5   1  5    223
18  2  36   443    a) Unique sum from feature 3.
47  2  94   631
48  1  48   331
60  4  240  853    b) Number of occurrences.
61  6  366  1451
94  2  188  229
99  12 1188 2659   c) Total value (a x b).
190 9  1710 1999
200 1  200  383
205 2  410  233    d) Total of their positions.
260 3  780  421
309 1  309  401
620 4  2480 487

Total of the unique sums (a): 2219 = 7 x 317.
Grand total in the passage (c): 8057 = 7 x 1151.
Total of their positions (d): 10871 = 7 x 1553. SF: 1560 = 2³ x 3 x 5 x 13.

3.6.274 of the unique sums have the total of their positions not as prime numbers.

a)  b) c)   d)        a)  b) c)   d)        a)  b) c)   d)        a)  b) c)   d)
2   1  2    49        41  16 656  3826      92  5  460  873       230 6  1380 975
6   1  6    438       42  1  42   183       93  1  93   203       240 2  480  208
8   1  8    345       43  3  129  916       95  17 1615 3903      270 3  810  470
9   12 108  3070      44  3  132  782       97  2  194  713       290 4  1160 1254
10  9  90   1356      45  27 1215 5905      100 10 1000 2323      300 4  1200 1136
11  2  22   142       49  2  98   678       101 1  101  210       307 2  614  812
12  2  24   208       50  1  50   279       105 2  210  667       490 1  490  189
13  4  52   1285      55  2  110  672       107 3  321  314       601 8  4808 1448
14  20 280  5012      64  1  64   258       110 14 1540 3038      603 1  603  160
15  3  45   314       65  2  130  460       120 16 1920 2751      604 1  604  82
16  4  64   1038      67  1  67   187       130 7  910  1953      605 4  2420 484
17  1  17   336       69  9  621  2665      140 15 2100 3603      608 1  608  32
19  42 798  7585      70  2  140  90        150 6  900  1781      610 2  1220 737
21  1  21   381       71  2  142  651       160 15 2400 3068      640 2  1280 725
29  6  174  1477      77  1  77   220       180 4  720  916       680 1  680  332
31  3  93   543       79  6  474  981       201 5  1005 1162      690 3  2070 882
35  1  35   390       80  3  240  935       207 1  207  224       700 5  3500 411
37  2  74   814       83  2  166  398       208 2  416  634
40  1  40   6         91  11 1001 2465      209 2  418  136
a) Unique sum from feature 3.     b) Number of occurrences.
c) Total values (a x b).          d) Total of positions in the list.

Grand total of the sums (c): 47964 = 2² x 3 x 7 x 571. SF: 585 = 3² x 5 x 13.
Total of the positions: 86149 = 7 x 31 x 397.

3.7Divide the list in feature 3 into groups of 44, and add up each group.

3.7.1Odd valued groups of 44: 31647 = 3 x 7 x 11 x 137.

3.7.2Even valued groups of 44: 24374 = 2 x 7 x 1741. SF: 1750 = 2 x 5³ x 7.

3.8The 440 sums in feature 3 divide perfectly into alternating groups of 143 and 154. (143 is divisible by 13, and 154 is a multiple of 7.)

3.8.1.The groups of 143 total: 36071 = 7 x 5153.

3.8.2The groups of 154 total: 19950 = 2 x 3 x 5² x 7 x 19.

3.8.3The difference between 3.8.1 and 3.8.2: 16121 = 7³ x 47.

3.929 of the sums in feature 3 are uniquely positioned to divide the rest of the list into what is between and what is not between their Nth and Nth last occurrences.

Between & *Not* Between
A	B	C	D	E	F
95	5	29540 = 2² x 5 x 7 x 211.	26481 = 3 x 7 x 13 x 97.	136	365
110	2	45724 = 2² x 7 x 23 x 71. SF: 105 = 3 x 5 x 7.	10297 = 7 x 1471.	10	362
41	5	26292 = 2² x 3 x 7 x 313.	29729 = 7 x 31 x 137. SF: 175 = 5² x 7.	113	337
41	7	9604 = 2² x 7⁴.	46417 = 7 x 19 x 349.	193	275
19	7	28714 = 2 x 7² x 293.	27307 = 7 x 47 x 83.	73	300
19	13	14525 = 5² x 7 x 83.	41496 = 2³ x 3 x 7 x 13 x 19.	114	233
15	1	33362 = 2 x 7 x 2383. SF: 2392 = 2³ x 13 x 23. SF: 42 = 2 x 3 x 7.	22659 = 3 x 7 x 13 x 83.	14	261
120	3	30961 = 7 x 4423.	25060 = 2² x 5 x 7 x 179. SF: 195 = 3 x 5 x 13. SF: 21 = 3 x 7.	36	278
120	8	3150 = 2 x 3² x 5² x 7.	52871 = 7² x 13 x 83.	152	164
45	11	12124 = 2² x 7 x 433.	43897 = 7 x 6271.	167	266
61	2	27216 = 2⁴ x 3⁵ x 7.	28805 = 5 x 7 x 823.	112	346
99	1	51065 = 5 x 7 x 1459.	4956 = 2² x 3 x 7 x 59.	29	433
91	1	49091 = 7 x 7013. SF: 7020 = 2² x 3³ x 5 x 13.	6930 = 2 x 3² x 5 x 7 x 11.	35	424
91	2	43603 = 7 x 6229.	12418 = 2 x 7 x 887. SF: 896 = 2⁷ x 7. SF: 21 = 3 x 7.	61	397
70	1	980 = 2² x 5 x 7².	55041 = 3 x 7 x 2621.	40	50
10	2	24836 = 2² x 7 x 887.	31185 = 3⁴ x 5 x 7 x 11. SF: 35 = 5 x 7.	51	232
260	1	33705 = 3² x 5 x 7 x 107.	22316 = 2² x 7 x 797.	45	313
140	3	30135 = 3 x 5 x 7² x 41. SF: 63 = 3² x 7. SF: 13.	25886 = 2 x 7 x 43².	128	363
130	3	2786 = 2 x 7 x 199. SF: 208 = 2⁴ x 13. SF: 21 = 3 x 7.	53235 = 3² x 5 x 7 x 13².	256	288
620	1	18886 = 2 x 7 x 19 x 71.	37135 = 5 x 7 x 1061.	70	212
69	3	8680 = 2³ x 5 x 7 x 31. SF: 49 = 7². SF: 14 = 2 x 7.	47341 = 7 x 6763.	267	350
69	4	5054 = 2 x 7 x 19².	50967 = 3² x 7 x 809.	301	348
100	3	16562 = 2 x 7² x 13². SF: 42 = 2 x 3 x 7.	39459 = 3 x 7 x 1879.	149	274
100	4	11074 = 2 x 7² x 113.	44947 = 7 x 6421.	177	272
201	1	18557 = 7 x 11 x 241. SF: 259 = 7 x 37.	37464 = 2³ x 3 x 7 x 223.	166	327
71	1	27314 = 2 x 7 x 1951. SF: 1960 = 2³ x 5 x 7².	28707 = 3 x 7 x 1367.	211	440
300	1	10493 = 7 x 1499.	45528 = 2³ x 3 x 7 x 271. SF: 287 = 7 x 41.	225	323
47	1	20377 = 7 x 41 x 71. SF: 119 = 7 x 17.	35644 = 2² x 7 x 19 x 67.	231	400
49	1	20300 = 2² x 5² x 7 x 29.	35721 = 3⁶ x 7².	253	425
A: First/last sum from feature 3. B: Nth/Nth last occurrence. C: Total of the first/last sums in between.			D: Total of the first/last sums not in between. E: Position in the list of the Nth occurrence. F: Position in the list of the Nth last occurrence.

3.9.1Providentially, the total of the Nth/Nth last occurrences (column 2) is a multiple of 7 twice:

5 2 5 7 7 13 1 3 8 11 2 1 1 2 1 2 1 3 3 1 3 4 3 4 1 1 1 1 1

Total: 98 = 2 x 7².

3.9.2The positions of the Nth occurrences in the list (second last column):

136 10 113 193 73 114 14 36 152 167 112 29 35 61 40 51 45 128 256 70 267 301 149 177 166 211 225 231 253

Total: 3815 = 5 x 7 x 109.

3.9.2.119 of the Nth occurrences have a first digit that is odd valued:

136 10 113 193 73 114 14 36 152 167 112 35 51 128 70 301 149 177 166

Total: 2197 = 13³. (Three factors of 13!)

3.9.3The positions of the Nth last occurrences in the list (last column):

365 362 337 275 300 233 261 278 164 266 346 433 424 397 50 232 313 363 288 212 350 348 274 272 327 440 323 400 425

Total: 9058 = 2 x 7 x 647.

3.9.4Since 3.9.2 and 3.9.3 are both divisible by 7, their sum is also guaranteed to be divisible by 7, but there is no reason why the sum of its factors is also a multiple of 7: 12873 = 3 x 7 x 613. SF: 623 = 7 x 89. SF: 96 = 2⁵ x 3. SF: 13.

3.9.5Nor is there any mathematical reason why the difference would have an extra multiple of 7: 5243 = 7² x 107.

3.9.6The even valued first/last sums in column 1 total 2080. (2⁵ x 5 x 13. SF: 28 = 2² x 7.)

3.9.7When the position is even valued in column E, the first/last sums in column 1 total 1701. (3⁵ x 7.)

3.9.8When the position is odd valued in column F, the first/lat sums in column 1 total 1351. (7 x 193.)

3.9.9Six of the first/last sums (column 1) have their Nth occurrence in a position divisible by 7.

15 61 91 620 69 47

Total of these six: 903 = 3 x 7 x 43.

3.10Consider the first number in feature 3's list to be a high number. Search for the next number that is lower in value. From that point, search for a number higher in value from that one. Continue the search, alternating high and low until the entire list is covered. This finds selects 204 numbers. The total of these numbers: 29224 = 2³ x 13 x 281.

3.11Arrange the 440 numbers from feature 3 into a 5 column, 8 row, 11 layered block.

3.11.1Outside: 34461 = 3² x 7 x 547. SF: 560 = 2⁴ x 5 x 7.

3.11.2Inside: 21560 = 2³ x 5 x 7² x 11.

3.11.3Odd positioned rows: 27531 = 3² x 7 x 19 x 23.

3.11.4Even positioned rows: 28490 = 2 x 5 x 7 x 11 x 37.

3.11.5Alternating first four rows: 29673 = 3³ x 7 x 157.

3.11.6Alternating first four rows (opposite): 26348 = 2² x 7 x 941. SF: 952 = 2³ x 7 x 17.

3.11.7Checker board alternating on each layer: 25543 = 7 x 41 x 89.

3.11.8Checker board alternating on each layer (opposite): 30478 = 2 x 7² x 311.

3.11.9There were many other ways of arranging the data into a three dimension block, but only this one produced all these complementary opposites. It is not coincidence this block has dimensions 5 x 8 x 11. The sizes for these dimensions could be run together into a single number: 5811. (5811 = 3 x 13 x 149.) None of the other arrangements (8511, 8115, 1185, 1158, 5118) are divisible by 13 (or 7).

Alpha: The First Letter Of Each Word

Having examined the first and last letters of each word together, now they are examined separately.

4Total of the first letters: 19649 = 7² x 401.

4.2From the list in feature 4, taking every Nth letter produces a total divisible by 7 when N is one of the following:

8 9 10 11 16 22 33 43 47 48 50 52 62 63 72 87 93 98 106 118 132 135 143 146 157 159 161 172 180 181 183 189 205 212 214 216 220

Total of the N values: 4053 = 3 x 7 x 193. SF: 203 = 7 x 29.

4.3Just over a thousand sub-features are possible when alternating groups of N-number of letters are added up, and the resulting lists are checked for other sub-groups.

4.4.1165 of the first letters are odd valued. Their total: 715 = 5 x 11 x 13.

4.4.2Exactly 42 are divisible by 7.

4.4.3Every 7th from the list adds up to a multiple of 13.

70 10 60 60 1 9 1 70 200 20 5 70 9 20 70 1 30 100 100 5 2 100 90 100 5 1 400 10 3 100 5 7 7 5 1 100 20 5 100 100 90 10 60 70 90 1 5 8 200 60 5 3 5 20 8 100 60 5 100 60 5 70

Total: 3107 = 13 x 239. SF: 252 = 2² x 3² x 7.

4.5Divide the first letters into groups of N-number of letters and add up each group. Gather all odd valued groups together, and all even valued groups together.

4.5.1.1Odd valued groups of 22 letters: 5299 = 7 x 757.

4.5.1.2Even valued groups of 22 letters: 14350 = 2 x 5² x 7 x 41.

4.5.1.3The difference between 4.5.1.1 and 4.5.1.2: 441 = 3² x 7².

4.5.2.1Odd valued groups of 88 letters: 10731 = 3 x 7² x 73.

4.5.2.2Even valued groups of 88 letters: 8918 = 2 x 7³ x 13.

4.5.2.3The difference between 4.5.2.1 and 4.5.2.2: 1813 = 7² x 37.

4.5.3It is curious how 22 and 88, both symmetrical numbers with repeating digits, are the only two ways of grouping the first letters that succeed. It is also peculiar how their sum, 110 is an exact quarter of the number of words.

4.6As stated before, this is a prophecy from God transmitted through His son Jesus. Both numbers, 7 and 13 can be applied at the same time. Thus the first letters can be grouped into alternating groups of M and N-number of letters where M and N are multiples of 7 and 13.

4.6.1Alternating groups of 42 and 13.

4.6.1.1Groups of 42: 14315 = 5 x 7 x 409.

4.6.1.2Groups of 13: 5334 = 2 x 3 x 7 x 127.

4.6.2Alternating groups of 84 and 26.

4.6.2.1Groups of 84: 15743 = 7 x 13 x 173.

4.6.2.2Groups of 26: 3906 = 2 x 3² x 7 x 31.

4.6.3Alternating groups of 52 and 168.

4.6.3.1Groups of 52: 3122 = 2 x 7 x 223.

4.6.3.2Groups of 168: 16527 = 3 x 7 x 787.

4.7Similar to feature 3.9, precisely 29 of the first letters successfully divide the rest of the list into what is between, and what is not between their Nth and Nth last occurrences.

Between & *Not* Between
A	B	C	D	E	F
5	27	7490 = 2 x 5 x 7 x 107.	12159 = 3² x 7 x 193.	141	309
5	33	3486 = 2 x 3 x 7 x 83.	16163 = 7 x 2309.	170	266
4	5	12488 = 2³ x 7 x 223.	7161 = 3 x 7 x 11 x 31. SF: 52 = 2² x 13.	108	369
100	4	15330 = 2 x 3 x 5 x 7 x 73.	4319 = 7 x 617. SF: 624 = 2⁴ x 3 x 13.	71	392
100	11	8043 = 3 x 7 x 383.	11606 = 2 x 7 x 829.	128	305
100	12	7259 = 7 x 17 x 61.	12390 = 2 x 3 x 5 x 7 x 59.	133	296
100	13	7028 = 2² x 7 x 251.	12621 = 3 x 7 x 601. SF: 611 = 13 x 47.	137	292
100	17	3752 = 2³ x 7 x 67.	15897 = 3 x 7 x 757. SF: 767 = 13 x 59.	168	254
100	18	2849 = 7 x 11 x 37.	16800 = 2⁵ x 3 x 5² x 7.	176	252
100	19	2373 = 3 x 7 x 113.	17276 = 2² x 7 x 617.	180	243
100	22	532 = 2² x 7 x 19.	19117 = 7 x 2731.	215	229
100	23	91 = 7 x 13.	19558 = 2 x 7 x 11 x 127. SF: 147 = 3 x 7².	221	225
10	1	19005 = 3 x 5 x 7 x 181. SF: 196 = 2² x 7².	644 = 2² x 7 x 23.	6	435
10	12	8820 = 2² x 3² x 5 x 7².	10829 = 7² x 13 x 17.	78	282
10	22	3633 = 3 x 7 x 173.	16016 = 2⁴ x 7 x 11 x 13. SF: 39 = 3 x 13.	150	213
10	26	588 = 2² x 3 x 7². SF: 21 = 3 x 7.	19061 = 7² x 389. SF: 403 = 13 x 31.	184	191
70	1	19376 = 2⁴ x 7 x 173.	273 = 3 x 7 x 13.	7	440
70	4	17745 = 3 x 5 x 7 x 13².	1904 = 2⁴ x 7 x 17.	22	412
70	6	12929 = 7 x 1847.	6720 = 2⁶ x 3 x 5 x 7.	72	362
70	10	7224 = 2³ x 3 x 7 x 43.	12425 = 5² x 7 x 71.	105	269
1	3	18123 = 3 x 7 x 863.	1526 = 2 x 7 x 109.	27	424
1	11	10675 = 5² x 7 x 61. SF: 78 = 2 x 3 x 13.	8974 = 2 x 7 x 641. SF: 650 = 2 x 5² x 13.	97	346
1	22	1491 = 3 x 7 x 71.	18158 = 2 x 7 x 1297.	205	245
20	6	7406 = 2 x 7 x 23².	12243 = 3 x 7 x 11 x 53.	107	277
60	4	17339 = 7 x 2477.	2310 = 2 x 3 x 5 x 7 x 11. SF: 28 = 2² x 7.	36	402
2	4	455 = 5 x 7 x 13.	19194 = 2 x 3 x 7 x 457. SF: 469 = 7 x 67.	134	147
8	3	203 = 7 x 29.	19446 = 2 x 3 x 7 x 463.	331	341
7	4	7770 = 2 x 3 x 5 x 7 x 37.	11879 = 7 x 1697.	224	379
40	2	1435 = 5 x 7 x 41.	18214 = 2 x 7 x 1301.	281	321
A: First letter from feature 4. B: Nth/Nth last occurrence. C: Total of the first letters in between.			D: Total of the first letters not in between. E: Position in the list of the Nth occurrence. F: Position in the list of the Nth last occurrence.

4.7.1From column 1 of the above table, the 29 first letters that successfully divide the list:

5 5 4 100 100 100 100 100 100 100 100 100 10 10 10 10 70 70 70 70 1 1 1 20 60 2 8 7 40

Their total is not a multiple of 7 or 13: 1374 = 2 x 3 x 229. The feature is hidden in the sum of the factors: 234 = 2 x 3² x 13. SF: 21 = 3 x 7.

4.7.2From column 2 of the above table, the Nth/Nth last occurrences of the 29 first letters:

27 33 5 4 11 12 13 17 18 19 22 23 1 12 22 26 1 4 6 10 3 11 22 6 4 4 3 4 2

Again the total is not a multiple of 7 or 13: 345 = 3 x 5 x 23. Factor 23 appears because the prophecy and its completion concern people (i.e. Israel). It is strange that the first and the last in this list add to 29.

4.7.3From the last column of the table above, the positions in the list for the Nth last occurrence:

309 266 369 392 305 296 292 254 252 243 229 225 435 282 213 191 440 412 362 269 424 346 245 277 402 147 341 379 321

Here is a spectacular: 8918 = 2 x 7³ x 13.
(It is remarkable that working with the first letters of each word, is now linked with the last occurrence of a letter. But there is something more remarkable with this list.)

4.7.3.1The first and last numbers in 4.7.3: 630 = 2 x 3² x 5 x 7.

4.7.3.2The odd valued positions from 4.7.3:

309 369 305 243 229 225 435 213 191 269 245 277 147 341 379 321

Total: 4498 = 2 x 13 x 173.

4.7.2.3The even valued from 4.7.3:

266 392 296 292 254 252 282 440 412 362 424 346 402

Total: 4420 = 2² x 5 x 13 x 17. SF: 39 = 3 x 13.

4.7.4Since there is one God, check the table for the letter 1. It appeared three times. Its Nth occurrences total 329 (7 x 47). Its Nth last occurrences total 1015 (5 x 7 x 29). The difference in the Nth and Nth last totals: 686 = 2 x 7³. (And astonishingly, the sum of the factors is 23.)

4.7.5The lowest number in the table is 1, and it appeared 3 times for a total of 3. The highest number is 100, and it appeared 9 times for a total of 900. Lowest and highest form a complementary opposite. The total: 903 = 3 x 7 x 43. The total of their second column values: 175 = 5² x 7.

4.8Load the first letters into a 5 x 8 x 11 block.

4.8.1The outside: 11333 = 7 x 1619.

4.8.2The inside: 8316 = 2² x 3³ x 7 x 11.

4.8.3Odd positioned layers: 10206 = 2 x 3⁶ x 7.

4.8.4Even positioned layers: 9443 = 7 x 19 x 71.

4.8.5There aren't as many features compared with the first and last letters together in feature 3.11, but the first letters on their own have a separate feature that 3.11 does not. The first letters can be re-arranged as a 5 x 11 x 8 block.

4.8.5.1The outside of this new block: 11158 = 2 x 7 x 797. SF: 806 = 2 x 13 x 31.

4.8.5.2The inside of this block: 8491 = 7 x 1213.

Omega: The Last Letter Of Each Word

The study now moves to the last letter of each word.

5Total of the last letters: 36372 = 2² x 3 x 7 x 433.

5.1The letter values of God’s name in Hebrew (10-5-6-5) are applied 17 times to count through the list of 440 last letters.

a) 10 5  6  5  10 5  6  5  10 5  6  5  10 5  6  5   10  5   6   5   10
b) 10 15 21 26 36 41 47 52 62 67 73 78 88 93 99 104 114 119 125 130 140
c) 10 15 21 26 36 41 47 52 62 67 73 78 88 93 99 104 114 119 125 130 140
d) 40 60 1  9  60 9  40 40 9  40 9  9  90 9  40 40  9   1   40  9   40

a) 5   6   5   10  5   6   5   10  5   6   5   10  5   6   5   10  5
b) 145 151 156 166 171 177 182 192 197 203 208 218 223 229 234 244 249
c) 145 151 156 166 171 177 182 192 197 203 208 218 223 229 234 244 249
d) 9   40  5   200 9   40  200 40  7   90  9   40  1   90  90  40  90

a) 6   5   10  5   6   5   10  5   6   5   10  5   6   5   10  5   6
b) 255 260 270 275 281 286 296 301 307 312 322 327 333 338 348 353 359
c) 255 260 270 275 281 286 296 301 307 312 322 327 333 338 348 353 359
d) 9   90  40  40  40  40  200 9   9   40  60  200 40  5   9   40  90

a) 5   10  5   6   5   10  5   6   5   10  5   6   5
b) 364 374 379 385 390 400 405 411 416 426 431 437 442
c) 364 374 379 385 390 400 405 411 416 426 431 437 2
d) 40  60  9   5   5   40  40  40  90  9   60  7   5

a) Value from the Name.
b) Count.
c) Count adjusted to 440.
d) Last letter found.

Total: 2975 = 5² x 7 x 17.

5.1.1Only seven of the last letters found in the previous feature are prime numbers. Their total: 39 = 3 x 13.

5.2.1Beginning with the first of the last letters and taking every Nth after, the following values of N produce totals divisible by 7:

20 30 31 38 41 49 59 67 87 93 99 104 108 122 136 138 140 142 158 187 196 216

Total of the N values: 2261 = 7 x 17 x 19.

5.2.2Beginning with the first of the last letters and taking every Nth after, the following values of N produce totals divisible by 13:

13 15 19 22 27 41 47 57 80 82 87 130 149 151 153 165 183 189 194 200 215 217

Total of the N values: 2436 = 2² x 3 x 7 x 29.

5.2.3Whether one begins with the first of the last letters and takes every Nth after, or simply takes every Nth, only two values of N produces totals divisible by 13. Providentially, the two values are 13 and 22. (These are also the only two that produce totals of 91.) The total of these two: 35 = 5 x 7.

5.3Over 400 sub-features can be found when every other group of N-number of the last letters are added together, and this is re-applied to the results over and over.

5.4Divide the last letters into two groups: odd valued and even valued.

5.4.1The total of the 148 odd valued last letters has no feature. The feature is in the total of their positions in the list: 32795 = 5 x 7 x 937. SF: 949 = 13 x 73.

5.4.2This is also seen in the total of the positions of the even valued letters: 64225 = 5² x 7 x 367.

5.5Use prime numbers and non-prime numbers to divide the list of last letters.

5.5.1Exactly 42 (2 x 3 x 7) of the last letters are prime numbers.

a) 2 14 20 38 39 51 89 92 94 100 108 124 126 131 156 163 168 170 179 197
b) 5 5  7  7  5  5  5  5  5  5   5   2   7   5   5   7   7   7   5   7

a) 202 209 220 232 254 268 299 338 356 369 376 377 385 387 390 393 413
b) 5   5   7   5   5   5   5   5   5   5   7   7   5   5   5   5   5

a) 421 432 436 437 438 (Position in list.)
b) 5   5   7   7   5   (Prime number last letter.)

Total of the primes: 231 = 3 x 7 x 11. SF: 21 = 3 x 7.

5.5.2The remaining 398 last letters are not prime numbers. Their total: 36141 = 3 x 7 x 1721.

5.5.3The difference between last letters that are prime numbers and not prime numbers: 35910 = 2 x 3³ x 5 x 7 x 19. SF: 42 = 2 x 3 x 7.

