Table of contents 目次

  1. About 700...001 700...001 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 700...001 700...001 の形の素数
    1. Last updated 最終更新日
    2. Known (probable) prime numbers 既知の (おそらく) 素数
    3. Range of search 捜索範囲
    4. Prime factors that appear periodically 周期的に現れる素因数
    5. Difficulty of search 捜索難易度
  3. Factor table of 700...001 700...001 の素因数分解表
    1. Last updated 最終更新日
    2. Range of factorization 分解範囲
    3. Terms that have not been factored yet まだ分解されていない項
    4. Factor table 素因数分解表
  4. Related links 関連リンク

1. About 700...001 700...001 について

1.1. Classification 分類

Quasi-repdigit of the form ABB...BBC ABB...BBC の形のクワージレプディジット (Quasi-repdigit)

1.2. Sequence 数列

70w1 = { 71, 701, 7001, 70001, 700001, 7000001, 70000001, 700000001, 7000000001, 70000000001, … }

1.3. General term 一般項

7×10n+1 (1≤n)

2. Prime numbers of the form 700...001 700...001 の形の素数

2.1. Last updated 最終更新日

May 14, 2014 2014 年 5 月 14 日

2.2. Known (probable) prime numbers 既知の (おそらく) 素数

  1. 7×101+1 = 71 is prime. は素数です。
  2. 7×102+1 = 701 is prime. は素数です。
  3. 7×103+1 = 7001 is prime. は素数です。
  4. 7×104+1 = 70001 is prime. は素数です。
  5. 7×105+1 = 700001 is prime. は素数です。
  6. 7×108+1 = 700000001 is prime. は素数です。
  7. 7×109+1 = 7000000001<10> is prime. は素数です。
  8. 7×1045+1 = 7(0)441<46> is prime. は素数です。
  9. 7×10136+1 = 7(0)1351<137> is prime. は素数です。
  10. 7×10142+1 = 7(0)1411<143> is prime. は素数です。
  11. 7×10158+1 = 7(0)1571<159> is prime. は素数です。
  12. 7×10243+1 = 7(0)2421<244> is prime. は素数です。
  13. 7×10923+1 = 7(0)9221<924> is prime. は素数です。
  14. 7×101235+1 = 7(0)12341<1236> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1984 1984 年 12 月 31 日)
  15. 7×102196+1 = 7(0)21951<2197> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1990 1990 年 12 月 31 日)
  16. 7×104650+1 = 7(0)46491<4651> is prime. は素数です。 (Makoto Kamada / July 29, 2004 2004 年 7 月 29 日)
  17. 7×106119+1 = 7(0)61181<6120> is prime. は素数です。 (Makoto Kamada / July 29, 2004 2004 年 7 月 29 日)
  18. 7×107324+1 = 7(0)73231<7325> is prime. は素数です。 (Makoto Kamada / July 29, 2004 2004 年 7 月 29 日)
  19. 7×109543+1 = 7(0)95421<9544> is prime. は素数です。 (Makoto Kamada / July 29, 2004 2004 年 7 月 29 日)
  20. 7×1013494+1 = 7(0)134931<13495> is prime. は素数です。 (Yves Gallot / Proth.exe / February 20, 1999 1999 年 2 月 20 日)
  21. 7×1020310+1 = 7(0)203091<20311> is prime. は素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  22. 7×1020360+1 = 7(0)203591<20361> is prime. は素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  23. 7×10232920+1 = 7(0)2329191<232921> is prime. は素数です。 (Edward Trice / OpenPFGW / January 11, 2013 2013 年 1 月 11 日)
  24. 7×10830865+1 = 7(0)8308641<830866> is prime. は素数です。 (Edward Trice / OpenPFGW / May 12, 2014 2014 年 5 月 12 日)
  25. 7×10902708+1 = 7(0)9027071<902709> is prime. は素数です。 (Edward Trice / OpenPFGW / June 28, 2013 2013 年 6 月 28 日)

