Vernier/SG Sophie Germain Prime Table

Companion to Vernier/SG // kmsp42.com rev 2.2
Algorithm: Multiplicative walk with digit-sum extraction
Walk: s(n) = g × s(n-1) mod q, starting from s(0) = 1
Extract: pad_digit = (sum of decimal digits of s(n)) mod 10
Period: exactly 2p digits (Fermat-Euler theorem)
Generator: smallest primitive root g ≥ 5 of q
Primes: 1171
Range: 2 – 99,839
p ≥ 83: 1163
Minimum kernel: p ≥ 83 (166-digit stream). Generator g and table are public. Only kernel p is secret. Chaining: find next p strictly greater than last s(n).
#pq=2p+1gstream2550100
125-4000
237-6000
3511-10000
41123-22000
52347-46100
62959-58210
74183-82310
853107-106421
9831675166631
10891796178731
111132275226942
1213126352621052
1317334753461363
1417935973581473
1519138353821573
1623346754661894
17239479134781994
18251503550220105
19281563556222115
20293587558623115
213597191171828147
224198391183833168
23431863586234178
24443887588635178
25491983598239199
265091,01961,018402010
275931,18751,186472311
286411,28351,282512512
296531,30751,306522613
306591,319131,318522613
316831,36751,366542713
327191,43971,438572814
337431,48751,486592914
347611,52351,522603015
358091,61961,618643216
369111,82351,822723618
379531,90751,906763819
381,0132,02752,026814020
391,0192,03972,038814020
401,0312,06352,062824120
411,0492,09962,098834120
421,1032,20752,206884422
431,2232,44752,446974824
441,2292,45962,458984924
451,2892,57962,5781035125
461,4092,81962,8181125628
471,4392,87972,8781155728
481,4512,90352,9021165829
491,4812,96352,9621185929
501,4992,999172,9981195929
511,5113,02353,0221206030
521,5593,11973,1181246231
531,5833,16753,1661266331
541,6013,20353,2021286432
551,7333,46753,4661386934
561,8113,62353,6221447236
571,8893,77963,7781517537
581,9013,80353,8021527638
591,9313,86353,8621547738
601,9733,94753,9461577839
612,0034,00754,0061608040
622,0394,079114,0781638140
632,0634,12754,1261658241
642,0694,13964,1381658241
652,1294,25964,2581708542
662,1414,28354,2821718542
672,2734,54754,5461819045
682,3394,679114,6781879346
692,3514,70354,7021889447
702,3934,78754,7861919547
712,3994,79974,7981919547
722,4594,919134,9181969849
732,5435,08755,08620310150
742,5495,09965,09820310150
752,6935,38755,38621510753
762,6995,39975,39821510753
772,7415,48355,48221910954
782,7535,50755,50622011055
792,8195,63975,63822511256
802,9035,80755,80623211658
812,9395,879115,87823511758
822,9635,92755,92623711859
832,9695,93965,93823711859
843,0236,04756,04624112060
853,2996,599136,59826313165
863,3296,65966,65826613366
873,3596,719116,71826813467
883,3896,77966,77827113567
893,4136,82756,82627313668
903,4496,89966,89827513768
913,4916,98356,98227913969
923,5397,07977,07828314170
933,5937,18757,18628714371
943,6237,24757,24628914472
953,7617,52357,52230015075
963,7797,559137,55830215175
973,8037,60757,60630415276
983,8217,64357,64230515276
993,8517,70357,70230815477
1003,8637,72757,72630915477
1013,9117,82357,82231215678
1024,0198,039118,03832116080
1034,0738,14758,14632516281
1044,2118,42358,42233616884
1054,2718,54358,54234117085
1064,3498,69968,69834717386
1074,3738,74758,74634917487
1084,3918,78358,78235117587
1094,4098,81968,81835217688
1104,4818,96358,96235817989
1114,7339,46759,46637818994
1124,7939,58759,58638319195
1134,8719,74359,74238919497
1144,9199,83979,83839319698
1154,9439,88759,88639519798
1165,00310,007510,006400200100
1175,03910,0791110,078403201100
1185,05110,103510,102404202101