5.5.3In the list, 85 of the last letters are in positions that are prime numbers.

a) 2 3   5  7  11 13 17  19 23 29 31 37 41 43 47 53 59 61 67 71  73 79
b) 5 600 90 40 40 40 200 40 90 90 40 90 9  1  40 9  80 90 40 600 9  9

a) 83  89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167
b) 200 5  40 40  20  600 40  40  1   5   60  60  40  40  9   7   40

a) 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263
b) 60  5   40  9   40  7   9   1   1   90  90  9   600 90  90  600 9

a) 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367
b) 9   40  90  40  40  200 9   40  200 90  40  40  9   9   40  90  90

a) 373 379 383 389 397 401 409 419 421 431 433 439 (List position.)
b) 40  9   100 9   90  9   9   40  5   60  90  60  (Last letter.)

Total (b): 6846 = 2 x 3 x 7 x 163. SF: 175 = 5² x 7.

5.5.4355 letters are in positions that are not prime numbers. Their total: 29526 = 2 x 3 x 7 x 19 x 37.

5.633 of the last letters in the list are in positions that are multiples of 13.

40 9 5 40 40 9 90 40 9 9 60 5 1 200 90 9 60 90 90 90 90 40 5 40 9 5 90 40 7 5 9 90 40

Total of these letters: 1456 = 2⁴ x 7 x 13. SF: 28 = 2² x 7.

5.7When the last letters are added one by one, 29 times the total will be divisible by 13.

a)  b)  c)         a)  b)  c)         a)  b)  c)         a)  b)  c)
9   90  1664       119 1   13195      242 200 23101      358 90  32214
19  40  2197       121 9   13234      270 40  24986      379 9   33150
39  5   4784       151 40  14391      272 90  25116      387 5   33488
75  9   8151       170 7   16965      290 90  26013      401 9   34164
85  60  10478      195 90  18486      307 9   27274      426 9   35828
99  40  11570      205 600 19435      315 9   27742
109 40  13000      210 1   19630      320 600 28470
112 60  13078      227 90  21528      353 40  31369
a) Position in list.     b) Last letter.     c) Accumulated total.

Total of the positions where this occurs (a): 6265 = 5 x 7 x 179.

5.7.137 times the position in the list, the last letter, and the accumulated total will all be odd valued.

a) b) c)         a) b) c)         a) b) c)
1   9 9          123 9 13253      335 9 30037
21  1 2205       127 1 13303      361 9 32373
41  9 4803       131 5 13397      369 5 32777
49  1 5325       135 9 13595      377 7 33101
53  9 5419       157 9 15755      385 5 33283
69  9 6915       179 5 17539      389 9 33697
73  9 8133       209 5 19629      393 5 33887
75  9 8151       211 1 19631      399 9 34115
79  9 8969       237 9 22081      403 9 34263
89  5 10591      255 9 23885      413 5 34757
93  9 10755      263 9 24743      427 9 35837
117 9 13185      289 9 25923
119 1 13195      325 9 28979
a) List position.   b) Last letter.
c) Accumulated total.

Total of the last letters (b): 259 = 7 x 37.

5.7.274 times the position in the list, the last letter, and the accumulated total will all be even valued.

a)  b)  c)         a)  b)  c)         a)  b)  c)         a)  b)  c)
4   200 814        112 60  13078      230 90  21798      332 600 29948
6   30  934        122 10  13244      234 90  21942      334 40  30028
8   600 1574       134 90  13586      236 40  22072      358 90  32214
10  40  1704       146 60  14172      260 90  24684      360 60  32364
16  90  1948       148 40  14302      262 40  24734      388 200 33688
36  60  4682       164 60  16620      270 40  24986      392 90  33882
40  10  4794       166 200 16910      272 90  25116      396 40  33976
44  200 5094       172 40  17014      274 90  25296      398 40  34106
46  40  5194       174 90  17164      284 40  25704      402 90  34254
48  90  5324       176 40  17294      286 40  25834      410 40  34622
52  40  5410       178 200 17534      288 40  25914      412 90  34752
56  90  5578       192 40  18296      292 200 26222      416 90  34946
64  40  6666       194 60  18396      302 90  27094      418 40  35586
66  70  6776       200 90  18610      308 40  27314      434 40  36202
68  90  6906       214 90  20330      310 90  27444
82  600 10178      216 90  20510      312 40  27524
84  40  10418      218 40  20640      320 600 28470
88  90  10586      224 200 21038      322 60  28570
96  40  10890      226 200 21438      324 200 28970
98  600 11530      228 90  21618      330 40  29308
a) List position.    b) Last letter.     c) Accumulated total.

Total of the positions (a): 15782 = 2 x 13 x 607.
Total of the letters (b): 8450 = 2 x 5² x 13².

5.7.340 times the accumulated total will be a prime number.

a)  b)  c)         a)  b)  c)         a)  b)  c)         a)  b)  c)
12  9   1753       114 9   13127      252 40  23831      344 60  30539
32  600 4483       131 5   13397      266 40  24923      355 60  32029
33  40  4523       162 9   16553      294 9   26431      362 40  32413
53  9   5419       179 5   17539      297 200 26891      406 90  34483
59  80  5867       180 40  17579      298 90  26981      413 5   34757
77  200 8951       187 60  17977      314 9   27733      414 90  34847
79  9   8969       212 600 20231      316 9   27751      427 9   35837
86  9   10487      239 600 22721      325 9   28979      430 40  36007
90  60  10651      240 90  22811      338 5   30091      431 60  36067
110 9   13009      241 90  22901      342 9   30389      436 7   36299
a) List position.    b) Last letter.     c) Accumulated total.

Total of the positions (a): 9576 = 2³ x 3² x 7 x 19.

5.7.4400 times the accumulated total will not be a prime number. Total of the positions of the last letters: 87444 = 2² x 3² x 7 x 347. SF: 364 = 2² x 7 x 13.

5.8Letter 70 and letter 40 are a pair forming a complementary opposite. Letter 70 is one of the letters appearing only once as a last letter, and its single position in the list is 66, which is the least of all the letters. Letter 40 appeared 106 times, which is the most of all the letters. The total of all its positions is the highest: 25120. Lowest and highest: 66 + 25120 = 25186. (2 x 7² x 257. SF: 273 = 3 x 7 x 13.)

5.8.1Total number of occurrences of the letters 7 and 70: 13.

5.9Divide the last letters into groups of 44 and add up each group.

5.9.1Odd valued groups of 44: 12586 = 2 x 7 x 29 x 31.

5.9.2Even valued groups of 44: 23786 = 2 x 7 x 1699. SF: 1708 = 2² x 7 x 61.

5.10Divide the last letters into alternating groups of M and N-number of letters where M and N are multiples of 7 and 13.

5.10.1Alternating groups of 7 and 13.

5.10.1.1Groups of 7: 12579 = 3 x 7 x 599. SF: 609 = 3 x 7 x 29. SF: 39 = 3 x 13.

5.10.1.2Groups of 13: 23793 = 3 x 7 x 11 x 103.

5.10.1.3Difference between 5.10.1.1 and 5.10.1.2: 11214 = 2 x 3² x 7 x 89. SF: 104 = 2³ x 13.

5.10.2Alternating groups of 13 and 42.

5.10.2.1Groups of 13: 7966 = 2 x 7 x 569.

5.10.2.2Groups of 42: 28406 = 2 x 7 x 2029.

5.10.2.3Difference between 5.10.2.1 and 5.10.2.2: 20440 = 2³ x 5 x 7 x 73. SF: 91 = 7 x 13.

5.1141 of the last letters divide the rest of the list into two groups: what is between their Nth and Nth last occurrences, and what is not between them.

Between & *Not* Between A Last Letter
Last Letter	Nth/Nth Last Occurrence	Total Between	Total Not Between
9	1	35819 = 7² x 17 x 43.	553 = 7 x 79.
9	5	32354 = 2 x 7 x 2311.	4018 = 2 x 7² x 41.
9	10	28140 = 2² x 3 x 5 x 7 x 67.	8232 = 2³ x 3 x 7³.
9	16	24612 = 2² x 3 x 7 x 293.	11760 = 2⁴ x 3 x 5 x 7².
9	20	20125 = 5³ x 7 x 23.	16247 = 7 x 11 x 211.
9	27	15785 = 5 x 7 x 11 x 41.	20587 = 7 x 17 x 173.
9	39	8792 = 2³ x 7 x 157.	27580 = 2² x 5 x 7 x 197.
9	45	3577 = 7² x 73.	32795 = 5 x 7 x 937. SF: 949 = 13 x 73.
9	46	3332 = 2² x 7² x 17. SF: 35 = 5 x 7.	33040 = 2⁴ x 5 x 7 x 59.
5	14	4242 = 2 x 3 x 7 x 101.	32130 = 2 x 3³ x 5 x 7 x 17.
600	3	27636 = 2² x 3 x 7² x 47.	8736 = 2⁵ x 3 x 7 x 13.
600	5	23387 = 7 x 13 x 257.	12985 = 5 x 7² x 53.
600	6	17458 = 2 x 7 x 29 x 43.	18914 = 2 x 7² x 193.
600	11	4963 = 7 x 709.	31409 = 7² x 641.
600	13	140 = 2² x 5 x 7.	36232 = 2³ x 7 x 647.
200	12	1743 = 3 x 7 x 83.	34629 = 3 x 7 x 17 x 97.
90	8	29771 = 7 x 4253.	6601 = 7 x 23 x 41.
90	9	29491 = 7 x 11 x 383.	6881 = 7 x 983.
90	18	18718 = 2 x 7² x 191.	17654 = 2 x 7 x 13 x 97. SF: 119 = 7 x 17.
90	23	13489 = 7 x 41 x 47.	22883 = 7² x 467. SF: 481 = 13 x 37.
90	25	11249 = 7 x 1607.	25123 = 7 x 37 x 97.
90	31	7049 = 7 x 19 x 53.	29323 = 7 x 59 x 71.
90	35	5894 = 2 x 7 x 421.	30478 = 2 x 7² x 311.
40	6	31703 = 7² x 647.	4669 = 7 x 23 x 29.
40	8	29428 = 2² x 7 x 1051.	6944 = 2⁵ x 7 x 31.
40	16	22211 = 7 x 19 x 167.	14161 = 7² x 17².
40	18	21287 = 7 x 3041.	15085 = 5 x 7 x 431.
40	28	15925 = 5² x 7² x 13.	20447 = 7 x 23 x 127.
40	30	14917 = 7 x 2131.	21455 = 5 x 7 x 613.
40	31	14637 = 3 x 7 x 17 x 41.	21735 = 3³ x 5 x 7 x 23.
40	34	10430 = 2 x 5 x 7 x 149.	25942 = 2 x 7 x 17 x 109.
40	36	9940 = 2² x 5 x 7 x 71.	26432 = 2⁶ x 7 x 59. SF: 78 = 2 x 3 x 13.
40	37	9646 = 2 x 7 x 13 x 53.	26726 = 2 x 7 x 23 x 83.
40	39	8015 = 5 x 7 x 229.	28357 = 7 x 4051.
40	44	4935 = 3 x 5 x 7 x 47.	31437 = 3² x 7 x 499.
40	53	0 =	36372 = 2² x 3 x 7 x 433.
60	5	26481 = 3 x 7 x 13 x 97.	9891 = 3² x 7 x 157.
60	10	11690 = 2 x 5 x 7 x 167.	24682 = 2 x 7 x 41 x 43.
60	14	3885 = 3 x 5 x 7 x 37. SF: 52 = 2² x 13.	32487 = 3 x 7² x 13 x 17.
7	4	16527 = 3 x 7 x 787.	19845 = 3⁴ x 5 x 7².
7	5	3773 = 7³ x 11.	32599 = 7 x 4657.

5.11.1Total of the Nth/Nth last values (column 2):

1 5 10 16 20 27 39 45 46 14 3 5 6 11 13 12 8 9 18 23 25 31 35 6 8 16 18 28 30 31 34 36 37 39 44 53 5 10 14 4 5

Total: 840 = 2³ x 3 x 5 x 7. SF: 21 = 3 x 7.

5.11.220 of the letters in the above table have an odd valued Nth/Nth last occurrence.

9 9 9 9 9 600 600 600 600 90 90 90 90 90 40 40 40 40 60 7

Total of these letters: 3122 = 2 x 7 x 223.

5.11.321 of the letters have an even valued Nth/Nth last occurrence.

9 9 9 9 5 600 200 90 90 40 40 40 40 40 40 40 40 40 60 60 7

Total of these letters: 1508 = 2² x 13 x 29.

5.11.4Four of the letters have an Nth/Nth last occurrence divisible by 7.

5 90 40 60

Total of these letters: 195 = 3 x 5 x 13. SF: 21 = 3 x 7.

5.11.5From column 1 of the table above, every other last letter:

9 9 9 9 5 600 600 200 90 90 90 40 40 40 40 40 40 40 60 7

Total: 2058 = 2 x 3 x 7³. SF: 26 = 2 x 13.

5.11.6From column 1 of the table, all last letters with an even first digit:

600 600 600 600 600 200 40 40 40 40 40 40 40 40 40 40 40 40 40 60 60 60

Total: 3900 = 2² x 3 x 5² x 13.

5.11.7From column 2 of the table, the odd valued Nth occurrences:

1 5 27 39 45 3 5 11 13 9 23 25 31 35 31 37 39 53 5 5

Total: 442 = 2 x 13 x 17.

5.12Just like the first and last letters in feature 3.11 and the first letters on their own in feature 4.8, the last letters can also be placed into a 5 x 8 x 11 block.

5.12.1Outside: 23128 = 2³ x 7² x 59.

5.12.2Inside: 13244 = 2² x 7 x 11 x 43. SF: 65 = 5 x 13.

5.12.3Difference between outside and inside: 9884 = 2² x 7 x 353. SF: 364 = 2² x 7 x 13.

5.12.4Seventh row through all layers: 5993 = 13 x 461.

5.12.5Seventh row through all layers with 7th layer: 8407 = 7 x 1201.

5.13And just like the first letters in feature 4.8.5, the last letters have a second block arrangement: 8 x 11 x 5.

5.13.1Outside: 23135 = 5 x 7 x 661.

5.13.2Inside: 13237 = 7 x 31 x 61.

5.13.3Difference: 9898 = 2 x 7² x 101. SF: 117 = 3² x 13.

5.13.4Four pillars: 3059 = 7 x 19 x 23. SF: 49 = 7². SF: 14 = 2 x 7.

5.14The last letters have an additional shape as a 22 x 20 rectangle.

5.15.1A series of outlines: 17542 = 2 x 7² x 179. SF: 195 = 3 x 5 x 13. SF: 21 = 3 x 7. (Totals for each marked rectangle from outside to inside: 6698, 3437, 3449, 2485, 1473.)

5.15.1.1The outermost rectangle (first), third, and fifth rectangles (odd positioned):

6698 3449 1473

Total: 11620 = 2² x 5 x 7 x 83.

5.15.1.2The second, and fourth rectangles (even positioned):

3437 2485

Total: 5922 = 2 x 3² x 7 x 47.

5.15.2Since the total of the last letters is a multiple of 7, this automatically means the opposite series would also be divisible by 7: 18830 = 2 x 5 x 7 x 269.

5.15.3Four corners: 140 = 2² x 5 x 7.

5.15.4First and last columns: 3757 = 13 x 17².

5.15.5First and last rows: 3081 = 3 x 13 x 79.

5.15.6Large 11 x 10 checker: 19955 = 5 x 13 x 307.

Letters Not First Or Last

6Defining letters that are first or last in a word automatically creates an opposite category: letters that are not first or last in a word.

9 90 5 20 8 60 40 100 7 90 60 9 1 70 5 80 40 1 60 200 80 60 90 7 20 8 5 200 100 10 1 100 60 40 100 1 80 400 60 1 80 1 10 1 20 600 200 100 60 1 5 3 600 200 80 9 1 9 60 5 2 20 7 100 1 9 10 9 1 80 1 20 200 100 9 10 60 5 9 40 600 1 90 1 40 9 6 60 30 5 40 60 1 5 3 5 200 100 7 90 60 200 3 20 8 600 5 80 1 70 5 200 90 200 100 60 1 70 60 10 80 9 8 5 9 10 1 100 60 40 100 1 80 400 60 300 200 80 9 200 9 30 10 1 40 60 40 60 70 7 100 5 3 7 9 90 5 20 8 7 20 20 60 40 60 9 70 60 3 60 1 1 8 7 90 5 100 1 1 9 60 1 1 3 40 8 80 600 70 60 9 30 70 50 60 200 90 9 1 400 600 30 1 200 100 60 100 80 1 100 9 600 100 1 1 5 3 60 200 100 60 80 5 200 8 7 100 1 60 80 5 200 5 100 1 1 20 20 80 400 60 1 80 400 5 100 1 1 60 200 20 60 60 9 7 90 60 60 200 100 1 60 9 5 10 60 200 90 1 7 90 60 200 8 1 200 30 1 90 1 9 70 60 9 10 60 20 60 200 8 60 200 90 9 30 7 5 3 30 9 200 4 90 80 1 7 60 90 1 200 100 7 9 90 100 9 200 80 60 5 3 30 9 100 60 20 20 60 70 40 1 100 60 20 600 1 200 90 30 600 50 60 200 90 1 40 1 10 20 9 8 7 90 60 40 100 1 5 100 2 80 1 1 1 90 1 1 1 1 10 600 1 90 9 20 5 9 600 200 80 1 40 600 9 60 7 1 90 9 20 5 9 1 10 2 20 7 8 7 90 60 40 100 1 9 10 60 100 60 50 600 100 5 80 60 10 5 90 100 1 20 1 200 8 30 60 1 80 200 3 30 60 600 4 60 40 100 600 1 9 70 5 7 90 60 200 10 1 100 60 40 100 1 80 400 70 1 3 1 70 9 90 100 5 200 90 1 5 40 7 8 7 100 60 1 1 8 1 9 200 100 60 80 10 5 9 40 1 20 8 600 7 90 60 200 9 7 9 10 9 1 5 100 80 60 9 4 7 5 40 8 5 80 1 200 100 60 5 2 20 7 30 5 40 7 1 200 80 5 90 90 60 200 90 1 1 500 1 100 7 5 9 80 60 200 100 7 1 300 7 10 5 200 100 7 200 80 5 100 60 1 3 5 80 8 1 9 7 10 60 40 5 200 100 60 9 500 9 1 5 40 60 30 5 40 7 80 60 90 7 40 5 3 10 1 200 100 1 9 30 60 40 9 6 60 30 5 40 60 200 60 20 20 60 200 1 50 5 2 1 20 40 5 200 30 1 100 60 3 1 1 40 100 1 60 200 1 10 600 400 60 40 100 1 8 5 80 1 70 5 200 90 5 70 600 20 7 80 600 8 7 8 5 9 90 1 9 60 60 80 60 300 7 100 60 5 3 60 40 100 60 200 100 60 1 90 8 5 40 5 9 1 30 600 20 1 2 1 1 60 90 60 200 2 1 90 100 1 90 5 1 70 5 8 7 10 1 70 1 40 7 5 300 1 20 7 200 100 60 7 9 100 9 1 200 100 60 5 3 80 1 30 30 5 40 7 200 100 60 90 100 9 7 90 60 200 1 90 9 20 5 200 600 60 200 4 1 9 600 60 100 100 1 200 80 60 200 40 100 1 200 200 100 200 7 90 100 1 9 5 50 9 600 1 9 200 600 40 200 30 600 1 80 1 70 60 80 5 200 60 30 5 40 60 2 20 1 90 300 7 30 60 200 200 100 60 9 40 60 200 40 100 5 1 5 300 1 20 1 200 100 600 1 5 3 60 40 100 5 1 100 1 20 200 600 60 1 60 1 80 9 90 9 30 5 80 1 9 9 10 60 4 60 30 600 600 90 60 5 1 200 100 60 9 60 60 5 60 1 100 1 2 7 8 70 60 100 1 200 80 60 30 60 9 600 1 80 400 9 5 80 5 9 30 70 1 9 6 60 40 100 5 5 100 600 80 1 30 30 1 100 5 600 1 80 5 90 2 200 100 5 80 600 20 5 3 60 20 20 60 200 90 600 90 5 1 200 100 60 200 40 1 100 1 600 90 1 1 90 9 20 5 200 90 80 1 7 90 100 1 100 1 2 1 100 200 70 60 100 1 200 80 60 1 9 90 100 5 200 90 60 30 5 200 100 60 5 70 60 9 8 5 70 60 5 60 200 90 1 90 8 200 200 100 60 5 20 5 200 100 60 9 70 1 100 5 60 9 30 9 60 200 100 1 7 90 100 1 200 90 100 1 200 80 600 8 5 40 100 5 200 100 40 5 9 4 9 6 60 200 100 70 10 100 7 80 1 10 60 100 60 3 5 40 5 100 70 1 90 1 7 7 600 80 1 40 1 100 7 5 80 7 40 1 100 7 80 1 40 5 2 60 7 90 5 7 90 60 200 600 40 5 3 1 20 5 3 600 20 20 1 30 1 2 1 400 8 1 40 60 200 90 100 5 60 5 60 40 1 100 3 10 1 100 5 20 9 70 5 9 40 5 600 10 5 90 100 600 100 600 10 60 200 90 1 40 100 5 20 5 3 60 100 20 9 1 600 40 5 200 100 60 1 200 8 5 600 80 1 30 600 9 200 100 600 1 1 2 600 70 60 3 3 60 20 7 90 1 50 60 200 1 5 80 9 8 5 9 1 20 1 30 70 60 100 9 6 5 200 100 60 60 9 70 60 20 5 3 60 300 5 4 600 30 5 80 400 5 100 1 20 9 1 600 90 600 200 100 60 7 90 60 200 1 20 9 80 1 50 1 600 40 5 3 1 20 300 7 10 40 5 200 30

There are 1293 letters that are not first or last in a word. Their total is 98062 (2 x 49031), which is not divisible by 7 or 13. This contrasts with the total for the combined passage, which was divisible by 13, and with the first and last letters of each word, which were divisible by 7. As the total represented God, and the first and last represented Jesus, letters not first or last would seem to represent people, and the darkness in the prophecy. Since it is not divisible by 7 or 13, consistency should not be expected in this section.