2.3. Range of search 捜索範囲

  1. n≤100000 / Completed 終了 / Dmitry Domanov / March 8, 2010 2010 年 3 月 8 日
  2. n≤300000 / Completed 終了 / Edward Trice / January 11, 2013 2013 年 1 月 11 日

2.4. Prime factors that appear periodically 周期的に現れる素因数

  1. 7×1013k+10+1 = 53×(7×1010+153+63×1010×1013-19×53×k-1Σm=01013m)
  2. 7×1016k+15+1 = 17×(7×1015+117+63×1015×1016-19×17×k-1Σm=01016m)
  3. 7×1018k+15+1 = 19×(7×1015+119+63×1015×1018-19×19×k-1Σm=01018m)
  4. 7×1021k+7+1 = 43×(7×107+143+63×107×1021-19×43×k-1Σm=01021m)
  5. 7×1022k+12+1 = 23×(7×1012+123+63×1012×1022-19×23×k-1Σm=01022m)
  6. 7×1028k+22+1 = 29×(7×1022+129+63×1022×1028-19×29×k-1Σm=01028m)
  7. 7×1032k+21+1 = 353×(7×1021+1353+63×1021×1032-19×353×k-1Σm=01032m)
  8. 7×1033k+13+1 = 67×(7×1013+167+63×1013×1033-19×67×k-1Σm=01033m)
  9. 7×1035k+1+1 = 71×(7×101+171+63×10×1035-19×71×k-1Σm=01035m)
  10. 7×1046k+31+1 = 47×(7×1031+147+63×1031×1046-19×47×k-1Σm=01046m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 29.23%. 捜索難易度 (周期的に現れる素因数で割り切れない項の割合) は 29.23% です。

3. Factor table of 700...001 700...001 の素因数分解表

3.1. Last updated 最終更新日

June 15, 2014 2014 年 6 月 15 日

3.2. Range of factorization 分解範囲

3.3. Terms that have not been factored yet まだ分解されていない項

n=205, 206, 210, 212, 214, 216, 217, 221, 223, 224, 225, 231, 232, 237, 238, 239, 242, 244, 246, 247, 249 (21/250)