1195,08110,163510,162406203101
1205,17110,343510,342413206103
1215,23110,463510,462418209104
1225,27910,5592310,558422211105
1235,30310,607510,606424212106
1245,33310,667510,666426213106
1255,39910,7991910,798431215107
1265,44110,883510,882435217108
1275,50111,003511,002440220110
1285,63911,279711,278451225112
1295,71111,423511,422456228114
1305,74111,483511,482459229114
1315,84911,699611,698467233116
1325,90311,807511,806472236118
1336,05312,107512,106484242121
1346,10112,203512,202488244122
1356,11312,227512,226489244122
1366,13112,263512,262490245122
1376,17312,347512,346493246123
1386,26312,527512,526501250125
1396,26912,539612,538501250125
1406,32312,647512,646505252126
1416,32912,659612,658506253126
1426,44912,899612,898515257128
1436,49112,983512,982519259129
1446,52113,043513,042521260130
1456,55113,103513,102524262131
1466,56313,127513,126525262131
1476,58113,163513,162526263131
1486,76113,523513,522540270135
1496,89913,799713,798551275137
1506,98313,967513,966558279139
1517,04314,087514,086563281140
1527,07914,1591314,158566283141
1537,10314,207514,206568284142
1547,12114,243514,242569284142
1557,15114,303514,302572286143
1567,19314,387514,386575287143
1577,21114,423514,422576288144
1587,34914,699614,698587293146
1597,43314,867514,866594297148
1607,54115,083515,082603301150
1617,64315,287515,286611305152
1627,64915,299615,298611305152
1637,69115,383515,382615307153
1647,82315,647515,646625312156
1657,84115,683515,682627313156
1667,88315,767515,766630315157
1677,90115,803515,802632316158
1688,06916,139616,138645322161
1698,09316,187516,186647323161
1708,11116,223516,222648324162
1718,24316,487516,486659329164
1728,27316,547516,546661330165
1738,51317,027517,026681340170
1748,66317,327517,326693346173
1758,69317,387517,386695347173
1768,74117,483517,482699349174
1778,95117,903517,902716358179
1788,96917,939617,938717358179
1799,02918,059618,058722361180
1809,05918,1191718,118724362181
1819,22118,443518,442737368184
1829,29318,587518,586743371185
1839,37118,743518,742749374187
1849,41918,839718,838753376188
1859,47318,947518,946757378189
1869,47918,9591318,958758379189
1879,53919,079719,078763381190
1889,62919,259619,258770385192
1899,68919,379619,378775387193
1909,79119,583519,582783391195
19110,06120,123520,122804402201
19210,09120,183520,182807403201
19310,16320,327520,326813406203
19410,25320,507520,506820410205
19510,27120,543520,542821410205
19610,31320,627520,626825412206
19710,33120,663520,662826413206
19810,52921,059621,058842421210
19910,58921,179621,178847423211
20010,61321,227521,226849424212
20110,69121,383521,382855427213
20210,70921,419621,418856428214
20310,73321,467521,466858429214
20410,78121,563521,562862431215
20510,79921,599721,598863431215
20610,88321,767521,766870435217
20711,17122,343522,342893446223
20811,32122,643522,642905452226
20911,36922,739622,738909454227
21011,39322,787522,786911455227
21111,47122,943522,942917458229
21211,51923,039723,038921460230
21311,54923,099623,098923461230
21411,57923,1591123,158926463231
21511,69923,3991723,398935467233
21611,78323,567523,566942471235
21711,80123,603523,602944472236
21811,81323,627523,626945472236
21911,83123,663523,662946473236
22011,90923,819623,818952476238
22111,93923,879723,878955477238
22212,01124,023524,022960480240
22312,04124,083524,082963481240
22412,10124,203524,202968484242
22512,11924,2391324,238969484242
22612,20324,407524,406976488244
22712,26324,527524,526981490245