6.11264 paired groups of these letters, positioned Nth and Nth last, together and individually are divisible by 13.

a) 1     1     2     3     3     3     3     3     4     4     5
b) 451   513   455   117   182   530   543   585   347   613   86
c) 69485 79586 70928 18889 27872 81926 84461 89336 52910 92417 12740

a) 5     5     5     6    6    6     6     6     7     8     8     8
b) 121   234   440   15   31   249   288   457   411   123   261   270
c) 19370 35607 68107 1469 4550 38441 43134 70642 62400 19032 39546 40547

a) 8     8     8     8     8     9     9     9     11    11    12   12
b) 303   406   413   510   634   181   357   493   254   481   28   328
c) 44902 60996 62465 78169 93925 27196 53755 75283 38532 73060 3055 47437

a) 12    12    12    12    13    13    13    13    13    14    14
b) 482   536   614   628   74    159   267   269   368   218   369
c) 73060 82511 91806 93366 10140 24479 39949 40105 54756 32110 54756

a) 14    14    15    15    15    15    16   16    16    16    17    17
b) 458   502   378   483   571   599   31   249   288   457   468   519
c) 69602 76466 56355 72449 86450 89076 3081 36972 41665 69173 70486 78468

a) 17    18    18    19    19    19    20    20    20    21    21
b) 626   425   564   333   382   386   93    214   632   210   247
c) 92339 63336 85371 47463 56524 57694 12675 31473 92456 30394 36322

a) 21    21    22    22    22    23   24   24    24    24    25   25
b) 314   612   119   235   410   60   42   494   527   583   67   108
c) 44629 90298 16731 33449 59566 7462 4186 73359 78858 86567 7553 15197

a) 25    25    25    25    25    26   26    26    26    26    27    28
b) 236   390   552   638   645   53   101   165   336   478   227   179
c) 33176 57629 83070 92755 95004 6344 13195 22867 47489 70642 32032 24609

a) 28    28    28    28    29    29    29    29    29    30    30
b) 298   317   544   563   328   482   536   614   628   253   349
c) 41678 44148 81575 84006 44382 70005 79456 88751 90311 35204 48932

a) 30    30    31    31    31    31    31    32    32    32    33   33
b) 528   608   456   491   503   523   537   249   288   457   39   134
c) 77545 87620 66092 70564 73411 75933 79157 33891 38584 66092 1352 17745

a) 33    33    34    34    34    34    34    35    36    37    37
b) 512   592   128   356   412   420   534   229   581   244   480
c) 74230 85332 16315 49452 57928 59865 78364 30069 83967 32890 68562

a) 37    38   38    39    39    39    40    40    40    41    41    42
b) 596   97   388   268   434   504   134   512   592   436   450   47
c) 85371 9893 54080 34840 60411 72098 16393 72878 83980 60476 62985 1209

a) 42    42    42    42    43    43    43    44    44    44    45
b) 259   422   472   514   494   527   583   143   609   624   319
c) 33059 57967 65936 72449 69173 74672 82381 16783 84877 86996 40274

a) 45    45    45    46   46    46    47    47    48    48    48    48
b) 327   426   615   57   163   471   245   418   259   422   472   514
c) 40937 58032 85696 2457 18239 65468 30355 56147 31850 56758 64727 71240

a) 49   49   49    49    49    50   50    52    52    52    52    53
b) 55   109  438   446   602   104  152   155   435   547   582   96
c) 1508 9711 59228 60697 83200 8242 16198 16432 58162 76934 80821 6240

a) 53    53    53    53    53    53    53    54   54    54    54    55
b) 133   353   363   405   427   569   621   101  165   336   478   73
c) 13676 45370 46943 53014 56758 79144 84734 6851 16523 41145 64298 1443

a) 55    55    56   56    56    56    57    57    57    57    58    58
b) 545   561   109  438   446   602   135   475   542   591   163   471
c) 75504 77558 8203 57720 59189 81692 12896 63583 74620 80353 15782 63011

a) 60   60    60    60    62    62    62    63    63    64  64    64
b) 103  276   539   636   274   404   419   302   500   69  220   262
c) 6435 32344 74308 85514 31915 51428 54678 35074 67249 182 23907 30069

a) 64    65    66  66    66    66    66    66    67    67    67    67
b) 511   586   72  205   278   280   496   641   172   180   228   322
c) 68731 79183 247 21723 32318 32474 66274 86970 16250 17563 24687 37557

a) 68   68    68    68    68    68    69   69    70    70    70    71
b) 108  236   390   552   638   645   91   285   220   262   511   186
c) 7644 25623 50076 75517 85202 87451 3640 32734 23725 29887 68549 17589

a) 71    72   72    72    73    73    73    73    73    74    74    75
b) 351   95   158   556   205   278   280   496   641   545   561   159
c) 43212 4173 14911 75920 21476 32071 32227 66027 86723 74061 76115 14339

a) 75    75    75    76    76    76    77    78    78    78    79   79
b) 267   269   368   213   297   627   201   242   318   469   127  147
c) 29809 29965 44616 22191 33592 83057 20410 26104 36075 61074 9750 12753

a) 79    79    79    79    80    80    81    81    81    81    81
b) 149   294   488   517   326   515   136   243   248   313   620
c) 12948 33072 63219 68757 36816 68328 11596 26143 27131 35256 81783

a) 82    82    82    82    82    83  83    83    83    83    85    85
b) 146   230   354   487   525   84  217   392   453   567   217   392
c) 11921 23088 42003 62426 69342 221 21463 48438 58019 75569 21242 48217

a) 85    85    86    87   87    87    88   88    88    88    88    89
b) 453   567   160   121  234   440   92   334   350   362   374   448
c) 57798 75348 12519 6630 22867 55367 1105 36634 40170 42432 44330 56069

a) 90   90    90    90    90    91    91    92    93    93    93    93
b) 112  192   346   358   559   373   403   285   334   350   362   374
c) 4797 15548 39351 40872 73346 43485 47697 29094 35529 39065 41327 43225

a) 94    94    95    95    95    96    96    97   97    97    97    97
b) 214   632   423   619   635   158   556   133  353   363   405   427
c) 18798 79781 50479 78455 80522 10738 71747 7436 39130 40703 46774 50518

a) 97    97    98    99    99    99    99    100   100   101   101
b) 569   621   388   379   431   524   572   252   529   310   429
c) 72904 78494 44187 42575 50050 65117 72410 23543 66209 30511 49673

a) 101   101   102  102   102   103   104   104   104   105  106   106
b) 486   640   165  336   478   321   276   539   636   152  304   414
c) 58383 81211 9672 34294 57447 31525 25909 67873 79079 7956 28964 46527

a) 106   107  107   107   107   107   108 108   108   108   108   109
b) 577   140  292   308   331   370   111 375   461   531   535   236
c) 72436 6396 26871 28912 31876 39143 286 39468 53365 64857 65442 17979

a) 109   109   109   109   110   110   110   111   112   112   112
b) 390   552   638   645   438   446   602   315   375   461   531
c) 42432 67873 77558 79807 49517 50986 73489 28938 39182 53079 64571

a) 112   113   113   113   113   114   114   114   114   115   115
b) 535   192   346   358   559   312   466   507   629   428   499
c) 65156 10751 34554 36075 68549 28080 53651 59917 75842 46722 58669

a) 115   115   116   117   117   117   117   117   117   118  118   118
b) 558   574   465   250   338   387   464   506   573   182  530   543
c) 67951 69706 53196 19942 31915 40755 52871 59423 69381 8983 63037 65572

a) 118   119   119   119   119   120   120   121  121   121   121   122
b) 585   399   421   565   631   235   410   176  246   320   540   234
c) 70447 42003 45773 68198 75257 16718 42835 8281 19110 28340 65091 16237

a) 122   123   124   124   124   124   124   124   124   125   126  126
b) 440   607   261   270   303   406   413   510   634   367   162  400
c) 48737 72007 20514 21515 25870 41964 43433 59137 74893 35373 5148 40859

a) 126   126   126   126   127   128  128  128   128   128   129   129
b) 467   588   630   637   601   147  149  294   488   517   356   412
c) 51818 69433 74009 75127 70447 3003 3198 23322 53469 59007 33137 41613

a) 129   129   130  130   130   130   130   132  132   132   132   132
b) 420   534   145  391   593   598   644   199  341   393   443   460
c) 43550 62049 2548 39130 68965 69342 76362 7813 30121 38480 46423 49153

a) 132   133  133   133   134   134   134   134   134   134   135   135
b) 589   190  361   548   353   363   405   427   569   621   512   592
c) 67808 7007 33280 63323 31694 33267 39338 43082 65468 71058 56485 67587

a) 136   136   136   137   137   137   137   138  138   138   138   138
b) 475   542   591   243   248   313   620   188  239   385   433   470
c) 50687 61724 67457 14547 15535 23660 70187 5603 13416 35919 43225 49335

a) 138   138   139   140   140   140   141   141   141   141   142
b) 485   611   295   355   395   497   292   308   331   370   233
c) 51090 68991 21268 30927 37479 53794 20475 22516 25480 32747 12012

a) 142   142   142   142   142   143   143   143   143   144   144
b) 332   343   397   430   439   226   352   408   580   609   624
c) 25571 29068 37297 42003 44408 11154 30082 38116 65390 68094 70213

a) 145   145   146   146   146   146   147   147   147   147   148 148
b) 224   597   391   593   598   644   230   354   487   525   149 294
c) 10959 66833 36582 66417 66794 73814 11167 30082 50505 57421 195 20319

a) 148   148   149   149   149   150   150   150   151  151   151   151
b) 488   517   416   508   590   294   488   517   193  241   282   311
c) 50466 56004 39156 54392 65754 20124 50271 55809 5044 13130 18629 22308

a) 151   151   152  152   152   154  154   154   155  155  155   155
b) 489   551   185  340   501   200  359   394   178  196  277   279
c) 50349 61516 3601 27066 53521 5590 29900 35867 2912 4901 17693 17849

a) 155   155   155   156   156   156   157  157  157   157   157   157
b) 389   532   538   435   547   582   198  209  291   344   432   473
c) 35516 58149 59267 41730 60502 64389 4901 7436 18928 27911 40885 48009

a) 158  158  158   158   158   158   159   160   160   160   163   163
b) 194  215  290   364   477   622   556   267   269   368   400   467
c) 4381 8502 18850 30472 48464 68601 61009 15470 15626 30277 35711 46670

a) 163   163   163   164   165   165   165   165   165   165   166
b) 588   630   637   471   296   301   377   383   415   437   336
c) 64285 68861 69979 47229 19006 19513 31746 33462 37596 41197 24622

a) 166   167   167   167   167   167   167   168   168   169   169
b) 478   325   441   479   490   604   617   265   546   266   376
c) 47775 21827 42068 47177 48321 65169 66742 14222 58799 14222 30901

a) 170  170  170   170   170   170   171  171   171   171   171   172
b) 203  211  263   335   516   518   238  271   273   579   633   575
c) 5135 6097 13819 23751 53339 53664 9451 14911 15379 62556 67990 61945

a) 172   172   173  173  173   174   174   174   176   177   177   177
b) 594   606   180  228  322   289   533   623   643   246   320   540
c) 63817 65078 1313 8437 21307 17043 56602 67067 70187 10829 20059 56810

a) 178  178   179  179   179   179   179   179   180   180   180   180
b) 231  251   196  277   279   389   532   538   298   317   544   563
c) 7436 11219 1989 14781 14937 32604 55237 56355 17069 19539 56966 59397

a) 181  181   182   182   183   183   183   185   185   185   185   186
b) 228  322   357   493   530   543   585   281   283   454   595   340
c) 7124 19994 26559 48087 54054 56589 61464 14833 14976 42354 62361 23465

a) 186   187   188  188  188   188   189  189   189   189   189   189
b) 501   351   195  219  417   444   239  385   433   470   485   611
c) 49920 25623 1196 5616 35139 40339 7813 30316 37622 43732 45487 63388

a) 190   190   190   190   191   191   192   192   192   192   193
b) 324   380   442   642   361   548   284   306   337   492   346
c) 18967 29328 39364 68354 26273 56316 13858 16627 21593 46189 23803

a) 193   193   194  194   194   194   194   195  195   195   195   195
b) 358   559   241  282   311   489   551   215  290   364   477   622
c) 25324 57798 8086 13585 17264 45305 56472 4121 14469 26091 44083 64220

a) 196  196   196   197   197   197   197   197   198  198   198   198
b) 219  417   444   277   279   389   532   538   202  293   305   365
c) 4420 33943 39143 12792 12948 30615 53248 54366 1768 14456 15860 25753

a) 199  199   199   199   199   200   200   200   200   200   201   201
b) 209  291   344   432   473   341   393   443   460   589   359   394
c) 2535 14027 23010 35984 43108 22308 30667 38610 41340 59995 24310 30277

a) 203   203   203   204 204  204   204   204   205   205   206   206
b) 293   305   365   211 263  335   516   518   401   476   278   280
c) 12688 14092 23985 962 8684 18616 48204 48529 29471 41639 10595 10751

a) 206   206   207   207   207   208   208   208   209   210   210
b) 496   641   345   505   562   287   299   550   570   291   344
c) 44551 65247 20852 46254 55081 10985 12636 53521 55315 11492 20475

a) 210   210   211  211   211   212  212   212   212   213   213   213
b) 432   473   247  314   612   263  335   516   518   371   396   618
c) 33449 40573 5928 14235 59904 7722 17654 47242 47567 23842 27690 59891

a) 214   214   215   216   216   216   216   217   217   217   218
b) 297   627   632   290   364   477   622   495   584   605   392
c) 11401 60866 60983 10348 21970 39962 60099 42991 55809 58071 26975

a) 218   218   219   219   219   220   220   221  221   222  222   222
b) 453   567   369   458   502   417   444   262  511   257  330   553
c) 36556 54106 22646 37492 44356 29523 34723 6162 44824 5486 14911 51896

a) 222   223   223   223   224 224   224   225   226   226   227   227
b) 646   300   309   625   225 323   402   597   323   402   352   408
c) 63635 10595 11999 59748 468 13494 26936 55874 13026 26468 18928 26962

a) 227   229   231   231   231   232  233  233   233   233   233   234
b) 580   322   354   487   525   251  256  342   398   459   498   332
c) 54236 12870 18915 39338 46254 3783 4017 16861 25558 35672 41886 13559

a) 234   234   234   234   235   236   237   237   237   237   238  239
b) 343   397   430   439   440   410   390   552   638   645   307  271
c) 17056 25285 29991 32396 32500 26117 24453 49894 59579 61828 9932 5460

a) 239  239   239   240   240   240   240   240   242  242  242   242
b) 273  579   633   385   433   470   485   611   282  311  489   551
c) 5928 53105 58539 22503 29809 35919 37674 55575 5499 9178 37219 48386

a) 243  243   244 244  244   245   245   246   247  247   248  248
b) 318  469   248 313  620   480   596   418   320  540   314  612
c) 9971 34970 988 9113 55640 35672 52481 25792 9230 45981 8307 53976

a) 249  249   250  250   251   251   251   251   251   253   254   254
b) 313  620   288  457   338   387   464   506   573   529   349   528
c) 8125 54652 4693 32201 11973 20813 32929 39481 49439 42666 13728 42341

a) 254   255   256   256   257   257   257   257   258  258   258   259
b) 608   481   447   484   342   398   459   498   330  553   646   578
c) 52416 34528 29601 34736 12844 21541 31655 37869 9425 46410 58149 49400

a) 260   260   260   261   261   261   262  262  262   262   262   262
b) 422   472   514   409   509   554   270  303  406   413   510   634
c) 24908 32877 39390 21866 38454 46124 1001 5356 21450 22919 38623 54379

a) 263   264  264   264   265   265   266   267   268 268   269   269
b) 511   335  516   518   560   576   546   376   269 368   434   504
c) 38662 9932 39520 39845 46631 48165 44577 16679 156 14807 25571 37258

a) 270   271  271   271   271   271   272 272   272   274   274   275
b) 368   303  406   413   510   634   273 579   633   579   633   404
c) 14651 4355 20449 21918 37622 53378 468 47645 53079 47177 52611 19513

a) 275   276   277   277   278 278   278   278   279 279   279   280
b) 419   407   539   636   279 389   532   538   280 496   641   389
c) 22763 19656 41964 53170 156 17823 40456 41574 156 33956 54652 17667

a) 280   280   281   281   282 282   282   283  283   283   284   284
b) 532   538   496   641   283 454   595   311  489   551   454   595
c) 40300 41418 33800 54496 143 27521 47528 3679 31720 42887 27378 47385

a) 285  285  285   287  287   288  288   289   290   290   291   291
b) 306  337  492   329  549   299  550   457   533   623   364   477
c) 2769 7735 32331 5811 42549 1651 42536 27508 39559 50024 11622 29614

a) 291   292  292   292   293  293  293   294  294   295   295   297
b) 622   344  432   473   308  331  370   305  365   488   517   301
c) 49751 8983 21957 29081 2041 5005 12272 1404 11297 30147 35685 507

a) 297   297   297   297   298   299  299   299   300   301  301   302
b) 377   383   415   437   627   317  544   563   550   309  625   377
c) 12740 14456 18590 22191 49465 2470 39897 42328 40885 1404 49153 12233

a) 302   302   302   303   304   304   304   304   305   305   306  307
b) 383   415   437   500   406   413   510   634   414   577   365  337
c) 13949 18083 21684 32175 16094 17563 33267 49023 17563 43472 9893 4966

a) 307   309  309   310   311   311   311   312   312   313   313   313
b) 492   331  370   625   429   486   640   489   551   466   507   629
c) 29562 2964 10231 47749 19162 27872 50700 28041 39208 25571 31837 47762

a) 314   315   317   318   318   319   320 320   320   321   324   325
b) 620   612   639   544   563   469   327 426   615   540   402   380
c) 46527 45669 49621 37427 39858 24999 663 17758 45422 36751 13442 10361

a) 325   325   326   326   326   326   326   327   328   328   329
b) 442   642   441   479   490   604   617   515   426   615   482
c) 20397 49387 20241 25350 26494 43342 44915 31512 17095 44759 25623

a) 329   329   329   330   331   331   332  333  333   333   333   334
b) 536   614   628   549   553   646   370  343  397   430   439   382
c) 35074 44369 45929 36738 36985 48724 7267 3497 11726 16432 18837 9061

a) 334   335  335  335  336   336   337   338   339  339   339   339
b) 386   350  362  374  516   518   478   492   387  464   506   573
c) 10231 3536 5798 7696 29588 29913 23153 24596 8840 20956 27508 37466

a) 340   340   341   342  342   342   342   343  343   343   344  344
b) 520   557   501   393  443   460   589   398  459   498   397  430
c) 29588 35711 26455 8359 16302 19032 37687 8697 18811 25025 8229 12935

a) 344   345   345   346   346   347  347   348   349   349   350   350
b) 439   432   473   505   562   358  559   613   526   541   528   608
c) 15340 12974 20098 25402 34229 1521 33995 39507 28353 31330 28613 38688

a) 351  351  353  353   354  354  354   354   354   355   355   356
b) 362  374  408  580   363  405  427   569   621   487   525   395
c) 2262 4160 8034 35308 1573 7644 11388 33774 39364 20423 27339 6552

a) 356   357  357   357   358   359   360  362   363  364  364  364
b) 497   412  420   534   493   559   394  548   374  405  427  569
c) 22867 8476 10413 28912 21528 32474 5967 30043 1898 6071 9815 32201

a) 364   365   365   367   370   370   372  372   373  373   374  376
b) 621   477   622   463   458   502   396  618   381  521   403  461
c) 37791 17992 38129 15951 14846 21710 3848 36049 1339 23426 4212 13897

a) 376   376   378  378  378  379   379   379   380  380   380   381
b) 531   535   383  415  437  483   571   599   431  524   572   442
c) 25389 25974 1716 5850 9451 16094 30095 32721 7475 22542 29835 10036

a) 381   382   383  384  384  385   385   385   386  386   386   386
b) 642   521   386  415  437  555   568   610   433  470   485   611
c) 39026 22087 1170 4134 7735 27118 28535 32981 7306 13416 15171 33072

a) 388   388   388   390   390   391   391   391   392   392   392
b) 464   506   573   532   538   552   638   645   593   598   644
c) 12116 18668 28626 22633 23751 25441 35126 37375 29835 30212 37232

a) 393  393   394  394   394   396   397   398  398  399   399   400
b) 453  567   443  460   589   497   618   430  439  459   498   421
c) 9581 27131 7943 10673 29328 16315 32201 4706 7111 10114 16328 3770

a) 400   400   401   401   401   401   402   405  406  406   406   407
b) 565   631   467   588   630   637   476   419  427  569   621   413
c) 26195 33254 10959 28574 33150 34268 12168 3250 3744 26130 31720 1469

a) 407   407   409   410   410   413  413   414   414   415   416  417
b) 510   634   580   509   554   420  534   510   634   577   437  508
c) 17173 32929 27274 16588 24258 1937 20436 15704 31460 25909 3601 15236

a) 417   418  421   422   422   423  423   424   424   425   425   426
b) 590   444  534   565   631   472  514   619   635   566   616   564
c) 26598 5200 18499 22425 29484 7969 14482 27976 30043 22243 27833 22035

a) 427   428   428   429   429   429   430  430   431  432   432   433
b) 615   569   621   499   558   574   486  640   439  524   572   473
c) 27664 22386 27976 11947 21229 22984 8710 31538 2405 15067 22360 7124

a) 434  434  434   435   436   436   437  439  439   442  442  442
b) 470  485  611   504   547   582   450  446  602   479  490  604
c) 6110 7865 25766 11687 18772 22659 2509 1469 23972 5109 6253 23101

a) 442   443   444  444   446  447   448  452   453   454   455   457
b) 617   642   460  589   474  602   484  513   522   567   595   491
c) 24674 28990 2730 21385 4407 22503 5135 10101 10608 17550 20007 4472

a) 457  457  457   459  460  461   462   462   465  465   467  467
b) 503  523  537   502  498  589   531   535   506  573   507  629
c) 7319 9841 13065 6864 6214 18655 11492 12077 6552 16510 6266 22191

a) 468   468   468   469  469   471  471   473  476   476   478   480
b) 588   630   637   519  626   485  611   514  542   591   622   490
c) 17615 22191 23309 7982 21853 1755 19656 6513 11037 16770 20137 1144

a) 480   480   481   483  483   483   484   484   486   487   488  489
b) 604   617   596   536  614   628   571   599   611   640   525  517
c) 17992 19565 16809 9451 18746 20306 14001 16627 17901 22828 6916 5538

a) 490   491   491   492  492  492  495  495   496   496   497   500
b) 551   604   617   503  523  537  527  583   584   605   641   558
c) 11167 16848 18421 2847 5369 8593 5499 13208 12818 15080 20696 9282

a) 500   504  504  506  507  508   509   510  511   513   517 520   521
b) 574   523  537  562  573  629   590   554  634   592   518 626   557
c) 11037 2522 5746 8827 9958 15925 11362 7670 15756 11102 325 13871 6123

a) 524  525  527  528  529   531  531  532 533  534   537  537   540
b) 537  572  541  583  608   543  585  535 538  623   614  628   636
c) 3224 7293 2977 7709 10075 2535 7410 585 1118 10465 9295 10855 11206

a) 543  544  545  546  548  553  553   554   556  556  559  561  566
b) 591  585  563  561  582  638  645   646   568  610  574  576  631
c) 5733 4875 2431 2054 3887 9685 11934 11739 1417 5863 1755 1534 7059

a) 567  569  570  572  576  576  580  585  589  589  594 594  595  599
b) 616  610  621  599  594  606  633  605  630  637  598 644  606  644
c) 5590 4446 5590 2626 1872 3133 5434 2262 4576 5694 377 7397 1261 7020

a) 605  610  615  620  631  639
b) 617  624  628  635  637  645
c) 1573 2119 1560 2067 1118 2249

a) Start position of first group is from the beginning, and of the
      second group is from the end.
b) End position of first group is from the beginning, and of the
      second group is from the end.
c) Total of both groups.

Total of the positions (a + b): 828268 = 2² x 7 x 29581.

6.2Every Nth from the list can be taken in two ways: beginning with the first in the list, or beginning with the Nth in the list. Twelve values of N work both ways.

45 63 64 78 228 234 239 267 330 574 619 633

Total of the N values: 3374 = 2 x 7 x 241.

6.3Astonishingly, one can take every Nth from the list to produce a total divisible by seven in 91 (7 x 13) ways.

4 13 32 35 38 45 56 57 61 63 64 66 71 78 81 83 90 91 101 106 110 112 128 143 144 159 161 164 172 176 185 197 199 212 216 218 226 228 232 234 239 246 255 267 280 281 297 330 336 337 343 353 354 363 365 371 381 382 384 402 410 418 424 429 435 442 450 451 459 461 464 469 476 477 485 486 506 512 527 542 565 574 580 582 602 613 618 619 624 628 633

Total of the N values: 27378 = 2 x 3⁴ x 13².

6.3.1The smallest value is 4, and the largest value is 633. Small and large are complementary opposites. 4 + 633 = 637 (7² x 13).

6.3.2Odd valued from 6.3:

13 35 45 57 61 63 71 81 83 91 101 143 159 161 185 197 199 239 255 267 281 297 337 343 353 363 365 371 381 429 435 451 459 461 469 477 485 527 565 613 619 633

Total: 12220 = 2² x 5 x 13 x 47.

6.3.3Even valued from 6.3:

4 32 38 56 64 66 78 90 106 110 112 128 144 164 172 176 212 216 218 226 228 232 234 246 280 330 336 354 382 384 402 410 418 424 442 450 464 476 486 506 512 542 574 580 582 602 618 624 628

Total: 15158 = 2 x 11 x 13 x 53.

6.3.445 of the N values in 6.3 have a first digit that is odd valued:

13 32 35 38 56 57 71 78 90 91 101 106 110 112 128 143 144 159 161 164 172 176 185 197 199 330 336 337 343 353 354 363 365 371 381 382 384 506 512 527 542 565 574 580 582

Total: 11505 = 3 x 5 x 13 x 59.

6.3.546 of the N values in 6.3 have a first digit that is even valued:

4 45 61 63 64 66 81 83 212 216 218 226 228 232 234 239 246 255 267 280 281 297 402 410 418 424 429 435 442 450 451 459 461 464 469 476 477 485 486 602 613 618 619 624 628 633

Total: 15873 = 3 x 11 x 13 x 37.

6.4.1Beginning with the first number in feature 6 and taking every Nth after, only two numbers produce a total divisible by 91.

111 357

Total of the two numbers: 468 = 2² x 3² x 13.

6.4.2Taking every Nth from the list in feature 6, four numbers produce totals divisible by 19:

83 239 371 476

Total of the four numbers: 1169 = 7 x 167.

6.5.1218 letters are prime numbers. The total of their positions in the list: 149359 = 7 x 19 x 1123.

6.5.21083 of the letters are not in positions that are prime numbers. The total of these letters: = 80808 = 2³ x 3 x 7 x 13 x 37.

6.699 letters are in positions divisible by 13.

1 8 60 3 1 5 40 20 1 40 10 90 3 1 60 80 60 100 1 100 200 60 30 7 60 90 8 1 9 20 100 10 200 5 400 5 100 60 4 20 200 100 100 5 40 1 60 200 1 5 5 5 40 60 7 100 1 90 1 1 600 60 300 100 3 60 60 9 100 5 5 5 20 1 80 60 60 60 20 9 200 4 60 7 100 60 1 5 9 600 100 5 600 1 100 3 20 1 300

Total of these letters: 6888 = 2³ x 3 x 7 x 41.

6.7The middle N-number of letters in the list are divisible by 13 when N is one of the following:

1281 1275 1171 1135 1119 1109 1041 987 959 957 893 783 763 761 745 641 625 615 593 575 569 545 541 505 485 471 455 399 325 263 253 201 179 91

Total of the N values: 23310 = 2 x 3² x 5 x 7 x 37.