3.4. Factor table 素因数分解表

7×101+1 = 71 = definitely prime number 素数
7×102+1 = 701 = definitely prime number 素数
7×103+1 = 7001 = definitely prime number 素数
7×104+1 = 70001 = definitely prime number 素数
7×105+1 = 700001 = definitely prime number 素数
7×106+1 = 7000001 = 197 × 35533
7×107+1 = 70000001 = 43 × 61 × 26687
7×108+1 = 700000001 = definitely prime number 素数
7×109+1 = 7000000001<10> = definitely prime number 素数
7×1010+1 = 70000000001<11> = 53 × 1320754717<10>
7×1011+1 = 700000000001<12> = 41149 × 17011349
7×1012+1 = 7000000000001<13> = 23 × 304347826087<12>
7×1013+1 = 70000000000001<14> = 67 × 1044776119403<13>
7×1014+1 = 700000000000001<15> = 964517 × 725751853
7×1015+1 = 7000000000000001<16> = 17 × 19 × 4397 × 4928775671<10>
7×1016+1 = 70000000000000001<17> = 421 × 7057 × 23561114333<11>
7×1017+1 = 700000000000000001<18> = 7993 × 87576629550857<14>
7×1018+1 = 7000000000000000001<19> = 883 × 11897 × 666346122451<12>
7×1019+1 = 70000000000000000001<20> = 151 × 463576158940397351<18>
7×1020+1 = 700000000000000000001<21> = 1709 × 409596255119953189<18>
7×1021+1 = 7000000000000000000001<22> = 353 × 6909827 × 2869829928971<13>
7×1022+1 = 70000000000000000000001<23> = 29 × 2546657 × 947828114837717<15>
7×1023+1 = 700000000000000000000001<24> = 53 × 13207547169811320754717<23>
7×1024+1 = 7000000000000000000000001<25> = 373 × 366097 × 12904369 × 3972430109<10>
7×1025+1 = 70000000000000000000000001<26> = 1201 × 4091 × 14247069835676331811<20>
7×1026+1 = 700000000000000000000000001<27> = 103723 × 6748744251516057190787<22>
7×1027+1 = 7000000000000000000000000001<28> = 131 × 1165583 × 3256553 × 14077495236829<14>
7×1028+1 = 70000000000000000000000000001<29> = 43 × 8597482263017<13> × 189346942156171<15>
7×1029+1 = 700000000000000000000000000001<30> = 38557 × 1527616714369<13> × 11884485990197<14>
7×1030+1 = 7000000000000000000000000000001<31> = 22751 × 311728909 × 987007539137739739<18>
7×1031+1 = 70000000000000000000000000000001<32> = 17 × 47 × 7620101 × 11497158881471824049299<23>
7×1032+1 = 700000000000000000000000000000001<33> = 8933779 × 318157145149<12> × 246275468603831<15>
7×1033+1 = 7000000000000000000000000000000001<34> = 19 × 313 × 86837 × 13554867923990783781946759<26>
7×1034+1 = 70000000000000000000000000000000001<35> = 23 × 2039 × 2683 × 556329776746211678345922851<27>
7×1035+1 = 700000000000000000000000000000000001<36> = 971 × 138064909 × 3116790401<10> × 1675281919706159<16>
7×1036+1 = 7000000000000000000000000000000000001<37> = 53 × 71 × 149 × 12484683968060611357138653116623<32>
7×1037+1 = 70000000000000000000000000000000000001<38> = 6994839869<10> × 57678426193<11> × 173502949270994053<18>
7×1038+1 = 700000000000000000000000000000000000001<39> = 317 × 1829879 × 1206747491361166227530967239507<31>
7×1039+1 = 7000000000000000000000000000000000000001<40> = 2887 × 357974663581<12> × 388814273833<12> × 17420345593451<14>
7×1040+1 = 70000000000000000000000000000000000000001<41> = 2219623680068849293<19> × 31536877457456530777157<23>
7×1041+1 = 700000000000000000000000000000000000000001<42> = 163 × 1667 × 2576171882187979581997710887270398681<37>
7×1042+1 = 7000000000000000000000000000000000000000001<43> = 9913661 × 13905242467<11> × 50779148014500236425667623<26>
7×1043+1 = 70000000000000000000000000000000000000000001<44> = 59 × 22787 × 5115254569928473549<19> × 10178683817570268053<20>
7×1044+1 = 700000000000000000000000000000000000000000001<45> = 631 × 5273 × 283802089 × 1184863787<10> × 625643439962731117589<21>
7×1045+1 = 7000000000000000000000000000000000000000000001<46> = definitely prime number 素数