22812,32924,659624,658986493246
22912,65325,307525,3061012506253
23012,67125,343525,3421013506253
23112,79125,583525,5821023511255
23212,82125,643525,6421025512256
23312,89925,799725,7981031515257
23412,92325,847525,8461033516258
23512,95925,9191125,9181036518259
23613,00126,003526,0021040520260
23713,04926,099626,0981043521260
23813,22926,459626,4581058529264
23913,31326,627526,6261065532266
24013,45126,903526,9021076538269
24113,46326,927526,9261077538269
24213,55327,107527,1061084542271
24313,61927,239727,2381089544272
24413,64927,299627,2981091545272
24513,76327,527527,5261101550275
24613,88327,767527,7661110555277
24713,90127,803527,8021112556278
24813,91327,827527,8261113556278
24914,00928,019628,0181120560280
25014,08128,163528,1621126563281
25114,15328,307528,3061132566283
25214,15928,319728,3181132566283
25314,24928,499628,4981139569284
25414,30328,607528,6061144572286
25514,32128,643528,6421145572286
25614,48928,979628,9781159579289
25714,56129,123529,1221164582291
25814,62129,243529,2421169584292
25914,66929,339629,3381173586293
26014,69929,3991329,3981175587293
26114,74129,483529,4821179589294
26214,78329,567529,5661182591295
26314,83129,663529,6621186593296
26414,87929,759729,7581190595297
26514,93929,8791129,8781195597298
26615,10130,203530,2021208604302
26715,16130,323530,3221212606303
26815,17330,347530,3461213606303
26915,23330,467530,4661218609304
27015,26930,539630,5381221610305
27115,40130,803530,8021232616308
27215,56931,139631,1381245622311
27315,62931,259631,2581250625312
27415,77331,547531,5461261630315
27515,79131,583531,5821263631315
27615,80331,607531,6061264632316
27715,92331,847531,8461273636318
27816,00132,003532,0021280640320
27916,09132,183532,1821287643321
28016,25332,507532,5061300650325
28116,30132,603532,6021304652326
28216,42132,843532,8421313656328
28316,49332,987532,9861319659329
28416,55333,107533,1061324662331
28516,67333,347533,3461333666333
28616,81133,623533,6221344672336
28716,82333,647533,6461345672336
28816,88333,767533,7661350675337
28916,93133,863533,8621354677338
29017,15934,3191934,3181372686343
29117,18334,367534,3661374687343
29217,29134,583534,5821383691345
29317,33334,667534,6661386693346
29417,35134,703534,7021388694347
29517,57935,1591135,1581406703351
29617,66935,339635,3381413706353
29717,68135,363535,3621414707353
29817,93935,879735,8781435717358
29917,98135,963535,9621438719359
30018,04136,083536,0821443721360
30118,13136,263536,2621450725362
30218,14936,299636,2981451725362
30318,19136,383536,3821455727363
30418,23336,467536,4661458729364
30518,34136,683536,6821467733366
30618,44336,887536,8861475737368
30718,46136,923536,9221476738369
30818,73137,463537,4621498749374
30918,77337,547537,5461501750375
31018,80337,607537,6061504752376
31118,89937,7991137,7981511755377
31219,16338,327538,3261533766383
31319,30138,603538,6021544772386
31419,31938,6392938,6381545772386
31519,37338,747538,7461549774387
31619,39138,783538,7821551775387
31719,43338,867538,8661554777388
31819,55339,107539,1061564782391
31919,55939,1191139,1181564782391
32019,66139,323539,3221572786393
32119,70939,419639,4181576788394
32219,75139,503539,5021580790395
32319,88939,779639,7781591795397
32419,91339,827539,8261593796398
32519,91939,839739,8381593796398
32619,99139,983539,9821599799399
32720,06340,127540,1261605802401
32820,24940,499640,4981619809404
32920,36940,739640,7381629814407
33020,39340,787540,7861631815407