6.8When the letters in feature 6 are added one by one, 92 times the accumulated total will be a multiple of 13.

a)   b)  c)         a)   b)  c)         a)   b)  c)         a)   b)  c)         a)   b)  c)         a)   b)  c)         a)   b)  c)
3    5   104        254  9   17953      414  80  29016      631  1   42198      904  9   65052      1066 4   78793      1220 60  91806
10   90  429        286  60  19812      421  20  29302      643  100 43810      919  60  66417      1073 10  79248      1224 80  92092
44   1   2470       297  5   20501      426  60  29601      693  30  47333      931  100 67509      1097 1   80717      1230 20  92144
75   9   4992       304  80  20917      451  40  32032      698  1   47957      943  600 69277      1109 40  81185      1239 200 92625
87   6   5863       319  60  21931      481  100 33800      732  100 49686      959  60  70811      1115 5   81354      1244 70  92924
92   60  6058       327  20  22178      501  1   35035      748  100 50557      999  200 73918      1139 40  83512      1255 5   94016
105  8   6760       329  70  22308      513  80  35438      755  60  50973      1010 9   74607      1141 200 83772      1259 100 94601
118  70  8242       334  20  22529      549  300 38103      761  5   51298      1012 5   74620      1144 5   83967      1267 200 96122
144  1   10114      340  600 24050      565  8   38974      776  60  53573      1014 60  74750      1146 5   84032
151  100 10491      347  1   24492      577  500 39975      782  200 54314      1016 60  74815      1166 90  85215
175  90  11154      350  9   24531      597  100 40768      789  9   54821      1025 60  75764      1189 5   87984
185  40  11375      362  1   25025      613  20  41418      805  70  57317      1031 60  76154      1201 600 89869
213  100 15093      374  9   25831      615  200 41678      839  1   59709      1053 200 77597      1206 1   90779
224  200 15808      399  7   27651      627  100 42133      859  1   61867      1064 5   78780      1215 20  91598
a) Position in list.     b) Letter not first/last.     c) Accumulated total at that point.

Total of the positions (a): 63934 = 2 x 13 x 2459.

6.9The 1293 letters can be arranged as alternating groups of M and N-number of letters where M and N are multiples of 7 or 13.

6.9.1Alternating groups of 21 and 403.

6.9.1.1Groups of 21: 6139 = 7 x 877. SF: 884 = 2² x 13 x 17.

6.9.1.2Groups of 403: 91923 = 3 x 13 x 2357. SF: 2373 = 3 x 7 x 113.

6.9.2Alternating groups of 210 and 221.

6.9.2.1Groups of 210: 45331 = 11 x 13 x 317.

6.9.2.2Groups of 221: 52731 = 3⁵ x 7 x 31.

6.10Other features of these letters are hidden in their positions in the passage.

Positions of letters that are not first or last in a word:
2 3 4 5 6 7 8 9 16 17 18 21 24 25 26 27 28 29 30 31 34 35 36 37 38 39 40 43 44 47 48 49 50 51 52 53 54 55 56 59 60 61 62 63 64 65 68 69 70 73 76 77 78 81 82 83 87 88 91 94 95 96 97 98 99 106 107 108 111 112 113 114 115 116 117 118 119 122 123 124 125 128 129 130 131 132 133 134 135 136 137 138 141 144 145 146 149 150 154 155 156 157 160 163 164 165 168 169 170 171 172 173 174 177 178 179 182 185 186 187 188 189 190 191 192 196 197 198 199 200 201 202 203 204 205 208 211 212 213 216 219 220 223 224 225 226 229 232 235 238 241 242 243 244 247 248 249 250 251 252 255 256 259 260 261 264 265 268 269 270 273 276 277 278 279 280 281 282 286 287 290 293 296 299 302 303 304 305 306 307 310 311 314 317 318 319 320 321 322 325 326 331 332 333 334 335 338 339 340 341 342 343 344 345 348 351 352 355 356 357 360 361 362 363 364 365 366 369 372 373 374 375 376 377 378 381 384 385 388 389 390 393 396 397 398 399 400 403 408 409 410 413 416 417 418 419 420 423 424 425 428 431 432 433 436 437 438 439 440 446 447 448 449 452 453 454 455 456 457 460 463 464 467 468 471 472 473 474 475 476 477 478 479 480 483 484 487 488 491 492 495 496 503 504 505 506 509 510 511 512 513 514 517 518 519 520 523 524 525 528 529 534 535 538 541 542 543 544 547 550 551 552 553 554 555 558 561 562 563 564 567 568 569 570 573 576 577 578 579 580 581 582 583 584 585 586 587 590 591 594 595 596 597 600 603 604 605 608 611 612 613 620 621 622 623 624 625 628 631 632 633 634 635 642 643 646 649 650 651 652 653 654 655 658 659 660 661 662 663 664 665 666 667 668 671 676 677 678 679 684 685 686 687 688 689 692 693 696 697 698 702 703 704 705 706 707 710 714 715 716 717 718 721 724 725 726 727 728 731 734 735 736 740 741 742 743 748 749 750 751 752 753 754 755 756 759 760 761 764 769 770 771 772 773 774 775 776 779 780 781 782 783 784 787 790 793 794 798 799 802 803 804 811 814 815 816 817 820 823 824 825 829 830 831 832 835 838 841 842 843 844 847 848 849 850 853 854 857 860 861 862 863 864 865 868 869 870 873 874 875 876 877 878 879 880 883 886 887 888 889 890 891 892 893 894 897 900 901 902 905 908 909 910 911 914 915 916 919 922 923 924 925 928 929 930 934 935 936 937 938 941 944 945 946 947 950 953 954 955 956 957 958 961 962 963 964 967 968 969 974 975 976 977 978 979 980 983 984 985 986 987 988 989 990 991 994 995 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1013 1014 1015 1016 1017 1020 1023 1024 1025 1026 1027 1032 1033 1034 1035 1036 1037 1040 1041 1044 1047 1048 1049 1050 1053 1054 1057 1058 1059 1062 1063 1064 1065 1066 1069 1070 1071 1072 1073 1074 1075 1076 1077 1080 1081 1084 1085 1086 1087 1088 1093 1094 1095 1098 1101 1102 1103 1104 1107 1110 1111 1112 1113 1114 1115 1118 1119 1120 1121 1122 1123 1126 1127 1128 1131 1134 1135 1136 1137 1138 1139 1140 1143 1144 1147 1148 1149 1152 1155 1158 1159 1160 1161 1164 1165 1166 1167 1168 1169 1170 1173 1176 1177 1178 1179 1180 1181 1184 1185 1186 1189 1192 1193 1194 1195 1196 1199 1200 1201 1204 1207 1208 1209 1210 1213 1214 1215 1218 1219 1220 1221 1222 1223 1224 1225 1226 1229 1230 1231 1234 1235 1236 1239 1240 1241 1242 1246 1247 1248 1249 1250 1251 1254 1257 1258 1259 1260 1261 1262 1265 1266 1269 1270 1271 1272 1273 1274 1275 1276 1277 1280 1283 1284 1287 1290 1291 1292 1293 1296 1301 1302 1303 1304 1307 1310 1315 1316 1317 1318 1319 1320 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1342 1343 1344 1345 1346 1347 1348 1349 1350 1353 1354 1355 1358 1359 1360 1361 1362 1363 1364 1367 1370 1371 1372 1373 1374 1377 1378 1379 1382 1385 1386 1387 1388 1389 1390 1394 1395 1396 1397 1398 1399 1402 1405 1406 1409 1414 1415 1416 1417 1420 1421 1422 1423 1424 1427 1428 1429 1430 1431 1432 1433 1436 1437 1438 1441 1442 1443 1444 1445 1450 1451 1456 1459 1460 1463 1464 1465 1466 1467 1468 1471 1474 1477 1478 1479 1480 1481 1484 1485 1486 1487 1492 1497 1498 1499 1500 1501 1502 1503 1506 1507 1508 1509 1510 1511 1512 1513 1514 1517 1518 1521 1524 1525 1526 1527 1528 1529 1530 1531 1534 1537 1538 1539 1540 1541 1542 1543 1544 1545 1548 1549 1550 1551 1554 1555 1556 1557 1560 1561 1562 1563 1566 1567 1568 1569 1574 1575 1576 1577 1578 1581 1582 1583 1588 1589 1590 1591 1592 1593 1596 1597 1598 1599 1602 1603 1606 1607 1608 1609 1610 1611 1614 1617 1620 1623 1624 1625 1626 1627 1630 1633 1634 1635 1636 1637 1638 1639 1640 1641 1644 1645 1646 1649 1650 1651 1652 1653 1654 1657 1660 1663 1664 1667 1668 1669 1670 1671 1674 1677 1678 1679 1684 1685 1686 1689 1690 1691 1694 1695 1698 1701 1704 1705 1708 1709 1712 1713 1719 1720 1723 1728 1729 1730 1731 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1750 1751 1754 1755 1756 1757 1758 1759 1760 1763 1764 1767 1772 1773 1774 1777 1778 1781 1782 1783 1784 1787 1788 1789 1790 1791 1794 1797 1798 1799 1802 1805 1808 1811 1812 1815 1816 1817 1818 1821 1822 1827 1830 1831 1832 1833 1836 1837 1840 1841 1842 1843 1844 1845 1846 1850 1851 1852 1853 1856 1857 1860 1861 1862 1863 1866 1867 1868 1871 1874 1877 1878 1881 1882 1883 1884 1885 1886 1887 1890 1891 1894 1895 1898 1901 1904 1907 1910 1911 1912 1917 1918 1919 1920 1921 1922 1923 1924 1925 1928 1929 1930 1935 1938 1939 1942 1943 1944 1945 1946 1949 1950 1951 1952 1953 1954 1955 1956 1959 1960 1961 1962 1965 1968 1969 1970 1973 1974 1975 1978 1979 1980 1983 1986 1987 1988 1989 1992 1993 1994 1995 1998 2003 2004 2005 2008 2011 2012 2013 2016 2017 2018 2019 2020 2023 2024 2025 2026 2031 2032 2033 2036 2039 2040 2041 2042 2043 2044 2047 2048 2049 2050 2053 2054 2055 2056 2057 2058 2061 2062 2063 2070 2071 2072 2073 2076 2077 2078 2079 2082 2083 2086 2087 2088 2089 2094 2095 2096 2097 2098 2101 2102 2103 2106 2107 2108 2111 2112 2113 2119 2120 2121 2122 2125 2126 2127 2130 2131 2132 2133 2136 2137 2140 2141 2142 2143 2146 2147 2148 2153 2154 2155 2156

6.10.1These positions can be paired Nth and Nth last, where both are multiples of 7.

a) Nth position: 22   238  304  333  341  608  637 
b) Value:        35   385  504  553  567  1008 1057
c) Nth last:     1272 1056 990  961  953  686  657 
d) Value:        2121 1743 1624 1575 1561 1134 1085
e) Sum:          2156 2128 2128 2128 2128 2142 2142

There are exactly 7 of them. Sum of positions (a + c): 9058 = 2 x 7 x 647.

6.10.2Exactly 77 of them can be paired Nth and Nth last, where they are together a multiple of 13.

a) Nth position: 1    2    3    4    9    10   11   12   14   15   16
b) Value:        2    3    4    5    16   17   18   21   25   26   27
c) Nth last:     1293 1292 1291 1290 1285 1284 1283 1282 1280 1279 1278
d) Value:        2156 2155 2154 2153 2142 2141 2140 2137 2133 2132 2131
e) Sum:          2158 2158 2158 2158 2158 2158 2158 2158 2158 2158 2158

a) 17   39   43   44   47   48   50   132  133  134  136  165  166  167
b) 28   56   62   63   68   69   73   202  203  204  208  261  264  265
c) 1277 1255 1251 1250 1247 1246 1244 1162 1161 1160 1158 1129 1128 1127
d) 2130 2089 2083 2082 2077 2076 2072 1930 1929 1928 1924 1871 1868 1867
e) 2158 2145 2145 2145 2145 2145 2145 2132 2132 2132 2132 2132 2132 2132

a) 169  170  175  176  177  178  179  180  204  205  206  207  216  218
b) 269  270  279  280  281  282  286  287  333  334  335  338  351  355
c) 1125 1124 1119 1118 1117 1116 1115 1114 1090 1089 1088 1087 1078 1076
d) 1863 1862 1853 1852 1851 1850 1846 1845 1799 1798 1797 1794 1781 1777
e) 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132

a) 221  242  248  250  252  269  368  369  400  401  402  403  404  418
b) 360  393  403  409  413  440  608  611  664  665  666  667  668  696
c) 1073 1052 1046 1044 1042 1025 926  925  894  893  892  891  890  876
d) 1772 1739 1729 1723 1719 1679 1524 1521 1468 1467 1466 1465 1464 1436
e) 2132 2132 2132 2132 2132 2119 2132 2132 2132 2132 2132 2132 2132 2132

a) 436  437  440  441  442  445  446  452  453  454  456  457  458  471
b) 726  727  734  735  736  742  743  753  754  755  759  760  761  782
c) 858  857  854  853  852  849  848  842  841  840  838  837  836  823
d) 1406 1405 1398 1397 1396 1390 1389 1379 1378 1377 1373 1372 1371 1350
e) 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132 2132

a) 472  473  540  542  543  544  545  546  547  548 
b) 783  784  905  909  910  911  914  915  916  919
c) 822  821  754  752  751  750  749  748  747  746 
d) 1349 1348 1240 1236 1235 1234 1231 1230 1229 1226
e) 2132 2132 2145 2145 2145 2145 2145 2145 2145 2145

Sum of positions (a + c): 99638 = 2 x 7 x 11 x 647.

6.10.31205 paired groups from the list in feature 6.10, positioned Nth and Nth last are together and individually multiples of 13.

a) 1      1      1      1       1       2     2      2      2       3
b) 117    125    325    511     601     22    357    447    562     33
c) 251173 268281 694148 1091311 1284543 45292 760058 952081 1198587 66807

a) 3      3      4     4      4      4      4       5      5      5
b) 208    397    43    202    242    283    506     274    281    331
c) 441181 843284 86125 426231 511381 598520 1074099 577278 592124 698282

a) 5       6      6      6      6       7      7      7      7      7
b) 590     162    332    358    632     62     67     333    434    582
c) 1252303 336505 698256 753558 1340131 120406 131144 698230 913575 1230801

a) 7       8      8      8      8      8       9      9      9      9
b) 629     175    284    334    360    576     329    345    415    488
c) 1331551 359931 592020 698204 753506 1215747 685412 719446 868738 1024608

a) 10     10     10      10      10      10      11   11     11     11
b) 191    314    528     548     607     614     12   113    120    432
c) 389805 651378 1108367 1151254 1277991 1292967 4316 221065 236028 900679

a) 11      11      12    12     13     13     13     13      13
b) 538     547     35    228    113    120    432    538     547
c) 1127646 1146951 51701 464347 216749 231712 896363 1123330 1142635

a) 14   15     15     15     16     16     16     18     19     19
b) 16   197    265    469    197    265    469    278    156    187
c) 6474 391833 536614 970983 389675 534456 968825 557726 295659 361829

a) 20     20      21     21     21     22     22     22     22     22
b) 404    610     168    298    477    164    220    240    393    465
c) 821548 1262833 316953 593658 975117 306267 425763 468299 793754 947349

a) 22      22      23     23     23      24     24      25     25
b) 565     613     357    447    562     222    624     108    140
c) 1161901 1264939 714766 906789 1153295 425711 1284179 180180 248547

a) 25     25     25     25     25      25      25      26     27    27
b) 210    226    268    272    497     531     638     102    65    468
c) 397995 432055 521417 529906 1009463 1082445 1311999 165191 83720 942981

a) 27      27      28   28     28     28     28      29    29    29
b) 542     543     31   133    395    421    605     39    64    211
c) 1101724 1103869 8606 227162 785109 840554 1234896 23647 77272 391521

a) 29     29     29     29     30     30     30     30     30      30
b) 307    318    349    377    94     163    241    429    584     595
c) 595556 618904 684840 744458 139477 286910 453206 853320 1185522 1209156

a) 30      31     31     31     31      31      32     32     32
b) 597     126    394    405    518     545     133    395    421
c) 1213446 205751 776516 799994 1041651 1099553 218556 776503 831948

a) 32      33     33      33      34     34     35     35     35
b) 605     396    566     578     208    397    170    398    492
c) 1226290 776490 1140373 1166165 374374 776477 291083 776464 977197

a) 35      36     37     37     37      37      38     38     38
b) 508     228    433    483    623     637     92     123    409
c) 1011595 412646 846807 953537 1254071 1284049 118001 184288 793481

a) 39    39    39     40    40     40     40     40     40     41
b) 53    84    461    64    211    307    318    349    377    262
c) 32175 98722 902239 53625 367874 571909 595257 661193 720811 474279

a) 41     41     41     42     43     43     43      44     44     44
b) 269    299    446    145    306    464    622     202    242    283
c) 489138 552760 865943 222690 563342 900055 1239043 340106 425256 512395

a) 44     45     45      46     46     46     47     47     47     47
b) 506    114    572     128    463    486    294    337    428    445
c) 987974 150020 1127503 177814 891488 940667 529282 620646 814671 850941

a) 47     48     48      49     49     49     49      50    50      51
b) 509    479    641     103    151    501    556     93    527     635
c) 987987 921362 1269008 117923 220493 966511 1084525 94393 1020162 1249729

a) 52     52     53     53      54    54     55    55     55     55
b) 277    383    476    587     84    461    86    267    310    359
c) 482521 707889 904215 1142583 66547 870064 68692 454870 546104 650286

a) 55     55     56     56     57     57     58     59     59     59
b) 376    382    387    440    224    510    378    130    233    304
c) 686504 699322 707889 820976 359099 968695 684346 154219 373945 524784

a) 60      61     61     61     61     61     61     61      62     62
b) 606     198    256    303    459    507    512    611     225    244
c) 1168349 295113 418639 518362 850785 953667 964405 1176903 350493 390923

a) 62     62      63    63     63     63      63      64     64     64
b) 330    645     67    333    434    582     629     401    491    561
c) 573586 1247545 10738 577824 793169 1110395 1211145 720642 912821 1063101

a) 64      65     65     65     65     65     66     66      66
b) 620     211    307    318    349    377    468    542     543
c) 1189721 314249 518284 541632 607568 667186 859261 1018004 1020149

a) 67    67     67     68     68     68      68      69     69     69
b) 73    263    513    333    434    582     629     351    414    514
c) 15054 420628 953667 567086 782431 1099657 1200407 603226 737620 951509

a) 69     70     70     70     70     70     70     71     71     71
b) 535    229    252    285    379    417    426    209    315    348
c) 996541 341809 390793 460850 660712 741858 761046 297089 522366 592540

a) 71      72    73    73     74     74     75     75     75     75
b) 575     115   110   482    263    513    138    313    365    552
c) 1078155 94211 81380 874120 405574 938613 136903 509522 620100 1020110

a) 75      75      76    76     76     77    78   78     78     78
b) 585     618     83    402    467    82    81   219    246    580
c) 1091051 1161797 17160 696982 835627 12870 8580 303355 360815 1073865

a) 79   79     79     80    80    80     81     81     82     82
b) 80   364    480    85    106   276    364    480    219    246
c) 4290 609388 856960 12870 57798 420290 605098 852670 294775 352235

a) 82      84     84     85     86    86     87     87     87     87
b) 580     402    467    461    106   276    267    310    359    376
c) 1065285 679822 818467 803517 44928 407420 386178 477412 581594 617812

a) 87     88     88      89    89     89     89     89     89     89
b) 382    424    639     119   178    179    192    236    316    621
c) 630630 718146 1178879 66287 192257 194389 222183 315913 485862 1138189

a) 90    90     92     92     92     92      93    93     94     95
b) 122   529    291    355    471    631     123   409    527    163
c) 70564 938613 426374 562380 809861 1153191 66287 675480 925769 147433

a) 95     95     95      95      95      96     96     96     97
b) 241    429    584     595     597     218    250    416    173
c) 313729 713843 1046045 1069679 1073969 262665 330785 683982 164489

a) 97     98     99     100    100    100    102    102    102    102
b) 322    408    296    257    436    485    287    295    370    520
c) 481494 662662 422006 337129 718094 822718 396513 413465 572923 893646

a) 102    102    104    104    104    105   105    105    105    106
b) 524    537    151    501    556    112   425    427    460    472
c) 902226 930098 102570 848588 966602 17108 683917 688181 758589 782054

a) 107    108    108    109   109    109    109    109    109    109
b) 276    247    248    140   210    226    268    272    497    531
c) 362492 298714 300846 68367 217815 251875 341237 349726 829283 902265

a) 109     110    110    110    111    112    112    112    113    113
b) 638     411    439    441    482    167    203    258    425    427
c) 1131819 643383 703092 707356 792740 119600 196482 313586 666809 671073

a) 113    114   114    114    114    115    117    117     118   118
b) 460    120   432    538    547    572    516    628     125   325
c) 741481 14963 679614 906581 925886 977483 852995 1093313 17108 442975

a) 118    118     119    119    119     120    120    120    120    120
b) 511    601     235    286    603     178    179    192    236    316
c) 840138 1033370 249639 358046 1035515 125970 128102 155896 249626 419575

a) 120     121    121    121    122    122    122     123    124    125
b) 621     432    538    547    324    386    630     529    409    184
c) 1071902 664651 891618 910923 432289 564343 1086904 868049 609193 128089

a) 125    125    125    126    126    126     127    127    127    127
b) 215    216    589    325    511    601     394    405    518    545
c) 194259 196391 992641 425867 823030 1016262 570765 594243 835900 893802

a) 128   128    128    128     129    129    130    130    131    131
b) 160   232    570    626     463    486    317    448    233    304
c) 70460 224016 945386 1065506 713674 762853 400309 679536 219726 370565

a) 132    132    132    132    133   133    133    133    134    134
b) 180    188    412    551    149   481    502    560    395    421
c) 104572 121680 598481 895986 36296 743574 788736 913198 557947 613392

a) 134     135  136    136    136    136    137    137    137    137
b) 605     137  373    450    455    594    373    450    455    594
c) 1007734 6396 506649 671008 681668 979888 504517 668876 679536 977756

a) 139    139    139    139    139     140    140     141    141    141
b) 313    365    552    585    618     410    608     210    226    268
c) 372619 483197 883207 954148 1024894 577161 1001364 149448 183508 272870

a) 141    141    141    141     142   142    143     144    144    144
b) 272    497    531    638     146   309    625     350    385    489
c) 281359 760916 833898 1063452 10686 357721 1031342 440609 515203 737282

a) 145    147    148    148    148    148     149    149    149    150
b) 517    309    384    526    568    633     237    579    602    481
c) 795314 347035 504517 808210 898378 1037790 189800 919880 969280 707278

a) 150    150    151   151    151    151    151    152    152    153
b) 502    560    185   212    327    343    573    501    556    230
c) 752440 876902 74698 132340 376727 410761 902720 746018 864032 166374

a) 153    154    154    154    154    155    155    156   156    156
b) 534    206    207    362    487    466    577    196   403    495
c) 814684 113152 115284 444769 711620 664560 902772 87542 528047 724568

a) 156    157   158    158    159    159    159    159    159    160
b) 500    187   273    530    260    368    369    390    550    177
c) 735332 66170 247169 795444 217438 446875 449007 493883 836199 38402

a) 160    160    161    161    161    162    162    163    163    163
b) 567    615    232    570    626    435    563    332    358    632
c) 870610 973622 153556 874926 995046 583492 857740 361751 417053 1003626

a) 164    164    164    164    164    165    165    165    165    165
b) 241    429    584    595    597    220    240    393    465    565
c) 166296 566410 898612 922246 926536 119496 162032 487487 641082 855634

a) 165    166   166   166    167   167    168   168    169    169
b) 613    195   205   301    204   422    203   258    298    477
c) 958672 64064 85410 289471 81146 545077 76882 193986 276705 658164

a) 170    170    170     171    171    171    172   172    172    172
b) 239    430    642     398    492    508    217   245    271    399
c) 149240 555750 1010100 485381 686114 720512 98176 157768 213057 485381

a) 172    172    173    173    173    174    175  175    175    175
b) 532    539    293    380    549    322    176  366    381    499
c) 769860 784862 257569 442611 804180 317005 4264 408473 440479 692640

a) 175    176    176    176    176    177    177    177    177    178
b) 598    284    334    360    576    366    381    499    598    567
c) 905216 232089 338273 393575 855816 404209 436215 688376 900952 832208

a) 178    179   179    179    179    180   180    180    180    181
b) 615    192   236    316    621    192   236    316    621    188
c) 935220 29926 123656 293605 945932 27794 121524 291473 943800 17108

a) 181    181    182    182    183    183    184    184    185   185
b) 412    551    275    533    498    644    290    478    215   216
c) 493909 791414 200213 750672 673426 986648 227747 628303 66170 68302

a) 185    186   186    186    186    187  187    187    189    189
b) 589    212   327    343    573    190  420    609    412    551
c) 864552 57642 302029 336063 828022 8554 498121 903162 476801 774306

a) 190   190    191    191    192    192    192    192    192    193
b) 200   553    420    609    314    528    548    607    614    236
c) 23504 776464 489567 894608 261573 718562 761449 888186 903162 93730

a) 193    193    194    194    195    195    195    195    196   196
b) 316    621    302    338    279    288    392    490    205   301
c) 263679 916006 231803 308321 180895 199979 421291 630539 21346 225407