7×1046+1 = 70000000000000000000000000000000000000000000001<47> = 67 × 1723 × 167483 × 192326681 × 2965271891<10> × 6348383739954260377<19>
7×1047+1 = 700000000000000000000000000000000000000000000001<48> = 17 × 809 × 624595408303267<15> × 81489529409530467454585396451<29>
7×1048+1 = 7000000000000000000000000000000000000000000000001<49> = 335774807663894173723<21> × 20847305516162787430315360787<29>
7×1049+1 = 70000000000000000000000000000000000000000000000001<50> = 43 × 53 × 15749 × 20707 × 10102501 × 9322977717564135646809458279333<31>
7×1050+1 = 700000000000000000000000000000000000000000000000001<51> = 29 × 24137931034482758620689655172413793103448275862069<50>
7×1051+1 = 7(0)501<52> = 19 × 107 × 36571 × 8844086717<10> × 10645616898971703821463777637649471<35>
7×1052+1 = 7(0)511<53> = 331 × 5066744745133<13> × 510879105643829609<18> × 81700154832720689143<20>
7×1053+1 = 7(0)521<54> = 277 × 353 × 28969223382025922341<20> × 247119327220915612206258469081<30>
7×1054+1 = 7(0)531<55> = 2076617 × 609738900073<12> × 5528378025258263660015531789025244561<37>
7×1055+1 = 7(0)541<56> = 1733 × 746807 × 8300940757<10> × 6515740551155259920298211947108344303<37>
7×1056+1 = 7(0)551<57> = 232 × 65171 × 3663073 × 80356697 × 68979546095780249020263358014353219<35>
7×1057+1 = 7(0)561<58> = 431 × 872008382213547623659<21> × 18625164201652084566455624905345069<35>
7×1058+1 = 7(0)571<59> = 23627 × 131910613 × 22459998357768729911032893796446983194067544151<47>
7×1059+1 = 7(0)581<60> = 1063 × 222317 × 4530622027<10> × 5040195171932521817<19> × 129714019157402149748609<24>
7×1060+1 = 7(0)591<61> = 6260983 × 1128365662841<13> × 128449842236097864451<21> × 7713865790225245405717<22>
7×1061+1 = 7(0)601<62> = 31379 × 33840991 × 1053222795517808050831153<25> × 62588654898405631375738453<26>
7×1062+1 = 7(0)611<63> = 53 × 263 × 30606318229<11> × 1640798810097282938237794899318827947449057529871<49>
7×1063+1 = 7(0)621<64> = 17 × 411764705882352941176470588235294117647058823529411764705882353<63>
7×1064+1 = 7(0)631<65> = 155747 × 177830773 × 2527385174946935080064493411253552809147917330305471<52>
7×1065+1 = 7(0)641<66> = 911 × 4111 × 8725373753730989<16> × 21421414613986237422732343423725139036463429<44>
7×1066+1 = 7(0)651<67> = 179 × 3413 × 11457997436682287736505343518947435618330831670559657700510863<62>
7×1067+1 = 7(0)661<68> = 61 × 877 × 1041340910419<13> × 1256538156552716729623377520533044743728407425653107<52>
7×1068+1 = 7(0)671<69> = 18777609181<11> × 37278441214352803927387266884878937133950993374868450991221<59>
7×1069+1 = 7(0)681<70> = 19 × 1371427934093335549122631<25> × 268640475720764515979633440698742187063360909<45>
7×1070+1 = 7(0)691<71> = 43 × 8704354929404289446554626939267521<34> × 187022127423243424834177726936224067<36>
7×1071+1 = 7(0)701<72> = 71 × 144169 × 23996248319<11> × 3102680142255775117<19> × 918517534965761229165416642252824613<36>
7×1072+1 = 7(0)711<73> = 2843 × 5021 × 438439 × 21337290059<11> × 52418250189967080049323234426128298639333271509067<50>
7×1073+1 = 7(0)721<74> = 443 × 96130808681091469<17> × 9742871641117961701<19> × 168711519586986544202026669610698003<36>
7×1074+1 = 7(0)731<75> = 109 × 2857 × 38873 × 247607413 × 233533721798448810420708866439356342455756308842550402673<57>
7×1075+1 = 7(0)741<76> = 53 × 181 × 503 × 1163 × 6197 × 42073 × 2038369 × 530935502475713<15> × 4420652191725997735888870130542131409<37>
7×1076+1 = 7(0)751<77> = 191 × 130916809033144889755051<24> × 16904389146780147811198177<26> × 165603602344810655649299293<27>