33120,41140,823540,8221632816408
33220,44140,883540,8821635817408
33320,69341,387541,3861655827413
33420,75341,507541,5061660830415
33520,75941,519741,5181660830415
33620,77141,543541,5421661830415
33720,78941,579641,5781663831415
33820,87941,759741,7581670835417
33920,92141,843541,8421673836418
34020,93941,8791341,8781675837418
34120,96341,927541,9261677838419
34221,01142,023542,0221680840420
34321,08942,179642,1781687843421
34421,14942,299642,2981691845422
34521,17942,359742,3581694847423
34621,22142,443542,4421697848424
34721,34142,683542,6821707853426
34821,38342,767542,7661710855427
34921,41942,8391142,8381713856428
35021,61143,223543,2221728864432
35121,70143,403543,4021736868434
35221,71343,427543,4261737868434
35321,80343,607543,6061744872436
35421,89343,787543,7861751875437
35522,01344,027544,0261761880440
35622,07944,1591144,1581766883441
35722,13344,267544,2661770885442
35822,25944,5191344,5181780890445
35922,27144,543544,5421781890445
36022,34344,687544,6861787893446
36122,34944,699644,6981787893446
36222,40944,819644,8181792896448
36322,43344,867544,8661794897448
36422,46944,939644,9381797898449
36522,48144,963544,9621798899449
36622,54145,083545,0821803901450
36722,75145,503545,5021820910455
36822,85345,707545,7061828914457
36922,94345,887545,8861835917458
37023,09946,1991746,1981847923461
37123,27946,559746,5581862931465
37223,32146,643546,6421865932466
37323,33946,6791746,6781867933466
37423,45946,9191146,9181876938469
37523,56147,123547,1221884942471
37623,60347,207547,2061888944472
37723,66947,339647,3381893946473
37823,75347,507547,5061900950475
37923,81947,639747,6381905952476
38023,90947,819647,8181912956478
38123,98147,963547,9621918959479
38224,20348,407548,4061936968484
38324,23948,479748,4781939969484
38424,28148,563548,5621942971485
38524,47348,947548,9461957978489
38624,50949,019649,0181960980490
38724,55149,103549,1021964982491
38824,61149,223549,2221968984492
38924,68349,367549,3661974987493
39024,74949,499649,4981979989494
39124,97149,943549,9421997998499
39225,07350,147550,14620051002501
39325,22950,459650,45820181009504
39425,52351,047551,04620411020510
39525,60151,203551,20220481024512
39625,64351,287551,28620511025512
39725,67351,347551,34620531026513
39825,70351,407551,40620561028514
39925,79951,599751,59820631031515
40025,84151,683551,68220671033516
40125,91351,827551,82620731036518
40225,91951,839751,83820731036518
40326,11152,223552,22220881044522
40426,18952,379652,37820951047523
40526,45952,9191152,91821161058529
40626,50153,003553,00221201060530
40726,57353,147553,14621251062531
40826,63353,267553,26621301065532
40926,84953,699653,69821471073536
41026,87953,7591753,75821501075537
41126,89153,783553,78221511075537
41226,99353,987553,98621591079539
41327,14354,287554,28621711085542
41427,28154,563554,56221821091545
41527,47954,959754,95821981099549
41627,53955,0791355,07822031101550
41727,55155,103555,10222041102551
41827,58155,163555,16222061103551
41927,74355,487555,48622191109554
42027,77355,547555,54622211110555
42127,80955,619655,61822241112556
42227,89355,787555,78622311115557
42327,98355,967555,96622381119559
42428,00156,003556,00222401120560
42528,01956,039756,03822411120560
42628,40356,807556,80622721136568
42728,49956,9991356,99822791139569
42828,55957,1191957,11822841142571
42928,57157,143557,14222851142571
43028,64357,287557,28622911145572
43128,75157,503557,50223001150575
43228,79357,587557,58623031151575