a) 197    197    197    198    198    199    199    199    199    199
b) 403    495    500    265    469    256    303    459    507    512
c) 440505 637026 647790 144781 579150 123526 223249 555672 658554 669292

a) 199    200    201    202    203   203    203    204    205    206
b) 611    407    553    363    242   283    506    258    422    301
c) 881790 442637 752960 344409 85150 172289 647868 117104 463931 204061

a) 207    207    208    208    209    210    210    210    211   211
b) 362    487    362    487    397    315    348    575    226   268
c) 331617 598468 329485 596336 402103 225277 295451 781066 34060 123422

a) 211    211    211    211    212    212    212    212    213    213
b) 272    497    531    638    307    318    349    377    327    343
c) 131911 611468 684450 914004 204035 227383 293319 352937 244387 278421

a) 213    214   214   214    214    214    214    215    215    216
b) 573    227   253   270    557    596    640    319    372    589
c) 770380 29796 85163 121277 733850 817674 911898 223119 335881 798382

a) 217    218   218    218    218    218    219   219    220   220
b) 589    245   271    399    532    539    250   416    246   580
c) 796250 59592 114881 387205 671684 686686 68120 421317 57460 770510

a) 221   221    221    221    221    222   222   222    223    224
b) 240   393    465    565    613    234   243   555    624    321
c) 42536 367991 521586 736138 839176 27638 46800 712504 858468 208195

a) 224    224    225    226   226    226    227   227   227    227
b) 391    475    510    244   330    645    268   272   497    531
c) 357331 536536 609596 40430 223093 897052 89362 97851 577408 650390

a) 227    228   228   228    228    228    230   230    230    230
b) 638    253   270   557    596    640    252   285    379    417
c) 879944 55367 91481 704054 787878 882102 48984 119041 318903 400049

a) 230    231    232    232    232    233    233    234    235   235
b) 426    534    444    536    612    570    626    304    243   555
c) 419237 648310 453388 650468 813644 721370 841490 150839 19162 684866

a) 236    236    237    237    238    238    239    239    240    240
b) 286    603    316    621    579    602    346    431    430    642
c) 108407 785876 169949 822276 730080 779480 229489 410774 406510 860860

a) 241    241    241    241    242    242    242    242    243   243
b) 393    465    565    613    429    584    595    597    283   506
c) 325455 479050 693602 796640 400114 732316 755950 760240 87139 562718

a) 244    245    245    246   246    246    246    247    250   250
b) 555    330    645    271   399    532    539    580    255   586
c) 665704 182663 856622 55289 327613 612092 627094 713050 12779 719550

a) 251    252   252    253   253    253    253    254   254    254
b) 416    264   352    285   379    417    426    270   557    596
c) 353197 27638 214539 70057 269919 351065 370253 36114 648687 732511

a) 254    255    255    255    255    255    255    255    256    257
b) 640    312    353    521    523    559    581    627    586    303
c) 826735 123097 210275 569322 573612 650858 698152 796770 706771 99723

a) 257    257    257    257    258    258    260    261    261    261
b) 459    507    512    611    436    485    571    368    369    390
c) 432146 535028 545766 758264 380965 485589 666029 229437 231569 276445

a) 261    262    262    263   263   263    264    265    266    267
b) 550    442    588    269   299   446    513    352    469    297
c) 618761 385255 698321 14859 78481 391664 533039 186901 434369 65741

a) 268   268    268    268    269  269    269    269    270   270
b) 310   359    376    382    272  497    531    638    299   446
c) 91234 195416 231634 244452 8489 488046 561028 790582 63622 376805

a) 271    271    271    272    272    272    273    273    273    274
b) 557    596    640    399    532    539    497    531    638    530
c) 612573 696397 790621 272324 556803 571805 479557 552539 782093 548275

a) 275   275    275    276    278    280   280    280    281   281
b) 281   331    590    533    383    288   392    490    300   413
c) 14846 121004 675025 550459 225368 19084 240396 449644 42406 283088

a) 281    281    281    282    282    283    283    284    285    285
b) 473    522    643    331    590    367    470    506    334    360
c) 411073 516269 775827 106158 660179 180622 400439 475579 106184 161486

a) 285    286    286    286    287    288   288    288    288    288
b) 576    379    417    426    603    295   370    520    524    537
c) 623727 199862 281008 300196 677469 16952 176410 497133 505713 533585

a) 289    289    290    290    290    291    292    292    292    293
b) 392    490    456    458    564    478    355    471    631    326
c) 221312 430560 355719 359983 587327 400556 136006 383487 726817 72202

a) 293    293    293    294    294    295   295    295    295    296
b) 342    504    569    380    549    337   428    445    509    370
c) 106236 452205 591721 185042 546611 91364 285389 321659 458705 159458

a) 296    296    296    299    300    301    301    301    301    303
b) 520    524    537    477    446    413    473    522    643    338
c) 480181 488761 516633 381459 313183 240682 368667 473863 733421 76518

a) 304    304    304    304    306   306    306    306    307    307
b) 459    507    512    611    323   356    592    617    464    622
c) 332423 435305 446043 658541 38220 108420 613561 667121 336713 675701

a) 308   308   308    309   309   311    311    311    312    312
b) 318   349   377    328   344   359    376    382    361    449
c) 23348 89284 148902 42484 76518 104182 140400 153218 106314 294099

a) 312    312    313   313    313    313    313    313    314    314
b) 546    574    353   521    523    559    581    627    365    552
c) 501956 562133 87178 446225 450515 527761 575055 673673 110578 510588

a) 314    314    315    315    315    315    316   316    317    318
b) 585    618    528    548    607    614    348   575    621    448
c) 581529 652275 456989 499876 626613 641589 70174 555789 652327 279227

a) 319   319    320    321   321    321    321    322    322    324
b) 349   377    372    347   419    599    636    391    475    356
c) 65936 125554 112762 57434 210990 596739 675961 149136 328341 70200

a) 324    324    325    325    326    326    327   327    327    328
b) 592    617    386    630    511    601    342   504    569    343
c) 575341 628901 132054 654615 397163 590395 34034 380003 519519 34034

a) 328    329   330   330    330    331    332    333   333    334
b) 573    344   345   415    488    645    590    358   632    434
c) 525993 34034 34034 183326 339196 673959 554021 55302 641875 215345

a) 334    334    335   335    336   336    336    336    336    337
b) 582    629    360   576    340   389    400    443    503    388
c) 532571 633321 55302 517543 10634 115076 138580 230282 358709 110812

a) 337    338    338    338    340    341    341    341    341    343
b) 496    428    445    509    634    389    400    443    503    504
c) 341523 194025 230295 367341 631267 104442 127946 219648 348075 345969

a) 343    344    346    346    347    348    348    348    349    350
b) 569    573    415    488    431    419    599    636    575    377
c) 485485 491959 149292 305162 181285 153556 539305 618527 485615 59618

a) 351   351    352    352    352    354    354    354    354    354
b) 385   489    414    514    535    521    523    559    581    627
c) 74594 296673 134394 348283 393315 359047 363337 440583 487877 586495

a) 356    356    357    357    358    358    359    360   360   361
b) 471    631    592    617    447    562    632    376   382   576
c) 247481 590811 505141 558701 192023 438529 586573 36218 49036 462241

a) 362    362    362    363    365    366    366    366    367   367
b) 449    546    574    487    480    552    585    618    381   499
c) 187785 395642 455819 266851 247572 400010 470951 541697 32006 284167

a) 367    368    369   369    370   370    371    371    371    372
b) 598    470    390   550    390   550    520    524    537    541
c) 496743 219817 47008 389324 44876 387192 320723 329303 357175 363623

a) 372    374    374    374    375    375    375    376    376    376
b) 544    450    455    594    451    454    494    423    484    591
c) 370058 164359 175019 473239 164359 170755 256347 102479 232700 462527

a) 377   380   380    381    382    382    385    385    385    386
b) 382   417   426    549    499    598    526    568    633    489
c) 12818 81146 100334 361569 252161 464737 303693 393861 533273 222079

a) 387    388    389    390   390    390    391    392    393    394
b) 630    440    496    400   443    503    550    475    490    465
c) 522561 113087 230711 23504 115206 243633 342316 179205 209248 153595

a) 394    394    395   395    395    396   396    397    397    399
b) 565    613    405   518    545    421   605    566    578    492
c) 368147 471185 23478 265135 323037 55445 449787 363883 389675 200733

a) 399    400    400    401   401    402    402    402    403    404
b) 508    532    539    443   503    491    561    620    467    495
c) 235131 284479 299481 91702 220129 192179 342459 469079 138645 196521

a) 404    405    406    406    407    407    411    412   412   413
b) 500    610    518    545    457    505    608    439   441   551
c) 207285 441285 241657 299559 108771 211627 424203 59709 63973 297505

a) 414    414    414    415    415    416    418   419    420    420
b) 473    522    643    514    535    488    426   604    599    636
c) 127985 233181 492739 213889 258921 155870 19188 398593 385749 464971

a) 421    422    424    424    425    426  426   428   429   429    430
b) 609    605    484    591    639    427  460   460   445   509    584
c) 405041 394342 130221 360048 460733 4264 74672 70408 36270 173316 332202

a) 430    430    431    433    433    434    434    434    435    435
b) 595    597    642    538    547    483    623    637    582    629
c) 355836 360126 454350 226967 246272 106730 407264 437242 317226 417976

a) 436    437    440  443    444    445    445    446    448    450
b) 563    485    441  588    503    536    612    509    562    546
c) 274248 104624 4264 313066 128427 197080 360256 137046 246506 207857

a) 450    451   451    452  452   453   453    453    454   454    454
b) 574    455   594    454  494   474   600    646    474   600    646
c) 268034 10660 308880 6396 91988 46930 317486 415974 44798 315354 413842

a) 455   456    457  457    458    459    460    460    460    463
b) 494   594    458  564    505    564    507    512    611    593
c) 85592 298220 4264 231608 102856 227344 102882 113620 326118 281138

a) 464   465    466    466    467    469    469    472    474    474
b) 486   622    565    613    577    542    543    631    522    643
c) 49179 338988 214552 317590 238212 158743 160888 343330 105196 364754

a) 475    475    477    480    482   482    484    484    485    492
b) 600    646    587    641    502   560    623    637    591    561
c) 270556 369044 238368 347646 45162 169624 300534 330512 229827 150280

a) 492    493   494   496   498   498    499    500    502    503
b) 620    508   515   500   531   638    644    598    556    560
c) 276900 34398 47268 10764 72982 302536 313222 212576 118014 124462

a) 505    508   508    512    513    515   517    519   520    521  521
b) 569    512   611    601    611    535   628    545   616    524  537
c) 139516 10738 223236 193232 212498 45032 240318 57902 208182 8580 36452

a) 522  522   522    522    523    524   524    524    525   527   527
b) 523  559   581    627    643    559   581    627    537   568   633
c) 4290 81536 128830 227448 259558 77246 124540 223158 27872 90168 229580

a) 529   529    529    532    533   537    539   541   542  547   549
b) 548   607    614    638    539   612    547   558   544  574   607
c) 42887 169624 184600 229554 15002 163176 19305 38649 6435 60177 126737

a) 549    553   553    555    558   558    560   560    562    566
b) 614    585   618    619    596   640    581   627    620    613
c) 141713 70941 141687 139529 83824 178048 47294 145912 126620 103038

a) 567   568    569    571    580   582   583    585   585   586   593
b) 578   615    633    626    602   627   629    595   597   618   617
c) 25792 103012 139412 120120 49400 98618 100750 23634 27924 70746 53560

a) 596  597   600   601   608   624
b) 597  640   636   646   614   637
c) 4290 94224 79222 98488 14976 29978

a) Start position of group 1 is from the beginning, and of group 2 is from the end.
b) End position of group 1 is from the beginning, and of group 2 is from the end.
c) Total of both groups.

Total of the start and end positions (a + b): 787157 = 7 x 139 x 809.

6.11.1Take every Nth from the list in feature 6.10. 94 values of N produce multiples of 7.

2 9 20 23 38 44 46 50 53 61 63 66 81 98 107 110 121 128 131 144 165 176 181 185 186 191 195 196 211 218 229 233 238 244 246 261 265 267 273 287 289 296 303 305 307 313 326 330 356 360 363 364 365 378 385 394 399 403 406 409 412 415 419 436 456 462 463 467 468 472 486 499 504 512 513 532 540 541 550 551 558 564 565 566 567 572 581 583 606 618 626 633 638 644

Total of the N values: 30912 = 2⁶ x 3 x 7 x 23.

6.11.2Take every Nth from the list in feature 6.10. 11 values of N produce multiples of 91.

46 98 128 131 144 186 394 412 513 565 638

Total of the N values: 3255 = 3 x 5 x 7 x 31.

6.12Divide the letters in feature 6.10 into four groups.

Odd positioned in the list and odd valued.
Even positioned in the list and odd valued.
Odd positioned in the list and even valued.
Even positioned in the list and even valued.

Groups A and D are both odd, or both even in position and value. Their total: 947793 = 3 x 7 x 11² x 373.

6.13.1195 of these positions are prime numbers. (195 = 3 x 5 x 13. SF: 21 = 3 x 7.)

6.13.2210 (2 x 3 x 5 x 7) of these positions in the list of 6.10 are in prime positions.

6.13.31083 of these positions in the list of 6.10 are not in prime positions. Their total: 1176864 = 2⁵ x 3 x 13 x 23 x 41.

6.14176 of the positions listed in 6.10 are multiples of 7. Their total yields extra factors of 7: 190365 = 3 x 5 x 7³ x 37.

6.15.1The middle N positions in 6.10 are a multiple of 7 when N is one of the following:

1289 1281 1271 1259 1257 1255 1253 1251 1249 1247 1245 1233 1213 1199 1193 1177 1165 1157 1143 1133 1125 1111 1099 1089 1083 1077 1063 1061 1053 1045 1041 1029 1021 997 981 963 957 951 947 941 903 881 869 867 865 855 829 789 781 775 743 735 725 713 701 691 677 667 657 615 583 557 549 521 515 485 481 477 467 455 451 439 417 409 407 405 369 355 349 341 333 299 297 281 271 251 239 231 229 227 225 223 217 203 195 175 171 165 161 151 143 113 103 95 65 25 5 3 1

Total of the N values: 74571 = 3 x 7 x 53 x 67. SF: 130 = 2 x 5 x 13.

6.15.2The middle N positions in 6.10 are divisible by 13 when N is one of the following:

1255 1167 1143 1135 1127 1123 1103 1081 999 983 951 901 859 857 817 803 795 793 783 751 741 683 647 623 613 601 581 525 515 495 493 491 489 487 485 461 431 407 359 311 303 293 287 241 229 215 213 177 171 157 121 109 73 59 53 27

Total of the N values: 32592 = 2⁴ x 3 x 7 x 97.

6.16The first position in 6.10 is 2, an even number. Search through the list of positions for the next odd number, and continue alternating between even and odd. This selects 1277 positions. The total of these positions: 1367744 = 2⁶ x 7 x 43 x 71. SF: 133 = 7 x 19. SF: 26 = 2 x 13.

All The Letters

7Now all the letters are considered together.

All told, there are 2157 letters.

7.13446 paired groups of letters, positioned Nth and Nth last, are together and individually divisible by 13.

a) 1     1     1     1     1      1      2     2     2     2     2
b) 349   356   388   404   957    1038   84    86    435   459   562
c) 49348 51038 55575 58084 136851 146250 12987 13247 64467 67262 81484

a) 2      2      3    3     3     3     3     3     3     3      3
b) 998    1063   45   102   210   273   299   368   558   881    908
c) 142077 150566 6097 14417 30615 37700 39923 52793 80964 126399 131729

a) 3      4   4     4     4     4     4      4      5     5     5
b) 1045   13  272   280   632   693   859    953    253   264   302
c) 147303 949 37401 38064 90753 98618 123370 136032 35802 36608 40911

a) 5     5     5      5      6     6     6     6     6      6      7
b) 444   472   860    1041   78    161   341   679   743    937    613
c) 65273 67860 123370 146016 12142 22308 47216 96629 105755 134797 87776

a) 7     8    8     8     8      8      8      9     9     9     9
b) 685   37   158   266   823    1065   1069   155   300   347   455
c) 98007 4290 21398 36530 117546 150124 150475 20852 39832 47905 66170

a) 10    10    10    10     11    11    11     11     12    12    12
b) 454   507   647   749    184   494   728    750    515   546   720
c) 66027 72566 92729 106353 26247 70967 104169 106444 73840 78689 101140

a) 12     12     12     12     12     12     12     12     12     13
b) 741    845    869    871    906    910    978    1026   1075   39
c) 104923 121225 123643 124163 130286 131014 138957 143897 151346 3835

a) 13    13    13    13     13     13     14    14    14    14    14
b) 104   337   516   766    952    1023   272   280   632   693   859
c) 13546 45890 73645 109681 135135 143403 36452 37115 89804 97669 122421

a) 14     15    15    15    15     15     16    16    16     16     17
b) 953    376   382   551   757    945    370   417   895    935    139
c) 135083 51740 52741 78052 107042 134147 50973 60606 126646 133146 16692

a) 17    17    17    17    17     18    18    18    18    18    18
b) 245   390   640   684   837    215   335   353   513   581   828
c) 33540 54171 90844 95862 118274 30433 44837 48607 72449 82004 117260

a) 18     18     19   19    19    19     19     20    20    20    20
b) 933    1043   26   351   663   759    852    150   250   678   841
c) 132730 145210 1508 47892 92586 107757 120666 17563 33631 94458 118872

a) 21   21    21    22    22    22     22     23    23    23    23
b) 40   278   410   533   612   831    900    456   482   569   772
c) 2704 35945 58331 75140 84682 117143 127530 63856 66274 79833 108459

a) 23     23     24   24    24    24    24     24     24     24     24
b) 1049   1051   71   152   324   709   724    802    966    1014   1021
c) 145002 145353 8073 17212 41457 97396 100165 112138 134732 140569 141141

a) 25    25    25    25     25     26    26    26    26     26     26
b) 270   352   440   1035   1040   221   345   575   857    887    985
c) 34177 46553 61737 142480 142870 29302 44928 79508 120042 123955 136838

a) 26     27    27    27     27     28    28    28    28    28    28
b) 1068   351   663   759    852    95    224   284   316   550   736
c) 147524 46384 91078 106249 119158 10244 29926 34944 39897 76167 101829

a) 28     29    29     29     30    30    30    30    30    30     30
b) 1002   477   902    994    128   330   340   402   481   807    1016
c) 138827 64805 126282 137228 13897 42536 43615 54223 65533 112515 140257

a) 31    31    31    31    32    32     32     32     33    33    33
b) 182   193   387   596   457   789    821    1036   259   286   447
c) 23153 24635 51584 81692 62998 110149 113919 141934 32422 34541 61828

a) 33    33    33    33     33     34    34    34     35    35    35
b) 449   478   621   977    1070   179   192   808    145   700   776
c) 62127 64675 84903 135655 146926 22503 24115 112385 15145 95225 107471

a) 35     36    36    36    36     36     36     37   37    37    37
b) 917    168   227   263   818    833    876    74   111   177   212
c) 128557 19708 29354 32318 113373 115349 121446 6747 10790 21593 26754

a) 37    37    37     37     37     37     38    38    38     38
b) 576   687   822    853    984    991    158   266   823    1065
c) 78351 93899 113243 117975 135460 135863 17108 32240 113256 145834

a) 38     39    39    39    39    39    39     39     40   40    40
b) 1069   197   306   405   497   638   746    799    104  337   516
c) 146185 23777 37661 53781 67093 87659 102167 110162 9711 42055 69810

a) 40     40     40     41    41    42    42    42    42    42     43
b) 766    952    1023   278   410   384   471   657   661   894    137
c) 105846 131300 139568 33241 55627 49673 63063 89037 89570 123409 13325

a) 43    43    43    43    43     43     44    44    44    44    44
b) 231   298   377   629   882    1005   176   271   432   570   589
c) 29042 34853 48659 85605 121472 137605 20787 32383 59046 77649 79625

a) 44    44    44    44     45    45    45     45     45     46   46
b) 598   667   675   1077   170   597   854    888    919    102  210
c) 80977 89700 90922 147667 19448 80717 117923 122018 127569 8320 24518

a) 46    46    46    46    46     46     46     47    47    47    47
b) 273   299   368   558   881    908    1045   143   238   283   328
c) 31603 33826 46696 74867 120302 125632 141206 12636 28873 32292 39975

a) 47    47    47     47     47     47     47     48    48     48
b) 604   705   861    873    901    1022   1033   556   761    930
c) 80587 93977 117598 119405 123721 138281 139321 74516 103610 128037

a) 48     49   49    49    49    49    49    49     50   50    50
b) 1009   58   131   154   206   262   305   931    91   132   468
c) 136383 2548 11570 14846 23608 30290 36075 128115 6942 11440 61230

a) 50     50     50     50     50     51    51    51    51     51
b) 756    942    951    1031   1061   149   332   397   827    840
c) 101634 129064 129714 138723 143468 12519 39221 50557 111943 113880

a) 51     51     52    52    52    52     53    53    53    53     54
b) 874    927    357   697   729   897    488   592   662   1044   87
c) 118495 126568 43849 92079 97747 121797 62335 77285 86567 139243 5083

a) 54    54    54    54    54    55    55    55    55    55    55
b) 164   252   344   346   727   483   508   620   677   692   733
c) 15236 27872 40196 40378 96252 61061 65234 80548 88244 90597 96980

a) 55     55     56    56     56     57    57    57    57    57     57
b) 975    1053   248   891    898    203   493   495   637   814    928
c) 131339 140530 26962 119184 120445 20566 62894 63219 83733 108992 125307

a) 58   58    58    58    58    58    58     58     58     59   59
b) 94   317   378   420   469   525   795    825    1055   131  154
c) 4927 34697 44902 54054 59189 67080 105755 110032 140309 9022 12298

a) 59    59    59    59     60   60    60    60    60     61    61
b) 206   262   305   931    69   362   418   535   763    321   619
c) 21060 27742 33527 125567 1703 43238 53716 68640 101166 34970 79794

a) 61    61     61     61     62    62    62    62    62     62     62
b) 683   954    974    1029   311   503   519   627   768    858    896
c) 88582 127283 130546 135993 33865 64025 65923 80743 101855 114426 119977

a) 62     63    63    63    63     64    64    64    64    64    64
b) 1015   187   618   689   783    285   381   460   536   553   561
c) 134797 18980 79586 89661 103844 29081 44408 57655 68172 70499 71695

a) 64    64     64     65    65    65     65     65     65     65
b) 630   863    981    180   696   791    856    877    880    1052
c) 81133 114257 130377 17264 89453 104650 113854 116337 116688 138905

a) 65     66   66   66    66    66     66     66     67    67    67
b) 1054   97   117  416   722   850    916    1073   287   295   781
c) 139425 3926 5837 52117 93028 112216 122473 141609 28366 29471 102583

a) 67     67     67     67     68    68    69    69    69    69    69
b) 813    968    1004   1066   591   752   281   399   659   725   836
c) 107432 128349 132249 140439 74997 97136 27885 47372 83525 93587 109447

a) 69     70    70    70    70    71    71    72   72    72    72
b) 929    362   418   535   763   501   549   152  324   709   724
c) 123812 41535 52013 66937 99463 62270 68991 9139 33384 89323 92092

a) 72     72     72     72     73    73    73    73     74    74    74
b) 802    966    1014   1021   156   428   505   1034   365   473   475
c) 104065 126659 132496 133068 10192 52650 61854 134394 41080 56771 57044

a) 74    75   75    75    75    75    75     75     75     75     76
b) 568   111  177   212   576   687   822    853    984    991    109
c) 71136 4043 14846 20007 71604 87152 106496 111228 128713 129116 3926

a) 76    76    76    76    76    76    76     77    77    77    77
b) 225   339   407   624   634   737   1067   318   331   474   527
c) 22048 35815 48490 77584 79612 93951 139360 31824 34476 56407 64246

a) 77    77     77     77     77     78    78    78    78    78     78
b) 745   796    961    1011   1047   274   538   714   726   787    1072
c) 94627 102882 125554 131248 135876 26247 66300 89232 92365 102323 139945

a) 79    79    79    79    79     80    80    80    80    80    80
b) 161   341   679   743   937    174   294   361   554   557   753
c) 10166 35074 84487 93613 122655 12870 27170 39533 67496 68341 94965

a) 81   82    82    82    82    82    82    82    82     83    83
b) 103  277   369   409   412   499   510   649   806    301   367
c) 2002 25311 40014 47684 48529 59436 60944 80730 103376 27651 39858

a) 83    83    83     83     84    84    84    84    84    84    84
b) 434   567   846    955    354   373   398   526   579   669   839
c) 51506 69576 109213 123526 37752 40222 44902 63141 70928 82082 107900

a) 85  85    85    85    85     85     86   86    86    86     86
b) 86  435   459   562   998    1063   101  646   769   905    1001
c) 260 51480 54275 68497 129090 137579 1300 80314 98111 117871 129259

a) 87    87    87    87     87     88    88    88    88    88    89
b) 435   459   562   998    1063   164   252   344   346   727   122
c) 51220 54015 68237 128830 137319 10153 22789 35113 35295 91169 3159

a) 89    89    89    89    89    90   90    90    90     91  91    91
b) 461   523   544   586   710   108  441   754   872    92  336   364
c) 53950 62439 65585 71435 87451 2080 51857 94211 111605 273 33501 39065

a) 91    91    91    91    91     91     92   92    92    92     92
b) 521   636   670   702   794    886    132  468   756   942    951
c) 61984 78416 81679 86424 101101 113737 4498 54288 94692 122122 122772

a) 92     92     93    93    93    93    93    93    93     93     94
b) 1031   1061   336   364   521   636   670   702   794    886    269
c) 131781 136526 33228 38792 61711 78143 81406 86151 100828 113464 23764

a) 94    94    94    94    94     94     94     94     95    95    95
b) 429   453   489   666   820    988    990    1007   317   378   420
c) 50401 52858 57213 81120 104208 126672 126776 128921 29770 39975 49127

a) 95    95    95     95     95     96    96    96    96    96    96
b) 469   525   795    825    1055   224   284   316   550   736   1002
c) 54262 62153 100828 105105 135382 19682 24700 29653 65923 91585 128583

a) 97    97    97    97    97    97    97    97     97     97     98
b) 186   309   342   366   433   594   779   915    1008   1060   117
c) 14105 28886 33592 38675 50414 71383 98566 118547 128739 136019 1911

a) 98    98    98     98     98     99    99    99    99    99    99
b) 416   722   850    916    1073   202   358   360   411   625   711
c) 48191 89102 108290 118547 137683 14859 37531 37752 46917 74854 86450

a) 99     100  100   100   100   100    101   101    102   102   102
b) 844    118  490   571   626   972    260   1048   646   769   905
c) 107666 1859 56927 68614 74854 125177 22230 133497 79014 96811 116571

a) 102    103   103   103   103   103   103    103    103    105   105
b) 1001   210   273   299   368   558   881    908    1045   337   516
c) 127959 16198 23283 25506 38376 66547 111982 117312 132886 32344 60099

a) 105   105    105    106  106   106   106    106    106    107   107
b) 766   952    1023   124  565   588   838    899    932    235   279
c) 96135 121589 129857 1781 67600 70018 105950 114348 119782 19955 23491

a) 107   107   107   107   107   107    107    108  108   108   108
b) 322   355   446   512   713   920    1017   135  205   228   656
c) 29276 35958 50830 59397 86086 118196 129480 2769 14404 18421 78546

a) 108   108   108    108    108    109   109   109    110   110   110
b) 707   716   848    1000   1020   441   754   872    225   339   407
c) 84981 86060 106899 126789 128986 49777 92131 109525 18122 31889 44564

a) 110   110   110   110    111   111   111   111   111   111    111
b) 624   634   737   1067   219   242   256   415   742   911    1013
c) 73658 75686 90025 135434 17173 19760 20787 46163 90337 116428 127712

a) 111    111    111    112   112   112   112   112    112    112
b) 1018   1042   1058   177   212   576   687   822    853    984
c) 128830 131547 133744 10803 15964 67561 83109 102453 107185 124670

a) 112    113 113   113   113   113   113   113   113   113    113
b) 991    115 201   282   343   408   504   601   628   805    811
c) 125073 325 13494 22815 32565 44642 57603 70928 74841 100529 101699

a) 113    113    113    114   114   114   114   115   115   115    115
b) 830    843    890    195   220   406   680   374   380   804    815
c) 103753 106301 112164 12909 17030 44187 81328 37440 38116 100009 102011

a) 115    116   116   116   116   116   116   116   116    116    116
b) 1050   201   282   343   408   504   601   628   805    811    830
c) 132444 13169 22490 32240 44317 57278 70603 74516 100204 101374 103428

a) 116    116    117   117   117   117   117   117   117    118   118
b) 843    890    232   289   585   602   690   703   904    416   722
c) 105976 111839 18135 22763 68328 70564 82784 83863 114738 46280 87191

a) 118    118    118    119   119   119   119    120    120    120
b) 850    916    1073   490   571   626   972    870    943    964
c) 106379 116636 135772 55068 66755 72995 123318 108329 119418 121342

a) 120    120    121  121   121   121   121    121    121    122   122
b) 1039   1074   151  574   642   645   879    912    939    226   389
c) 129961 135642 4017 66573 76544 76908 109915 115661 118963 17225 39494

a) 122   122   122   122   122   122   122   122   123   123   123
b) 391   427   486   583   641   698   738   803   461   523   544
c) 39884 47528 53833 67678 76492 83044 89154 99190 50791 59280 62426

a) 123   123   124  124   124   124   124    124    125   125   125
b) 586   710   144  218   500   664   963    995    565   588   838
c) 68276 84292 2418 16263 55900 78312 121134 124618 65819 68237 104169

a) 125    125    126   126   126   126    127   127   127   127   127
b) 899    932    200   671   784   986    199   338   470   517   532
c) 112567 118001 11570 78325 95719 122954 11375 29653 50531 57252 59527

a) 127   127   127   127   127    128 128  128   128   128   128   128
b) 599   676   777   798   996    129 175  288   414   487   529   682
c) 68744 78884 94367 97526 124228 156 8476 21190 44057 52689 58526 79833

a) 128    129   129   129   129   129   129    130  130   130   130
b) 973    330   340   402   481   807   1016   175  288   414   487
c) 121927 28639 29718 40326 51636 98618 126360 8320 21034 43901 52533

a) 130   130   130    131   131   131   131    131    132  132   132
b) 529   682   973    308   660   767   962    970    154  206   262
c) 58370 79677 121771 25012 76661 93145 119665 121017 3276 12038 18720

a) 132   132    133   133   133    133    133    133    134   134   134
b) 305   931    468   756   942    951    1031   1061   254   450   788
c) 24505 116545 49790 90194 117624 118274 127283 132028 18018 48256 96109

a) 134   134    135    136   136   136   136   136   136    136    136
b) 809   948    959    205   228   656   707   716   848    1000   1020
c) 98553 118040 118963 11635 15652 75777 82212 83291 104130 124020 126217

a) 137   137    138   138   138   138   138    138    139   139   139
b) 706   1057   231   298   377   629   882    1005   229   247   297
c) 82017 131014 15717 21528 35334 72280 108147 124280 15457 17056 21398

a) 139   139   139    139    140   140   140   140   140    141   141
b) 578   699   1027   1064   245   390   640   684   837    241   304
c) 65351 81016 126269 132093 16848 37479 74152 79170 101582 16731 23101

a) 141   141   141    141    141    142   142   142   142   142    143
b) 438   480   875    960    1006   222   234   292   732   976    319
c) 46280 50466 107341 118534 124085 14196 16055 21086 86541 121095 25155

a) 143   143    144   144   144   144   144   144    144    144    144
b) 528   883    238   283   328   604   705   861    873    901    1022
c) 57382 107822 16237 19656 27339 67951 81341 104962 106769 111085 125645

a) 144    145   145   145   145    145    146   146   146    147   147
b) 1033   218   500   664   963    995    700   776   917    211   217
c) 126685 13845 53482 75894 118716 122200 80080 92326 113412 11362 13221

a) 147   147   147   147    148   148   148   148   148    149   149
b) 479   566   730   1046   448   555   715   817   987    371   509
c) 49452 62933 85618 128180 46514 61295 81991 98345 120926 33397 54080

a) 149    150   150   150   150    150    150    151   151   151    152
b) 868    332   397   827   840    874    927    250   678   841    574
c) 104832 26702 38038 99424 101361 105976 114049 16068 76895 101309 62556

a) 152   152   152    152    152    153   153   153   153   153    153
b) 642   645   879    912    939    324   709   724   802   966    1014
c) 72527 72891 105898 111644 114946 24245 80184 82953 94926 117520 123357

a) 153    154 154   154    154    155  155   155   155    156   156
b) 1021   160 832   903    989    206  262   305   931    300   347
c) 123929 910 98592 108979 119379 8762 15444 21229 113269 18980 27053

a) 156   157   157   157    158   158   158   159   159   159    159
b) 455   428   505   1034   261   359   511   266   823   1065   1069
c) 45318 42458 51662 124202 14794 30043 52104 15132 96148 128726 129077

a) 160   160   160   160   160   160    161   161    161    162   162
b) 239   350   605   658   731   926    832   903    989    341   679
c) 13065 27872 64740 72033 83070 111670 97682 108069 118469 24908 74321

a) 162   162    163  163  163  163   163   163   163   163   163   164
b) 743   937    167  209  213  293   419   524   530   547   708   329
c) 83447 112489 1391 7891 8931 17043 40066 53183 54210 56979 77805 22919

a) 164   164   164   164   164   164   164   164    165   165   165
b) 372   540   545   609   631   782   812   889    252   344   346
c) 29653 55068 55588 63596 67600 89583 94328 104312 12636 24960 25142

a) 165   166   166   166   166   167   167   167   167   167    167
b) 727   464   800   810   864   717   773   780   792   907    1071
c) 81016 43433 91247 93301 99944 77441 87399 88608 90337 107627 127634

a) 168  168  168   168   168   168   168   168   169  169   169   169
b) 209  213  293   419   524   530   547   708   227  263   818   833
c) 6500 7540 15652 38675 51792 52819 55588 76414 9646 12610 93665 95641

a) 169    170  170   170   170    171   171   171    171    172   172
b) 876    233  552   744   1028   597   854   888    919    312   734
c) 101738 9555 55120 81406 119977 61269 98475 102570 108121 18070 80340

a) 172    173   173   173   173   173   174   174   174   175   175
b) 946    563   577   614   673   770   290   615   816   294   361
c) 111111 56316 58565 63128 70811 86060 14144 62933 92430 14300 26663

a) 175   175   175   176   176   176   176   176   176    177   177
b) 554   557   753   288   414   487   529   682   973    271   432
c) 54626 55471 82095 12714 35581 44213 50050 71357 113451 11596 38259

a) 177   177   177   177   177   177    178  178   178   178   178
b) 570   589   598   667   675   1077   212  576   687   822   853
c) 56862 58838 60190 68913 70135 126880 5161 56758 72306 91650 96382

a) 178    178    179  179   179   179   179   179   179   179   179
b) 984    991    244  268   394   423   606   635   652   790   941
c) 113867 114270 8840 10894 30511 36985 60307 65234 67236 87776 108875

a) 179    180  180   181   181   181   181   181   181    181    182
b) 1019   192  808   696   791   856   877   880   1052   1054   243
c) 117884 1612 89882 72189 87386 96590 99073 99424 121641 122161 8333

a) 182   182   182   182   182   182   182   182    182    183  183
b) 363   559   573   623   644   651   793   909    944    193  387
c) 25415 53976 55978 62127 66131 66716 87516 104754 108784 1482 28431

a) 183   184   184   184   184   184   185   185   185   186   186
b) 596   431   543   610   681   849   494   728   750   303   426
c) 58539 37297 51584 59930 70252 95394 44720 77922 80197 13780 36218

a) 186   186   186   187   187   187   187   187   187   187    187
b) 465   639   775   309   342   366   433   594   779   915    1008
c) 39676 64883 84071 14781 19487 24570 36309 57278 84461 104442 114634

a) 187    188   188   188   189    190   190   190   190   190    191
b) 1060   618   689   783   967    463   485   751   778   936    396
c) 121914 60606 70681 84864 110344 39078 41405 79118 83707 106808 29055

a) 191   191   191   191    192   192   192   192   192    193   194
b) 564   701   704   1025   383   491   622   686   949    808   387
c) 53898 71500 71890 116363 26390 43212 60814 70317 107861 88270 26949

a) 194   195  195   195   195   195    196  196   196   197   197   197
b) 596   275  386   593   655   925    220  406   680   379   458   531
c) 57057 9503 26819 56719 65273 104975 4121 31278 68419 25155 38402 48256

a) 197    198   198   198   198   198   198   199   199   199   199
b) 1030   306   405   497   638   746   799   425   442   603   654
c) 116376 13884 30004 43316 63882 78390 86385 35048 36478 57928 65039

a) 200   200   200   200   200   200   200   200   200    201   201
b) 338   470   517   532   599   676   777   798   996    671   784
c) 18278 39156 45877 48152 57369 67509 82992 86151 112853 66755 84149

a) 201    202  202   202   202   202   202   202   202   202   202
b) 986    282  343   408   504   601   628   805   811   830   843
c) 111384 9321 19071 31148 44109 57434 61347 87035 88205 90259 92807

a) 202   203   203   203   203   203   203   204   204   204   204
b) 890   358   360   411   625   711   844   493   495   637   814
c) 98670 22672 22893 32058 59995 71591 92807 42328 42653 63167 88426

a) 204    205 205  205   205   206  206   206   206   206   206    206
b) 928    208 265  400   413   228  656   707   716   848   1000   1020
c) 104741 806 7202 28171 31668 4017 64142 70577 71656 92495 112385 114582

a) 207  207   207    208   208   208   208   209  209   209   210  210
b) 262  305   931    424   502   847   865   265  400   413   213  293
c) 6682 12467 104507 33501 42822 92001 93691 6396 27365 30862 1040 9152

a) 210   210   210   210   210   211  211  211   211   211   211    211
b) 419   524   530   547   708   273  299  368   558   881   908    1045
c) 32175 45292 46319 49088 69914 7085 9308 22178 50349 95784 101114 116688

a) 212  212   212   212   212    213   213   213   213   213    213
b) 217  479   566   730   1046   576   687   822   853   984    991
c) 1859 38090 51571 74256 116818 51597 67145 86489 91221 108706 109109

a) 214  214   214   214   214   214   215   215   215   215   215   216
b) 293  419   524   530   547   708   315   334   580   694   735   335
c) 8112 31135 44252 45279 48048 68874 11271 14495 51623 66768 73125 14404

a) 216   216   216   216   216    216    217   217    218   218   218
b) 353   513   581   828   933    1043   893   1056   479   566   730
c) 18174 42016 51571 86827 102297 114777 95641 116506 36231 49712 72397

a) 218    219   219   219    219    220  220  220   220   220   220
b) 1046   500   664   963    995    242  256  415   742   911   1013
c) 114959 39637 62049 104871 108355 2587 3614 28990 73164 99255 110539

a) 220    220    220    221   221   222   222   222   222   222    222
b) 1018   1042   1058   406   680   345   575   857   887   985    1068
c) 111657 114374 116571 27157 64298 15626 50206 90740 94653 107536 118222

a) 223  223  223   223    224   224   224   224   224   224    225  225
b) 234  292  732   976    326   421   542   740   760   983    284  316
c) 1859 6890 72345 106899 12441 29614 45097 72202 76544 106717 5018 9971

a) 225   225   225    226   226   226   226   226   226    227   227
b) 550   736   1002   339   407   624   634   737   1067   389   391
c) 46241 71903 108901 13767 26442 55536 57564 71903 117312 22269 22659

a) 227   227   227   227   227   227   227   228  228   228   228   229
b) 427   486   583   641   698   738   803   263  818   833   876   656
c) 30303 36608 50453 59267 65819 71929 81965 2964 84019 85995 92092 60125

a) 229   229   229   229    229    230  230  230   230   230    230
b) 707   716   848   1000   1020   247  297  578   699   1027   1064
c) 66560 67639 88478 108368 110565 1599 5941 49894 65559 110812 116636

a) 231  231   231   231   231    232  232   232   232   232    233  233
b) 276  392   476   758   938    298  377   629   882   1005   289  585
c) 4173 22386 34541 75179 101348 5811 19617 56563 92430 108563 4628 50193

a) 233   233   233   233   234   234   234    235  235   235    236
b) 602   690   703   904   552   744   1028   292  732   976    279
c) 52429 64649 65728 96603 45565 71851 110422 5031 70486 105040 3536

a) 236  236   236   236   236   236   236    237   237   237   237
b) 322  355   446   512   713   920   1017   587   719   755   785
c) 9321 16003 30875 39442 66131 98241 109525 49920 66950 72865 78871

a) 237    238   238   238   238   238    238    239  239   239   239
b) 940    492   518   548   914   956    1037   283  328   604   705
c) 100542 36621 39949 44785 97383 101738 111176 3419 11102 51714 65104

a) 239   239   239   239    239    240   240   240   240   240   242
b) 861   873   901   1022   1033   350   605   658   731   926   304
c) 88725 90532 94848 109408 110448 14807 51675 58968 70005 98605 6370

a) 242   242   242   242    242    243  243   243   243   243    243
b) 438   480   875   960    1006   256  415   742   911   1013   1018
c) 29549 33735 90610 101803 107354 1027 26403 70577 96668 107952 109070

a) 243    243    244   244   244   244   244   244   244   244   244
b) 1042   1058   363   559   573   623   644   651   793   909   944
c) 111787 113984 17082 45643 47645 53794 57798 58383 79183 96421 100451

a) 245  245   245   245   245   245   245   245    245    246   246
b) 268  394   423   606   635   652   790   941    1019   390   640
c) 2054 21671 28145 51467 56394 58396 78936 100035 109044 20631 57304

a) 246   246   247   247   247   247    248  248   248   248    248
b) 684   837   723   824   866   993    297  578   699   1027   1064
c) 62322 84734 67925 82784 88530 105248 4342 48295 63960 109213 115037

a) 249   249   250   250   251   251   252 252   252   252    252
b) 891   898   437   892   678   841   258 430   797   947    1012
c) 92222 93483 28886 92508 60827 85241 507 28275 79040 100152 107211

a) 253   253   253   254 254  254   254   254   254    255   255   255
b) 344   346   727   264 302  444   472   860   1041   450   788   809
c) 12324 12506 68380 806 5109 29471 32058 87568 110214 30238 78091 80535

a) 255    256   256   256   256   256    257   257   257   257    257
b) 948    333   672   826   885   979    415   742   911   1013   1018
c) 100022 10504 59683 82901 90753 103701 25376 69550 95641 106925 108043

a) 257    257    259   259   259   259    260  260   260   260   260
b) 1042   1058   430   797   947   1012   286  447   449   478   621
c) 110760 112957 27768 78533 99645 106704 2119 29406 29705 32253 52481

a) 260    260    261    262   262   263  263   264   264   264   265
b) 977    1070   1048   359   511   305  931   818   833   876   302
c) 103233 114504 111267 15249 37310 5785 97825 81055 83031 89128 4303

a) 265   265   265   265    266   266   267   267    267    268  268
b) 444   472   860   1041   400   413   823   1065   1069   323  395
c) 28665 31252 86762 109408 20969 24466 81016 113594 113945 7436 19942

a) 268   268   268    268    269   269   269   269   269   269   269
b) 653   801   1024   1059   394   423   606   635   652   790   941
c) 56472 77922 107328 112606 19617 26091 49413 54340 56342 76882 97981

a) 269    270   270   270   270   270   270    270    270    271   271
b) 1019   429   453   489   666   820   988    990    1007   352   440
c) 106990 26637 29094 33449 57356 80444 102908 103012 105157 12376 27560

a) 271    271    272   272   272   272   272   272   272    273 273
b) 1035   1040   432   570   589   598   667   675   1077   280 632
c) 108303 108693 26663 45266 47242 48594 57317 58539 115284 663 53352

a) 273   273   273   274  274   274   274   274   274    275   275
b) 693   859   953   299  368   558   881   908   1045   538   714
c) 61217 85969 98631 2223 15093 43264 88699 94029 109603 40053 62985

a) 275   275   275    276   276   276   276   277   277   277   277
b) 726   787   1072   386   593   655   925   392   476   758   938
c) 66118 76076 113698 17316 47216 55770 95472 18213 30368 71006 97175

a) 278   278   278   278   278   278   278   279   280  280   280   280
b) 369   409   412   499   510   649   806   410   322  355   446   512
c) 14703 22373 23218 34125 35633 55419 78065 22386 5785 12467 27339 35906

a) 280   280   280    281   281   281   281   282   282   282   282
b) 713   920   1017   632   693   859   953   399   659   725   836
c) 62595 94705 105989 52689 60554 85306 97968 19487 55640 65702 81562

a) 282   283  283   283   283   283   283   283   283   283   283   284
b) 929   343  408   504   601   628   805   811   830   843   890   328
c) 95927 9750 21827 34788 48113 52026 77714 78884 80938 83486 89349 7683

a) 284   284   284   284   284   284    284    285  285   285   285
b) 604   705   861   873   901   1022   1033   316  550   736   1002
c) 48295 61685 85306 87113 91429 105989 107029 4953 41223 66885 103883

a) 286   286   286   286   286   286   286   286    287   287   287
b) 381   460   536   553   561   630   863   981    447   449   478
c) 15327 28574 39091 41418 42614 52052 85176 101296 27287 27586 30134

a) 287   287    287    288  288   288   288   288    288    289   289
b) 621   977    1070   295  781   813   968   1004   1066   414   487
c) 50362 101114 112385 1105 74217 79066 99983 103883 112073 22867 31499

a) 289   289   289    290   290   290   290   290   291   291   293
b) 529   682   973    585   602   690   703   904   615   816   732
c) 37336 58643 100737 45565 47801 60021 61100 91975 48789 78286 65455

a) 293    294   294   294   294   294   295   295   295   295   296
b) 976    419   524   530   547   708   361   554   557   753   781
c) 100009 23023 36140 37167 39936 60762 12363 40326 41171 67795 73112

a) 296   296   296    296    297   297   297    298   298   298    298
b) 813   968   1004   1066   385   855   997    578   699   1027   1064
c) 77961 98878 102778 110968 15028 83577 102180 43953 59618 104871 110695

a) 299   299   299   299    300   300   300   300   300    301  301
b) 377   629   882   1005   368   558   881   908   1045   347  455
c) 13806 50752 86619 102752 12870 41041 86476 91806 107380 8073 26338

a) 302   302   302   302   302   303   303   303   303    304   304
b) 367   434   567   846   955   444   472   860   1041   426   465
c) 12207 23855 41925 81562 95875 24362 26949 82459 105105 22438 25896

a) 304   304   305   305   305   305   305    306   307   307   307
b) 639   775   438   480   875   960   1006   931   405   497   638
c) 51103 70291 23179 27365 84240 95433 100984 92040 16120 29432 49998

a) 307   307   308  308   308   308   308    309   309   309   309
b) 746   799   348  496   668   674   1078   660   767   962   970
c) 64506 72501 6435 29237 52234 53300 110305 51649 68133 94653 96005

a) 310  310  310   310   310   310   310   310    311   311   311   311
b) 342  366  433   594   779   915   1008  1060   403   467   520   718
c) 4706 9789 21528 42497 69680 89661 99853 107133 15041 24726 32227 58734

a) 311   311   311   312   312   312   312   312   312   312    313
b) 923   950   969   503   519   627   768   858   896   1015   734
c) 90532 93301 95732 30160 32058 46878 67990 80561 86112 100932 62270

a) 313   314   314   315   315   315   316  316   316   316   317   317
b) 946   422   466   607   633   924   334  580   694   735   550   736
c) 93041 20046 24232 43511 47645 90181 3224 40352 55497 61854 36270 61932

a) 317   318   318   318   318   318   318   318    319  319   319
b) 1002  378   420   469   525   795   825   1055   331  474   527
c) 98930 10205 19357 24492 32383 71058 75335 105612 2652 24583 32422

a) 319   319   319   319   319    320   320   321  321   321   321
b) 745   796   961   1011  1047   528   883   325  582   617   748
c) 62803 71058 93730 99424 104052 32227 82667 1183 39975 44733 63141

a) 321   321   322   322   322   322   322    323  323   323   323
b) 829   918   619   683   954   974   1029   355  446   512   713
c) 75231 88985 44824 53612 92313 95576 101023 6682 21554 30121 56810

a) 323   323    324   324   324   324   324    325   325   325   325
b) 920   1017   395   653   801   1024  1059   709   724   802   966
c) 88920 100204 12506 49036 70486 99892 105170 55939 58708 70681 93275

a) 325   325   326   326   326   326   326   327   327   327   327
b) 1014  1021  582   617   748   829   918   421   542   740   760
c) 99112 99684 38792 43550 61958 74048 87802 17173 32656 59761 64103

a) 327   328   328   328   328   328   329   329   329   329   329
b) 983   560   600   842   999   1032  604   705   861   873   901
c) 94276 35048 40443 75816 96200 99580 40612 54002 77623 79430 83746

a) 329   329   330  330   330   330   330   330   330   330   331  331
b) 1022  1033  372  540   545   609   631   782   812   889   340  402
c) 98306 99346 6734 32149 32669 40677 44681 66664 71409 81393 1079 11687

a) 331   331   331   332   332   332   332   332   332   332    333
b) 481   807   1016  474   527   745   796   961   1011  1047   397
c) 22997 69979 97721 21931 29770 60151 68406 91078 96772 101400 11336

a) 333   333   333   333   334   334   334   334   335   335   335
b) 827   840   874   927   672   826   885   979   580   694   735
c) 72722 74659 79274 87347 49179 72397 80249 93197 37128 52273 58630

a) 336  336   336   336   336   336    337  337   337   337   337   337
b) 353  513   581   828   933   1043   364  521   636   670   702   794
c) 3770 27612 37167 72423 87893 100373 5564 28483 44915 48178 52923 67600

a) 337   338   338   338   338   339   339   339   339   339   339
b) 886   516   766   952   1023  470   517   532   599   676   777
c) 80236 27755 63791 89245 97513 20878 27599 29874 39091 49231 64714