43328,85957,719757,71823081154577
43428,90157,803557,80223121156578
43528,94957,899657,89823151157578
43628,96157,923557,92223161158579
43729,02158,043558,04223211160580
43829,03358,067558,06623221161580
43929,20158,403558,40223361168584
44029,33958,6791158,67823471173586
44129,36358,727558,72623491174587
44229,45358,907558,90623561178589
44329,48358,967558,96623581179589
44429,53159,063559,06223621181590
44529,72359,447559,44623771188594
44629,87359,747559,74623891194597
44730,26960,539660,53824211210605
44830,32360,647560,64624251212606
44930,38960,779660,77824311215607
45030,44960,899660,89824351217608
45130,67161,343561,34224531226613
45230,68961,379661,37824551227613
45330,77361,547561,54624611230615
45430,85161,703561,70224681234617
45530,98361,967561,96624781239619
45631,01962,0391762,03824811240620
45731,15162,303562,30224921246623
45831,25362,507562,50625001250625
45931,31962,6391162,63825051252626
46031,46962,939662,93825171258629
46131,64963,299663,29825311265632
46231,72163,443563,44225371268634
46331,79363,587563,58625431271635
46431,79963,599763,59825431271635
46531,85963,7191363,71825481274637
46632,00364,007564,00625601280640
46732,00964,019664,01825601280640
46832,14164,283564,28225711285642
46932,15964,3191364,31825721286643
47032,38164,763564,76225901295647
47132,53165,063565,06226021301650
47232,56165,123565,12226041302651
47332,57365,147565,14626051302651
47432,63365,267565,26626101305652
47532,77165,543565,54226211310655
47632,78965,579665,57826231311655
47732,84365,687565,68626271313656
47832,93365,867565,86626341317658
47933,02366,047566,04626411320660
48033,05366,107566,10626441322661
48133,11966,2391766,23826491324662
48233,17966,3591366,35826541327663
48333,19166,383566,38226551327663
48433,46166,923566,92226761338669
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112595,561191,1235191,122764438221911
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113596,581193,1635193,162772638631931
113696,731193,4635193,462773838691934
113796,779193,5597193,558774238711935
113896,851193,7035193,702774838741937
113996,989193,9796193,978775938791939
114097,001194,0035194,002776038801940
114197,241194,4835194,482777938891944
114297,511195,0235195,022780039001950
114397,523195,0475195,046780139001950
114497,829195,6596195,658782639131956
114597,871195,7435195,742782939141957
114697,931195,8635195,862783439171958
114797,943195,8875195,886783539171958
114898,123196,2475196,246784939241962
114998,321196,6435196,642786539321966
115098,369196,7396196,738786939341967
115198,453196,9075196,906787639381969
115298,459196,9197196,918787639381969
115398,561197,1235197,122788439421971
115498,573197,1475197,146788539421971
115598,621197,2435197,242788939441972
115698,639197,27911197,278789139451972
115798,669197,3396197,338789339461973
115898,711197,4235197,422789639481974
115998,849197,6996197,698790739531976
116098,963197,9275197,926791739581979
116198,981197,9635197,962791839591979
116299,023198,0475198,046792139601980
116399,041198,0835198,082792339611980
116499,089198,1796198,178792739631981
116599,173198,3475198,346793339661983
116699,251198,5035198,502794039701985
116799,551199,1035199,102796439821991
116899,623199,2475199,246796939841992
116999,689199,3796199,378797539871993
117099,761199,5235199,522798039901995
117199,839199,6797199,678798739931996
kmsp42.com // Vernier/SG // rev 2.2 // s(n)=g*s(n-1) mod q, digit-sum, g≥5
Vernier spec · Article