a) 339   339   340   340   340   340   340    341   341   341   341
b) 798   996   407   624   634   737   1067   402   481   807   1016
c) 67873 94575 12675 41769 43797 58136 103545 10608 21918 68900 96642

a) 342   342   342   343  343   343   343   343   343   343    344
b) 679   743   937   366  433   594   779   915   1008  1060   408
c) 49413 58539 87581 5083 16822 37791 64974 84955 95147 102427 12077

a) 344   344   344   344   344   344   344   344   345 345   346   346
b) 504   601   628   805   811   830   843   890   346 727   575   857
c) 25038 38363 42276 67964 69134 71188 73736 79599 182 56056 34580 75114

a) 346   346   346    347   348   349   349   349   349    350  350
b) 887   985   1068   727   455   496   668   674   1078   356  388
c) 79027 91910 102596 55874 18265 22802 45799 46865 103870 1690 6227

a) 350  350   350   351   351   351   351   352   352   352   353   353
b) 404  957   1038  605   658   731   926   663   759   852   440   1035
c) 8736 87503 96902 36868 44161 55198 83798 44694 59865 72774 15184 95927

a) 353   354   354   354   354   354   355  355  355   355   355   355
b) 1040  513   581   828   933   1043  373  398  526   579   669   839
c) 96317 23842 33397 68653 84123 96603 2470 7150 25389 33176 44330 70148

a) 356   356   356   356   356   357  357  357   357   358   358   358
b) 446   512   713   920   1017  388  404  957   1038  697   729   897
c) 14872 23439 50128 82238 93522 4537 7046 85813 95212 48230 53898 77948

a) 359 359  359   359   359   360   361  361   361   361   362   362
b) 360 411  625   711   844   511   411  625   711   844   554   557
c) 221 9386 37323 48919 70135 22061 9165 37102 48698 69914 27963 28808

a) 362   363   363   363   364   364   364   364   364   364   364
b) 753   418   535   763   559   573   623   644   651   793   909
c) 55432 10478 25402 57928 28561 30563 36712 40716 41301 62101 79339

a) 364   365   365   365   365   365   365   366   366   366   367
b) 944   521   636   670   702   794   886   473   475   568   433
c) 83369 22919 39351 42614 47359 62036 74672 15691 15964 30056 11739

a) 367   367   367   367   367   368   368   368   368   369   369
b) 594   779   915   1008  1060  434   567   846   955   558   881
c) 32708 59891 79872 90064 97344 11648 29718 69355 83668 28171 73606

a) 369   369   370  370  370   370   370   370   371  371   371   372
b) 908   1045  409  412  499   510   649   806   417  895   935   509
c) 78936 94510 7670 8515 19422 20930 40716 63362 9633 75673 82173 20683

a) 372   373   373   373   373   373   373   373   374  374   374   374
b) 868   540   545   609   631   782   812   889   398  526   579   669
c) 71435 25415 25935 33943 37947 59930 64675 74659 4680 22919 30706 41860

a) 374   375 375   375   375   376   376   376   376   376   377  377
b) 839   380 804   815   1050  522   595   688   1003  1062  382  551
c) 67678 676 62569 64571 95004 21905 31941 45240 88946 96941 1001 26312

a) 377   377   378   378   378   379  379   379   379   379   379   380
b) 757   945   629   882   1005  420  469   525   795   825   1055  458
c) 55302 82407 36946 72813 88946 9152 14287 22178 60853 65130 95407 13247

a) 380   380   381   381   381   382   382   382   382   382   382
b) 531   1030  804   815   1050  460   536   553   561   630   863
c) 23101 91221 61893 63895 94328 13247 23764 26091 27287 36725 69849

a) 382   383   383   383   384   384   384   384   385   385   385
b) 981   551   757   945   491   622   686   949   471   657   661
c) 85969 25311 54301 81406 16822 34424 43927 81471 13390 39364 39897

a) 385   386   386   387   387   387   388   389  389   389   390 390
b) 894   855   997   593   655   925   596   404  957   1038  391 427
c) 73736 68549 87152 29900 38454 78156 30108 2509 81276 90675 390 8034

a) 390   390   390   390   390   390   391   391   391   392  392   392
b) 486   583   641   698   738   803   640   684   837   427  486   583
c) 14339 28184 36998 43550 49660 59696 36673 41691 64103 7644 13949 27794

a) 392   392   392   392   393   393   393   394   394   394   395  395
b) 641   698   738   803   476   758   938   762   884   1010  423  606
c) 36608 43160 49270 59306 12155 52793 78962 53092 69823 86060 6474 29796

a) 395   395   395   395   395   396   396   396   396   397   397
b) 635   652   790   941   1019  653   801   1024  1059  564   701
c) 34723 36725 57265 78364 87373 36530 57980 87386 92664 24843 42445

a) 397   397   398   398   398   398   399   399   399   399   400
b) 704   1025  827   840   874   927   526   579   669   839   659
c) 42835 87308 61386 63323 67938 76011 18239 26026 37180 62998 36153

a) 400   400   400   401  402   402   402   402   402   402   403   403
b) 725   836   929   413  539   541   665   712   739   819   481   807
c) 46215 62075 76440 3497 20306 20566 36881 42887 47645 59969 11310 58292

a) 403   404  404   404   404   404   404   405   405   406   406   406
b) 1016  467  520   718   923   950   969   957   1038  497   638   746
c) 86034 9685 17186 43693 75491 78260 80691 78767 88166 13312 33878 48386

a) 406   407   408   408   408   408   409   409   409   409   409
b) 799   680   624   634   737   1067  504   601   628   805   811
c) 56381 37141 29094 31122 45461 90870 12961 26286 30199 55887 57057

a) 409   409   409   410 410   410   410   410   412   412   412   413
b) 830   843   890   412 499   510   649   806   625   711   844   499
c) 59111 61659 67522 845 11752 13260 33046 55692 27937 39533 60749 10907

a) 413   413   413   415  415   415   415   416   416   416   416   416
b) 510   649   806   487  529   682   973   742   911   1013  1018  1042
c) 12415 32201 54847 8632 14469 35776 77870 44174 70265 81549 82667 85384

a) 416   417   417   417   417   418   418   419   419   420   420
b) 1058  722   850   916   1073  895   935   535   763   524   530
c) 87581 40911 60099 70356 89492 66040 72540 14924 47450 13117 14144

a) 420   420   421  421   421   421   421   422   422   422   422   423
b) 547   708   469  525   795   825   1055  542   740   760   983   466
c) 16913 37739 5135 13026 51701 55978 86255 15483 42588 46930 77103 4186

a) 424   424   424   424   424   424   425  425   425   426  426   426
b) 606   635   652   790   941   1019  502  847   865   442  603   654
c) 23322 28249 30251 50791 71890 80899 9321 58500 60190 1430 22880 29991

a) 427  427   427   428  428   428   428   428   428   429  429   430
b) 465  639   775   486  583   641   698   738   803   505  1034  453
c) 3458 28665 47853 6305 20150 28964 35516 41626 51662 9204 81744 2457

a) 430  430   430   430   430   430   431   431   431   432   432   432
b) 489  666   820   988   990   1007  797   947   1012  543   610   681
c) 6812 30719 53807 76271 76375 78520 50765 71877 78936 14287 22633 32955

a) 432   433   433   433   433   433   433   434   434   434   434
b) 849   570   589   598   667   675   1077  594   779   915   1008
c) 58097 18603 20579 21931 30654 31876 88621 20969 48152 68133 78325

a) 434   435   435   435   436  436   436   436   437   438   439  439
b) 1060  567   846   955   459  562   998   1063  616   892   480  875
c) 85605 18070 57707 72020 2795 17017 77610 86099 23998 63622 4186 61061

a) 439   439   440   440   440   440   440   440   440   440   441
b) 960   1006  537   643   650   695   721   747   774   834   1035
c) 72254 77805 12844 27963 28483 33865 37505 41977 46553 54691 80743

a) 441   442   442   443   443   444   444   445  445   445   446  446
b) 1040  754   872   603   654   835   922   472  860   1041  498  648
c) 81133 42354 59748 21450 28561 54444 67951 2587 58097 80743 6474 27898

a) 446   447  447   447   447   448 448  448   448   448   449   449
b) 862   512  713   920   1017  449 478  621   977   1070  555   715
c) 58175 8567 35256 67366 78650 299 2847 23075 73827 85098 14781 35477

a) 449   449   450  450   450   450   451   451   451   453   453   454
b) 817   987   478  621   977   1070  788   809   948   764   965   489
c) 51831 74412 2548 22776 73528 84799 47853 50297 69784 43576 71435 4355

a) 454   454   454   454   454   455  455   455   457  457   457   457
b) 666   820   988   990   1007  507  647   749   482  569   772   1049
c) 28262 51350 73814 73918 76063 6539 26702 40326 2418 15977 44603 81146

a) 457   458   458   458   459  459   460   460   460   461   461   461
b) 1051  789   821   1036  531  1030  562   998   1063  536   553   561
c) 81497 47151 50921 78936 9854 77974 14222 74815 83304 10517 12844 14040

a) 461   461   461   462  462   462   462   463   463   463   463   464
b) 630   863   981   523  544   586   710   851   913   971   980   485
c) 23478 56602 72722 8489 11635 17485 33501 55445 64844 72228 72605 2327

a) 464   464   464   465   465   465   466   466   468  468   468   468
b) 751   778   936   800   810   864   639   775   520  718   923   950
c) 40040 44629 67730 47814 49868 56511 25207 44395 7501 34008 65806 68575

a) 468   469   469   469   469   469   470  470   470   470   471  471
b) 969   756   942   951   1031  1061  525  795   825   1055  517  532
c) 71006 40404 67834 68484 77493 82238 7891 46566 50843 81120 6721 8996

a) 471   471   471   471   471   472   472   472   473   473   474 474
b) 599   676   777   798   996   657   661   894   860   1041  475 568
c) 18213 28353 43836 46995 73697 25974 26507 60346 55510 78156 273 14365

a) 475  475   475   475   475   475   476   477   477   478   478   479
b) 527  745   796   961   1011  1047  568   758   938   902   994   621
c) 7839 38220 46475 69147 74841 79469 14092 40638 66807 61477 72423 20228

a) 479   479   480   480   480   481   481   481   482   482   483
b) 977   1070  566   730   1046  875   960   1006  807   1016  569
c) 70980 82251 13481 36166 78728 56875 68068 73619 46982 74724 13559

a) 483   483   483   484  484   484   484   484   484   484   485   485
b) 772   1049  1051  508  620   677   692   733   975   1053  608   765
c) 42185 78728 79079 4173 19487 27183 29536 35919 70278 79469 17342 40586

a) 485   486   486   486   487   487   487   487   487   488  488   488
b) 786   751   778   936   583   641   698   738   803   529  682   973
c) 44252 37713 42302 65403 13845 22659 29211 35321 45357 5837 27144 69238

a) 489   489   489   490   490   490   490   490   491   491   491
b) 592   662   1044  666   820   988   990   1007  571   626   972
c) 14950 24232 76908 23907 46995 69459 69563 71708 11687 17927 68250

a) 492   492   492   493  493  493   493   493   494 494   494   494
b) 622   686   949   518  548  914   956   1037  495 637   814   928
c) 17602 27105 64649 3328 8164 60762 65117 74555 325 20839 46098 62413

a) 495   495   496   496   496   497   497   497   498   498   498
b) 728   750   637   814   928   668   674   1078  638   746   799
c) 33202 35477 20514 45773 62088 22997 24063 81068 20566 35074 43069

a) 499   499   500  500   500   501   501   501   502  503   503   504
b) 648   862   510  649   806   664   963   995   549  847   865   519
c) 21424 51701 1508 21294 43940 22412 65234 68718 6721 49179 50869 1898

a) 504   504   504   504   504   505   505   505   505   505   505
b) 627   768   858   896   1015  601   628   805   811   830   843
c) 16718 37830 50401 55952 70772 13325 17238 42926 44096 46150 48698

a) 505   506   507   507   507   508   508   509   509   509   509
b) 890   1034  584   878   958   647   749   620   677   692   733
c) 54561 72540 11089 52923 63622 20163 33787 15314 23010 25363 31746

a) 509   509   510   511   511   513   513   513   514  514   514   514
b) 975   1053  868   649   806   713   920   1017  581  828   933   1043
c) 66105 75296 50752 19786 42432 26689 58799 70083 9555 44811 60281 72761

a) 515   515   515   515   516  516   516   516   516   516   516   516
b) 691   867   982   1076  546  720   741   845   869   871   906   910
c) 24258 49517 65455 77727 4849 27300 31083 47385 49803 50323 56446 57174

a) 516   516   516   517   517   517   518  518   518   518   518   518
b) 978   1026  1075  766   952   1023  532  599   676   777   798   996
c) 65117 70057 77506 36036 61490 69758 2275 11492 21632 37115 40274 66976

a) 519  519   519   519   520   520   520   520   520   521   521   521
b) 548  914   956   1037  627   768   858   896   1015  718   923   950
c) 4836 57434 61789 71227 14820 35932 48503 54054 68874 26507 58305 61074

a) 521   522   522   522   522   522   523   523   523   523   524  524
b) 969   636   670   702   794   886   595   688   1003  1062  544  586
c) 63505 16432 19695 24440 39117 51753 10036 23335 67041 75036 3146 8996

a) 524   525  525  525   526   526   526   527  527   527   528   528
b) 710   530  547  708   795   825   1055  579  669   839   745   796
c) 25012 1027 3796 24622 38675 42952 73229 7787 18941 44759 30381 38636

a) 528   528   528   529   530   530   531  531   532   533  533   533
b) 961   1011  1047  883   682   973   547  708   1030  599  676   777
c) 61308 67002 71630 50440 21307 63401 2769 23595 68120 9217 19357 34840

a) 533   533   534  534   534   535  535   535   535   536   537  537
b) 798   996   612  831   900   572  921   934   992   763   553  561
c) 37999 64701 9542 42003 52390 5473 55562 57408 63271 32526 2327 3523

a) 537   537   537   538   538   538   538   538   538   538   539
b) 630   863   981   643   650   695   721   747   774   834   714
c) 12961 46085 62205 15119 15639 21021 24661 29133 33709 41847 22932

a) 539   539   539   540 540   540   540   540   541 541  541   541
b) 726   787   1072  541 665   712   739   819   545 609  631   782
c) 26065 36023 73645 260 16575 22581 27339 39663 520 8528 12532 34515

a) 541   541   542   542   542   542   543   543   543   544  544   544
b) 812   889   665   712   739   819   740   760   983   610  681   849
c) 39260 49244 16315 22321 27079 39403 27105 31447 61620 8346 18668 43810

a) 545  545   546  546   546   546   546   547   547   547   547   547
b) 586  710   609  631   782   812   889   720   741   845   869   871
c) 5850 21866 8008 12012 33995 38740 48724 22451 26234 42536 44954 45474

a) 547   547   547   547   547   548   549   549   549   551   551
b) 906   910   978   1026  1075  708   914   956   1037  736   1002
c) 51597 52325 60268 65208 72657 20826 52598 56953 66391 25662 62660

a) 552   552   553   553   554  554   554   554   555 555   556   556
b) 757   945   744   1028  561  630   863   981   557 753   715   817
c) 28990 56095 26286 64857 1196 10634 43758 59878 845 27469 20696 37050

a) 556   557   557   557   558   559   559   559   560  560  560   560
b) 987   761   930   1009  753   881   908   1045  573  623  644   651
c) 59631 29094 53521 61867 26624 45435 50765 66339 2002 8151 12155 12740

a) 560   560   560   561  561   561   561   562  562   562   563   563
b) 793   909   944   600  842   999   1032  630  863   981   998   1063
c) 33540 50778 54808 5395 40768 61152 64532 9438 42562 58682 60593 69082

a) 564  564  564   564   565   565   565   566  566   566   566   567
b) 577  614  673   770   701   704   1025  588  838   899   932   730
c) 2249 6812 14495 29744 17602 17992 62465 2418 38350 46748 52182 22685

a) 567   568   568   570   570   570   571  571  571   571   571   572
b) 1046  846   955   772   1049  1051  589  598  667   675   1077  626
c) 65247 39637 53950 28626 65169 65520 1976 3328 12051 13273 70018 6240

a) 572   573   573   573   574  574   574   574   574   574   575  575
b) 972   921   934   992   623  644   651   793   909   944   642  645
c) 56563 50089 51935 57798 6149 10153 10738 31538 48776 52806 9971 10335

a) 575   575   575   576   576   576   576   577   577   577   577
b) 879   912   939   857   887   985   1068  687   822   853   984
c) 43342 49088 52390 40534 44447 57330 68016 15548 34892 39624 57109

a) 577   578  578   578   579   579   579   580   580   581   581   582
b) 991   614  673   770   699   1027  1064  669   839   694   735   828
c) 57512 4563 12246 27495 15665 60918 66742 11154 36972 15145 21502 35256

a) 582   582   583  583   583   583   584  584   584   584   585   585
b) 933   1043  617  748   829   918   641  698   738   803   878   958
c) 50726 63206 4758 23166 35256 49010 8814 15366 21476 31512 41834 52533

a) 586  586   586   586   587   588   588   588   588   589   589   589
b) 602  690   703   904   710   719   755   785   940   838   899   932
c) 2236 14456 15535 46410 16016 17030 22945 28951 50622 35932 44330 49764

a) 590  590   590   590   591  591   592   593  593   594  594   595
b) 598  667   675   1077  611  771   752   662  1044  655  925   779
c) 1352 10075 11297 68042 1937 26351 22139 9282 61958 8554 48256 27183

a) 595   595   595   596   596   596   598   598   598   599  599  599
b) 915   1008  1060  688   1003  1062  854   888   919   667  675  1077
c) 47164 57356 64636 13299 57005 65000 37206 41301 46852 8723 9945 66690

a) 600   600   600   600   601   601   601   602  602   602   602   602
b) 676   777   798   996   842   999   1032  628  805   811   830   843
c) 10140 25623 28782 55484 35373 55757 59137 3913 29601 30771 32825 35373

a) 602   603   603   603   604  605   605   605   605   605   605   606
b) 890   690   703   904   654  705   861   873   901   1022  1033  658
c) 41236 12220 13299 44174 7111 13390 37011 38818 43134 57694 58734 7293

a) 606   606   607  607  607   607   607   608  608   609   609   610
b) 731   926   635  652  790   941   1019  633  924   765   786   631
c) 18330 46930 4927 6929 27469 48568 57577 4134 46670 23244 26910 4004

a) 610   610   610   611   611   612   613   613   614   615  615   616
b) 782   812   889   681   849   771   831   900   685   673  770   816
c) 25987 30732 40716 10322 35464 24414 32461 42848 10231 7683 22932 29497

a) 618   618   618   619   619   620  620   620   620   621  621   621
b) 748   829   918   689   783   683  954   974   1029  677  692   733
c) 18408 30498 44252 10075 24258 8788 47489 50752 56199 7696 10049 16432

a) 621   621   622   622   623  623   624  624  624   624   624   625
b) 975   1053  977   1070  686  949   644  651  793   909   944   634
c) 50791 59982 50752 62023 9503 47047 4004 4589 25389 42627 46657 2028

a) 625   625   626   626   627   628   628   628   628   629   629
b) 737   1067  711   844   972   768   858   896   1015  805   811
c) 16367 61776 11596 32812 50323 21112 33683 39234 54054 25688 26858

a) 629   629   629   630   630   631   631   632   632   632   633  633
b) 830   843   890   882   1005  863   981   782   812   889   693  859
c) 28912 31460 37323 35867 52000 33124 49244 21983 26728 36712 7865 32617

a) 633   634   635   635   636  636   636   636   637  637  637   637
b) 953   924   737   1067  652  790   941   1019  670  702  794   886
c) 45279 42536 14339 59748 2002 22542 43641 52650 3263 8008 22685 35321

a) 638   638   639   639   640   641  641   642  642   642   643 643
b) 814   928   746   799   775   684  837   698  738   803   645 879
c) 25259 41574 14508 22503 19188 5018 27430 6552 12662 22698 364 33371

a) 643   643   644 644  644  644   644   644   645 645   645   645
b) 912   939   650 695  721  747   774   834   651 793   909   944
c) 39117 42419 520 5902 9542 14014 18590 26728 585 21385 38623 42653

a) 646   646   646   647   647   647   648   649   650   651  651  651
b) 879   912   939   769   905   1001  749   862   806   695  721  747
c) 33007 38753 42055 17797 37557 48945 13624 30277 22646 5382 9022 13494

a) 651   651   652   652   652   653   653   653   654   654   654
b) 774   834   793   909   944   790   941   1019  801   1024  1059
c) 18070 26208 20800 38038 42068 20540 41639 50648 21450 50856 56134

a) 656   657  657  657   657   657   658 658   659   659   660   660
b) 925   707  716  848   1000  1020  661 894   731   926   725   836
c) 39702 6435 7514 28353 48243 50440 533 34372 11037 39637 10062 25922

a) 660   661   661   661   662   663   664   664   665   665   666  666
b) 929   767   962   970   894   1044  759   852   963   995   712  739
c) 40287 16484 43004 44356 33839 52676 15171 28080 42822 46306 6006 10764

a) 666   667   667   667   667   668  668   669  669   670   671  671
b) 819   820   988   990   1007  675  1077  674  1078  839   702  794
c) 23088 23088 45552 45656 47801 1222 57967 1066 58071 25818 4745 19422

a) 671   672   672   673   673   673   674   675   676   677   677
b) 886   784   986   826   885   979   770   1078  1077  777   798
c) 32058 17394 44629 23218 31070 44018 15249 57005 56745 15483 18642

a) 677   678  678  678   678   679   680  680   682   683   684   684
b) 996   692  733  975   1053  841   743  937   849   973   954   974
c) 45344 2353 8736 43095 52286 24414 9126 38168 25142 42094 38701 41964

a) 684   685   687   688   688   688   688   689   689   690   691  691
b) 1029  837   949   822   853   984   991   1003  1062  783   703  904
c) 47411 22412 37544 19344 24076 41561 41964 43706 51701 14183 1079 31954

a) 692   692   692   693  693   693   694   694   695  696  696  696
b) 867   982   1076  733  975   1053  859   953   735  721  747  774
c) 25259 41197 53469 6383 40742 49933 24752 37414 6357 3640 8112 12688

a) 696   697   697   697   697   697   697   698  698   699  699   700
b) 834   791   856   877   880   1052  1054  729  897   738  803   1027
c) 20826 15197 24401 26884 27235 49452 49972 5668 29718 6110 16146 45253

a) 700   701   701   702 702   703   703   704   705   706   706   706
b) 1064  776   917   704 1025  794   886   904   1025  861   873   901
c) 51077 12246 33332 390 44863 14677 27313 30875 44473 23621 25428 29744

a) 706   706   707   708  708   708   708   710  710   710   710   710
b) 1022  1033  1057  716  848   1000  1020  724  802   966   1014  1021
c) 44304 45344 48997 1079 21918 41808 44005 2769 14742 37336 43173 43745

a) 712   713  713   714   714   715  715   715   716   716   717   717
b) 844   739  819   920   1017  726  787   1072  817   987   848   1000
c) 21216 4758 17082 32110 43394 3133 13091 50713 16354 38935 20839 40729

a) 717   718  718   718   718   718   719   719   719   720  720   720
b) 1020  773  780   792   907   1071  923   950   969   755  785   940
c) 42926 9958 11167 12896 30186 50193 31798 34567 36998 5915 11921 33592

a) 721  721   721   721   721   721   721   721   721   722  722  722
b) 741  845   869   871   906   910   978   1026  1075  747  774  834
c) 3783 20085 22503 23023 29146 29874 37817 42757 50206 4472 9048 17186

a) 723   723   723   724   724   724   725   725   725   725   726
b) 850   916   1073  824   866   993   802   966   1014  1021  836
c) 19188 29445 48581 14859 20605 37323 11973 34567 40404 40976 15860

a) 726   727  727   729  730   731   732   733   734   734   735   737
b) 929   787  1072  750  897   1046  926   976   975   1053  946   1002
c) 30225 9958 47580 2275 24050 42562 28600 34554 34359 43550 30771 36998

a) 738   739   740   741  741   742   742   742   742   742   742   742
b) 1067  803   819   760  983   845   869   871   906   910   978   1026
c) 45409 10036 12324 4342 34515 16302 18720 19240 25363 26091 34034 38974

a) 742   743   743   743   743   743   744   745   746  746   746   746
b) 1075  911   1013  1018  1042  1058  937   1028  796  961   1011  1047
c) 46423 26091 37375 38493 41210 43407 29042 38571 8255 30927 36621 41249

a) 747  748  748   749   749   752  752   755   756  756   757   757
b) 799  774  834   829   918   778  936   872   785  940   942   951
c) 7995 4576 12714 12090 25844 4589 27690 17394 6006 27677 27430 28080

a) 757   757   758   759   760   761   762   762   763   763   765
b) 1031  1061  945   938   852   983   930   1009  884   1010  965
c) 37089 41834 27105 26169 12909 30173 24427 32773 16731 32968 27859

a) 766  767   767   768   768   769   769   769   770   770   773   773
b) 786  952   1023  962   970   858   896   1015  905   1001  1049  1051
c) 3666 25454 33722 26520 27872 12571 18122 32942 19760 31148 36543 36894

a) 774  774  774   774   775  777   778  778   779   780   780   780
b) 780  792  907   1071  834  917   798  996   936   915   1008  1060
c) 1209 2938 20228 40235 8138 21086 3159 29861 23101 19981 30173 37453

a) 781  781   781   782  782   782   782   783  783   785   786   788
b) 792  907   1071  813  968   1004  1066  812  889   986   940   1072
c) 1729 19019 39026 4849 25766 29666 37856 4745 14729 27235 21671 37622

a) 789  789   790  790   791   791   792  792   792   792   792   793
b) 809  948   821  1036  941   1019  856  877   880   1052  1054  907
c) 2444 21931 3770 31785 21099 30108 9204 11687 12038 34255 34775 17290

a) 793   794   794   795   796  796   797   797   797   798   798   799
b) 1071  909   944   886   825  1055  961   1011  1047  947   1012  996
c) 37297 17238 21268 12636 4277 34554 22672 28366 32994 21112 28171 26702

a) 801  801  802   802   803   803   803   805  805   806  806  806
b) 810  864  1024  1059  966   1014  1021  815  1050  811  830  843
c) 2054 8697 29406 34684 22594 28431 29003 2002 32435 1170 3224 5772

a) 806   808   810   811  812  812  812   813  814   814   814   815
b) 890   1016  948   864  830  843  890   889  968   1004  1066  928
c) 11635 27742 19487 6643 2054 4602 10465 9984 20917 24817 33007 16315

a) 816   818   819  819  821   821   821   822   823  823   823   824
b) 1050  987   833  876  988   990   1007  1036  853  984   991   1065
c) 30433 22581 1976 8073 22464 22568 24713 28015 4732 22217 22620 32578

a) 824   825  825   826   827  827   828  828  828   829   829   830
b) 1069  866  993   1055  885  979   840  874  927   933   1043  918
c) 32929 5746 22464 30277 7852 20800 1937 6552 14625 15470 27950 13754

a) 831  831  832   833   833   834  836   837   839  839   841  841
b) 843  890  900   903   989   876  922   929   899  932   874  927
c) 2548 8411 10387 10387 20787 6097 13507 14365 8398 13832 4615 12688

a) 843   843   844  846  846  846  846  846   846   846   847   848
b) 999   1032  890  869  871  906  910  978   1026  1075  955   865
c) 20384 23764 5863 2418 2938 9061 9789 17732 22672 30121 14313 1690

a) 849   849   851   851   852  852   852   854   854   855  855  856
b) 1000  1020  916   1073  913  971   980   984   991   888  919  997
c) 19890 22087 10257 29393 9399 16783 17160 17485 17888 4095 9646 18603

a) 857  857  857   857   858  858   858   859  859   860   861   862
b) 877  880  1052  1054  887  985   1068  896  1015  953   1041  873
c) 2483 2834 25051 25571 3913 16796 27482 5551 20371 12662 22646 1807

a) 862  862   862   864   867   868   868   870 870  870  870   870
b) 901  1022  1033  981   993   982   1076  871 906  910  978   1026
c) 6123 20683 21723 16120 16718 15938 28210 520 6643 7371 15314 20254

a) 870   871   871   871   871   872  872  872   872   872   874  874
b) 1075  943   964   1039  1074  906  910  978   1026  1075  901  1022
c) 27703 11089 13013 21632 27313 6123 6851 14794 19734 27183 4316 18876

a) 874   875  876   876   878 878   878   879   880  880  881   881
b) 1033  927  960   1006  880 1052  1054  958   912  939  1052  1054
c) 19916 8073 11193 16744 351 22568 23088 10699 5746 9048 22217 22737

a) 882  882   883   885   886   888   888   889  892  894   896  897
b) 908  1045  1005  1010  979   985   1068  919  898  1056  935  1015
c) 5330 20904 16133 16237 12948 12883 23569 5551 1261 20865 6500 14820

a) 900  902   902   903   904   906   907 907  907   907   908   909
b) 932  1022  1033  994   989   1001  910 978  1026  1075  1071  1045
c) 5434 14560 15600 10946 10400 11388 728 8671 13611 21060 20007 15574

a) 910  911  911   911   912   912   912   912   913  914  914  915
b) 944  978  1026  1075  1013  1018  1042  1058  939  971  980  956
c) 4030 7943 12883 20332 11284 12402 15119 17316 3302 7384 7761 4355

a) 915   916   916   917   921   922  922  924  924  931  934   935
b) 1037  1008  1060  1073  1017  934  992  950  969  1009 1043  992
c) 13793 10192 17472 19136 11284 1846 7709 2769 5200 8346 12480 5863

a) 942  943 943  943   944  944   944   948  951  952  952   953  955
b) 1019 951 1031 1061  964  1039  1074  1012 969  1031 1061  1023 974
c) 9009 650 9659 14404 1924 10543 16224 7059 2431 9009 13754 8268 3263

a) 955  957  958  961  962  962   963  964  965  965   967  967  969
b) 1029 1037 1038 1006 1011 1047  970  995  1039 1074  1014 1021 1004
c) 8710 9438 9399 5551 5694 10322 1352 3484 8619 14300 5837 6409 3900

a) 969   972 975  976  978   979  979   983   985 986   989 989  991
b) 1066  980 1029 1053 1070  1026 1075  1076  991 1068  990 1007 1007
c) 12090 377 5447 9191 11271 4940 12389 12272 403 10686 104 2249 2145

a) 999  1000 1001 1004 1005 1009 1012 1014 1014 1014 1015 1019 1019 1023
b) 1063 1032 1020 1062 1066 1060 1047 1018 1042 1058 1021 1042 1058 1033
c) 8489 3380 2197 7995 8190 7280 4628 1118 3835 6032 572  2717 4914 1040

a) 1025 1027 1028 1032 1036 1040 1043 1050 1053 1066
b) 1059 1075 1064 1061 1040 1074 1058 1051 1054 1069
c) 5278 7449 5824 4745 390  5681 2197 351  520  351

a) Start position of group 1 is from the beginning, and of group 2 is from the end.
b) End position of group 1 is from the beginning, and of group 2 is from the end.
c) Total of both groups.

Total of the start and end positions (a + b): 3742518 = 2 x 3 x 13 x 47981. SF: 47999 = 7 x 6857. SF: 6864 = 2⁴ x 3 x 11 x 13. SF: 35 = 5 x 7. (The factors are four levels deep.)

7.2Take every other letter.

7.2.1The odd positioned letters: 80873 = 13 x 6221.

7.2.2The even positioned letters: 72306 = 2 x 3³ x 13 x 103.

7.2.3Difference between the odd and even positioned letters: 8567 = 13 x 659. SF: 672 = 2⁵ x 3 x 7.

7.31791 letters are not prime numbers. The total of their positions in the passage: 1916157 = 3 x 638719. SF: 638722 = 2 x 7 x 43 x 1061. SF: 1113 = 3 x 7 x 53. SF: 63 = 3² x 7. SF: 13. The total of these letters: 151326 = 2 x 3² x 7 x 1201.

7.4142 letters are divisible by 7. Their total is a very nice round number and gives an extra factor of 7: 4900 = 2² x 5² x 7². SF: 28 = 2² x 7.

7.5When the letters are added one by one, 182 times the running total will be a multiple of 13. Providentially, the total of the positions where this happens is also a multiple of 13 twice: 192322 = 2 x 13² x 569.

7.5.1When the letters are added one by one, 189 times the running total will be a prime number. The total of the letters where this occurs: 13442 = 2 x 11 x 13 x 47.

7.5.2In the remaining 1968 times, the running total will not be a prime number. The total of the letters where this occurs: 139737 = 3 x 13 x 3583.

7.6For each letter, add up all its positions in the passage.

7.6.1Sum of the letters where the position total is an odd number: 63284 = 2² x 13 x 1217.

7.6.2Sum of the letters where the position total is an odd number: 89895 = 3 x 5 x 13 x 461.

7.6.3Sum of the letters where the position total is a prime number: 21450 = 2 x 3 x 5² x 11 x 13. SF: 39 = 3 x 13.

7.6.4Sum of the letters where the position total is not a prime number: 131729 = 13 x 10133.

7.7Divide the letters into alternating groups of M and N-number of letters where M and N are multiples of 7 or 13.

7.7.1Alternating groups of 42 and 663.

7.7.1.1Groups of 42: 12038 = 2 x 13 x 463.

7.7.1.2Groups of 663: 141141 = 3 x 7 x 11 x 13 x 47.

7.7.2Alternating groups of 663 and 56.

7.7.2.1Groups of 663: 141154 = 2 x 13 x 61 x 89.

7.7.2.2Groups of 56: 12025 = 5² x 13 x 37.

7.7.3Alternating groups of 329 and 585.

7.7.3.1Groups of 329: 67080 = 2³ x 3 x 5 x 13 x 43. SF: 70 = 2 x 5 x 7. SF: 14 = 2 x 7.

7.7.3.2Groups of 585: 86099 = 13 x 37 x 179.

7.8The Nth and Nth last occurrences of 99 letters serve to divide the rest of the letters into what is between them, and what is not between them.

Between & *Not* Between A Letter
A	B	C	D	E	F
5	13	136903 = 13 x 10531.	16276 = 2² x 13 x 313.	136	2058
5	20	126620 = 2² x 5 x 13 x 487.	26559 = 3² x 13 x 227.	191	1988
5	21	126243 = 3² x 13² x 83.	26936 = 2³ x 7 x 13 x 37. SF: 63 = 3² x 7. SF: 13.	195	1985
5	32	114660 = 2² x 3² x 5 x 7² x 13. SF: 42 = 2 x 3 x 7.	38519 = 13 x 2963.	309	1921
5	34	113698 = 2 x 13 x 4373.	39481 = 13 x 3037.	324	1915
5	45	96395 = 5 x 13 x 1483.	56784 = 2⁴ x 3 x 7 x 13².	451	1825
5	54	86814 = 2 x 3² x 7 x 13 x 53.	66365 = 5 x 13 x 1021.	532	1770
5	59	73658 = 2 x 13 x 2833.	79521 = 3 x 13 x 2039.	653	1704
5	66	68432 = 2⁴ x 7 x 13 x 47.	84747 = 3 x 13 x 41 x 53.	695	1656
5	67	65494 = 2 x 11 x 13 x 229.	87685 = 5 x 13 x 19 x 71.	733	1654
5	85	43875 = 3³ x 5³ x 13.	109304 = 2³ x 13 x 1051.	878	1502
9	2	150163 = 13 x 11551. SF: 11564 = 2² x 7² x 59. SF: 77 = 7 x 11.	3016 = 2³ x 13 x 29.	10	2118
9	5	142389 = 3² x 13 x 1217.	10790 = 2 x 5 x 13 x 83.	74	2092
9	15	132496 = 2⁴ x 7² x 13².	20683 = 13 x 37 x 43.	147	1998
9	22	119171 = 13 x 89 x 103.	34008 = 2³ x 3 x 13 x 109.	221	1923
9	25	116922 = 2 x 3 x 13 x 1499.	36257 = 13 x 2789.	247	1896
9	26	115752 = 2³ x 3 x 7 x 13 x 53.	37427 = 13 x 2879.	264	1888
9	49	79326 = 2 x 3³ x 13 x 113.	73853 = 13² x 19 x 23.	461	1604
9	50	78910 = 2 x 5 x 13 x 607.	74269 = 13 x 29 x 197.	463	1595
9	73	47814 = 2 x 3 x 13 x 613.	105365 = 5 x 13 x 1621.	644	1340
9	74	46735 = 5 x 13 x 719.	106444 = 2² x 13 x 23 x 89.	651	1323
9	75	44772 = 2² x 3 x 7 x 13 x 41.	108407 = 13 x 31 x 269.	654	1310
90	17	121056 = 2⁵ x 3 x 13 x 97.	32123 = 7 x 13 x 353.	240	1952
90	23	109837 = 7 x 13 x 17 x 71.	43342 = 2 x 13 x 1667.	320	1854
90	34	86060 = 2² x 5 x 13 x 331.	67119 = 3 x 13 x 1721.	503	1748
20	3	144066 = 2 x 3 x 13 x 1847.	9113 = 13 x 701. SF: 714 = 2 x 3 x 7 x 17.	64	2101
20	9	121407 = 3 x 11 x 13 x 283.	31772 = 2² x 13² x 47. SF: 77 = 7 x 11.	250	1968
20	23	69043 = 13 x 47 x 113.	84136 = 2³ x 13 x 809.	554	1548
20	28	41145 = 3 x 5 x 13 x 211.	112034 = 2 x 13 x 31 x 139.	702	1289
60	22	117533 = 13 x 9041.	35646 = 2 x 3 x 13 x 457.	226	1890
60	25	112840 = 2³ x 5 x 7 x 13 x 31.	40339 = 13 x 29 x 107.	259	1843
60	29	106964 = 2² x 11² x 13 x 17. SF: 56 = 2³ x 7. SF: 13.	46215 = 3² x 5 x 13 x 79.	284	1768
60	32	99840 = 2⁹ x 3 x 5 x 13. SF: 39 = 3 x 13.	53339 = 11 x 13 x 373.	315	1725
60	33	99645 = 3 x 5 x 7 x 13 x 73.	53534 = 2 x 13 x 29 x 71.	318	1721
60	44	83746 = 2 x 13 x 3221.	69433 = 7² x 13 x 109.	426	1639
60	49	76739 = 13 x 5903.	76440 = 2³ x 3 x 5 x 7² x 13.	467	1569
60	54	66846 = 2 x 3 x 13 x 857. SF: 875 = 5³ x 7.	86333 = 13 x 29 x 229.	509	1485
60	78	38298 = 2 x 3 x 13 x 491.	114881 = 13 x 8837.	738	1288
60	89	17615 = 5 x 13 x 271.	135564 = 2² x 3 x 11 x 13 x 79.	891	1158
60	94	10764 = 2² x 3² x 13 x 23.	142415 = 5 x 7 x 13 x 313. SF: 338 = 2 x 13². SF: 28 = 2² x 7.	956	1111
40	11	134446 = 2 x 13 x 5171.	18733 = 11 x 13 x 131.	137	2014
40	20	117676 = 2² x 13 x 31 x 73.	35503 = 13 x 2731. SF: 2744 = 2³ x 7³.	262	1929
40	21	116792 = 2³ x 13 x 1123.	36387 = 3² x 13 x 311.	271	1910
40	32	89895 = 3 x 5 x 13 x 461.	63284 = 2² x 13 x 1217.	521	1806
40	36	84058 = 2 x 13 x 53 x 61.	69121 = 13² x 409.	556	1761
40	40	75491 = 13 x 5807.	77688 = 2³ x 3² x 13 x 83.	616	1680
40	51	54548 = 2² x 13 x 1049. SF: 1066 = 2 x 13 x 41. SF: 56 = 2³ x 7. SF: 13.	98631 = 3³ x 13 x 281.	780	1564
40	62	36036 = 2² x 3² x 7 x 11 x 13.	117143 = 13 x 9011.	895	1407
40	72	23166 = 2 x 3⁴ x 11 x 13.	130013 = 13 x 73 x 137.	1032	1338
100	6	138762 = 2 x 3² x 13 x 593.	14417 = 13 x 1109.	69	2028
100	14	118365 = 3 x 5 x 13 x 607.	34814 = 2 x 13² x 103.	237	1927
100	38	72657 = 3⁵ x 13 x 23.	80522 = 2 x 13 x 19 x 163.	617	1645
100	39	71682 = 2 x 3 x 13 x 919.	81497 = 13 x 6269.	627	1635
100	42	66287 = 13 x 5099.	86892 = 2² x 3 x 13 x 557.	673	1611
100	77	3848 = 2³ x 13 x 37. SF: 56 = 2³ x 7. SF: 13.	149331 = 3 x 7 x 13 x 547.	1130	1200
4	1	150150 = 2 x 3 x 5² x 7 x 11 x 13.	3029 = 13 x 233.	11	2116
4	9	70200 = 2³ x 3³ x 5² x 13.	82979 = 13² x 491.	724	1717
600	3	143676 = 2² x 3² x 13 x 307.	9503 = 13 x 17 x 43.	65	2106
600	15	105547 = 13 x 23 x 353.	47632 = 2⁴ x 13 x 229.	358	1856
600	18	96824 = 2³ x 7² x 13 x 19. SF: 52 = 2² x 13.	56355 = 3 x 5 x 13 x 17².	411	1808
600	32	45266 = 2 x 13 x 1741.	107913 = 3 x 13 x 2767.	766	1436
7	1	151580 = 2² x 5 x 11 x 13 x 53.	1599 = 3 x 13 x 41.	16	2147
7	4	143234 = 2 x 7 x 13 x 787.	9945 = 3² x 5 x 13 x 17.	104	2119
7	12	99645 = 3 x 5 x 7 x 13 x 73.	53534 = 2 x 13 x 29 x 71.	418	1850
7	28	24479 = 7 x 13 x 269.	128700 = 2² x 3² x 5² x 11 x 13.	818	1204
7	37	10179 = 3³ x 13 x 29.	143000 = 2³ x 5³ x 11 x 13.	923	1085
200	17	100425 = 3 x 5² x 13 x 103.	52754 = 2 x 13 x 2029. SF: 2044 = 2² x 7 x 73. SF: 84 = 2² x 3 x 7. SF: 14 = 2 x 7.	313	1736
200	21	93483 = 3² x 13 x 17 x 47.	59696 = 2⁴ x 7 x 13 x 41.	356	1689
200	24	88556 = 2² x 13² x 131. SF: 161 = 7 x 23.	64623 = 3 x 13 x 1657. SF: 1673 = 7 x 239.	391	1667
200	25	86008 = 2³ x 13 x 827.	67171 = 13 x 5167. SF: 5180 = 2² x 5 x 7 x 37.	409	1647
200	27	83616 = 2⁵ x 3 x 13 x 67.	69563 = 13 x 5351.	424	1637
200	29	81562 = 2 x 13 x 3137.	71617 = 7 x 13 x 787.	449	1625
200	51	30836 = 2² x 13 x 593.	122343 = 3 x 13 x 3137.	868	1318
200	53	27690 = 2 x 3 x 5 x 13 x 71.	125489 = 7² x 13 x 197. SF: 224 = 2⁵ x 7.	886	1287
200	58	19981 = 13 x 29 x 53.	133198 = 2 x 13 x 47 x 109.	961	1258
10	4	139217 = 13 x 10709.	13962 = 2 x 3 x 13 x 179.	72	2035
10	33	23790 = 2 x 3 x 5 x 13 x 61. SF: 84 = 2² x 3 x 7. SF: 14 = 2 x 7.	129389 = 13 x 37 x 269.	658	1019
1	2	150618 = 2 x 3 x 13 x 1931.	2561 = 13 x 197. SF: 210 = 2 x 3 x 5 x 7.	29	2145
1	4	147927 = 3 x 13 x 3793. SF: 3809 = 13 x 293.	5252 = 2² x 13 x 101.	48	2133
1	14	137267 = 13 x 10559.	15912 = 2³ x 3² x 13 x 17. SF: 42 = 2 x 3 x 7.	111	2036
1	23	124189 = 13 x 41 x 233. SF: 287 = 7 x 41.	28990 = 2 x 5 x 13 x 223.	184	1948
1	31	114101 = 13 x 67 x 131.	39078 = 2 x 3² x 13 x 167.	276	1862
1	41	100100 = 2² x 5² x 7 x 11 x 13.	53079 = 3 x 13 x 1361.	348	1762
1	71	62088 = 2³ x 3 x 13 x 199. SF: 221 = 13 x 17.	91091 = 7² x 11 x 13².	600	1492
1	79	52507 = 7 x 13 x 577.	100672 = 2⁶ x 11² x 13.	649	1405
1	80	51272 = 2³ x 13 x 17 x 29. SF: 65 = 5 x 13.	101907 = 3² x 13² x 67.	655	1396
1	109	13689 = 3⁴ x 13².	139490 = 2 x 5 x 13 x 29 x 37.	950	1155
1	116	5967 = 3³ x 13 x 17. SF: 39 = 3 x 13.	147212 = 2² x 13 x 19 x 149.	1026	1102
70	11	106678 = 2 x 11 x 13 x 373. SF: 399 = 3 x 7 x 19.	46501 = 7² x 13 x 73.	306	1794
70	13	96512 = 2⁸ x 13 x 29.	56667 = 3 x 13 x 1453. SF: 1469 = 13 x 113. SF: 126 = 2 x 3² x 7.	329	1695
70	16	85228 = 2² x 11 x 13 x 149.	67951 = 13 x 5227.	415	1648
80	16	78689 = 13 x 6053.	74490 = 2 x 3 x 5 x 13 x 191.	388	1524
80	27	15002 = 2 x 13 x 577.	138177 = 3² x 13 x 1181.	864	1092
80	30	2028 = 2² x 3 x 13².	151151 = 7 x 11 x 13 x 151. SF: 182 = 2 x 7 x 13.	935	983
30	12	81159 = 3 x 13 x 2081.	72020 = 2² x 5 x 13 x 277. SF: 299 = 13 x 23.	483	1640
30	19	49543 = 13 x 37 x 103.	103636 = 2² x 13 x 1993.	717	1420
30	23	14599 = 13 x 1123.	138580 = 2² x 5 x 13² x 41.	1006	1223
3	16	15678 = 2 x 3² x 13 x 67.	137501 = 7 x 13 x 1511.	989	1217
2	1	135902 = 2 x 13 x 5227.	17277 = 3 x 13 x 443.	93	2012
A: First letter from feature 4. B: Nth/Nth last occurrence. C: Total of the first letters in between.			D: Total of the first letters not in between. E: Position in the list of the Nth occurrence. F: Position in the list of the Nth last occurrence.

7.8.1Total of the odd valued letters in column A: 203 = 7 x 29.

7.8.2Total of the letters (column A) when the Nth occurrence (column B) is odd valued: 3864 = 2³ x 3 x 7 x 23. SF: 39 = 3 x 13.

7.8.3Total of the letters (column A) when the position of the Nth occurrence (column E) is even valued: 3304 = 2³ x 7 x 59.

7.8.4Total of the Nth occurrences (column B) when the position of the Nth last occurrence (column F) is even valued: 1981 = 7 x 283.

7.8.5Total of the position of the Nth last occurrences (column F) when the position of the Nth last occurrence (column F) is even valued: 92573 = 13 x 7121.

7.8.6Total of the Nth occurrences (column B) when the position of the Nth last occurrence (column F) is odd valued: 1313 = 13 x 101.

7.8.7Total of the positions of the Nth occurrence (column E) when the position of the Nth last occurrence (column F) is odd valued: 18606 = 2 x 3 x 7 x 443. SF: 455 = 5 x 7 x 13.

7.8.8Total of the positions of the Nth and Nth last occurrences (columns E and F): 212403 = 3 x 101 x 701. This is not a multiple of 7 or 13, but 101 is encouraging as the one God who is beginning and end. The sum of the factors goes further: 805 = 5 x 7 x 23. SF: 35 = 5 x 7. SF: 12 = 2² x 3. SF: 7.

7.8.9Only three letters (column A) have Nth/Nth last occurrences of 1 (column B). Unlike the other letters, it is their first and last occurrences that divide the remaining letters of the passage into two groups. Providentially, these letters just so happen to be 4, 7 and 2. Their total: 13.

7.8.9.1The three letters with Nth/Nth last occurrences of 1 have the lowest N value. Their opposite is the letter 1 with highest Nth/Nth last occurrence of 116. The lowest and highest N values together would be 117 (3² x 13). And of course, the four letters together would now have a value of 14 (2 x 7).

7.9The first letter has the value 5. It is odd valued. Search through the letters for the next even number. Continue the search alternating between odd and even. This covers 1129 letters. Their total: 52941 = 3 x 7 x 2521.

Conclusion

Jesus prophesied this dark future while he was performing a multitude of miracles/signs to show he was fulfilling Isaiah's prophecy, and at the same time prove the truth of his own words. Thus Jesus' prophecy is also very important. The abundance of numeric features stand as an eternal witness for all generations to see Jesus' prophecy being fulfilled at the time of his death. The sons of the kingdom were cast into outer/extreme darkness.

This answers the first question as to when Israel was cast into darkness. For a possible answer to the second question, see this.

Back: Prophetic Confirmation > Two Dark Prophecies Concerning Israel > Dark Prophecy Arrives > God’s Kingdom Given To Another People > Recognizing The Second Witness

Notes

English reference quotes are from the Revised Standard Version, Thomas Nelson Inc., 1972.
The F.H.A Scrivener 1881 - Theodore Beza 1598 Textus Receptus Greek New Testament (GNS), ASCII edition copyright 1992 by Dr. Kirk D. DiVietro, Grace Baptist Church.

Dark Prophecy Arrives

Primary Features

The Verses

The Words

First And Last

Alpha: The First Letter Of Each Word

Omega: The Last Letter Of Each Word

Letters Not First Or Last

All The Letters

Conclusion

Notes

Numeric Study Links

Extended Old Testament Passages

Extended New Testament Passages (GNT)

Further Numeric Experiments

The Rational Bible

Bible Issues