7×1077+1 = 7(0)761<78> = 47 × 2953 × 37507 × 224629 × 96912111559<11> × 6177041607312669385954348727264644004250809539685743<52>
7×1078+1 = 7(0)771<79> = 23 × 29 × 9052035909381906005231<22> × 1159380356943895725035755204692052417643220887504346013<55>
7×1079+1 = 7(0)781<80> = 17 × 67 × 7433 × 64957250287<11> × 2104847299828787515681<22> × 60473061555825894732690012430445685827309<41>
7×1080+1 = 7(0)791<81> = 1709686599653<13> × 29046208851986050526491<23> × 14095876190325431000221984046542857295930081687<47>
7×1081+1 = 7(0)801<82> = 1917887 × 80978482637540183<17> × 45071850576775516869573739586045324426052488100321878261081<59>
7×1082+1 = 7(0)811<83> = 15889141 × 14747139615121<14> × 298737559793260759146850073050986309527116916277283924218166541<63>
7×1083+1 = 7(0)821<84> = 252960538573<12> × 2767230034964493908395091215727935925673484749582139323602459161340773637<73>
7×1084+1 = 7(0)831<85> = 10784957 × 372912963901<12> × 1740492438042218441600795654554179784546137928409913148690052494393<67>
7×1085+1 = 7(0)841<86> = 353 × 8457781026839364786981083<25> × 23445899421709539751838042733667823710889768177163251387699<59>
7×1086+1 = 7(0)851<87> = 1577653981<10> × 5021705514998995631491<22> × 88355795491020302517303932518723295632640532937242680231<56>
7×1087+1 = 7(0)861<88> = 19 × 593 × 607 × 751 × 4051 × 336433221704369803061231886913782658143785716072528301445460952243148626329<75>
7×1088+1 = 7(0)871<89> = 53 × 1789 × 47133224833<11> × 123493451992541<15> × 6005920050222233<16> × 21118409050452993269124024319544304371346397<44>
7×1089+1 = 7(0)881<90> = 16529 × 6243817 × 397081413119922646343245506851472307<36> × 17081332072428353100585483934303689653375251<44>
7×1090+1 = 7(0)891<91> = 1499 × 4669779853235490326884589726484322881921280853902601734489659773182121414276184122748499<88>
7×1091+1 = 7(0)901<92> = 43 × 97 × 19559 × 8920251484891621327<19> × 138822435642830570322917<24> × 692906196600348666579091765215947239101551<42>
7×1092+1 = 7(0)911<93> = 3819198191<10> × 2448841163382511<16> × 74845419553176991590681628881541137812735208625185046937629625522401<68>
7×1093+1 = 7(0)921<94> = 1657 × 687312877619899348261627<24> × 6146403260884787336746557339603038490831997243563850080314216456459<67>
7×1094+1 = 7(0)931<95> = 151 × 4135397809<10> × 34135832070661090930273<23> × 59299334117980730945669<23> × 55378793445353177835710883773416871947<38>
7×1095+1 = 7(0)941<96> = 17 × 287191 × 142648321 × 1005105451437390945022542405895081794619391226822138248536885606765570286907375223<82>
7×1096+1 = 7(0)951<97> = 113 × 8646955367<10> × 22159917465967<14> × 323286999680819274641136173183578158286785122252061218497706849870919593<72>
7×1097+1 = 7(0)961<98> = 19035585744111823<17> × 52639681454775704063<20> × 69858385186026643924161034207590802616119188445855778196765649<62>
7×1098+1 = 7(0)971<99> = 1031 × 3502244828934538713156144576629<31> × 193862081747557226714681138891356596234903148078641452959796245499<66>
7×1099+1 = 7(0)981<100> = 22501 × 2136181 × 450480450735019<15> × 320186759530822356575497238971417<33> × 1009668610319485011591771706987015657322627<43>
7×10100+1 = 7(0)991<101> = 23 × 86614592761<11> × 35138169722365234470784794732495630356286437616663986391742843166619544065547252492235167<89>
7×10101+1 = 7(0)1001<102> = 53 × 59 × 8263 × 27091459723068776585671845560412194237561372315570146929757766357136418774520915593809384721601<95>
7×10102+1 = 7(0)1011<103> = 673 × 11813 × 494459880209<12> × 6789844280473557307399700579<28> × 262259904248636684132091769713556091513551905597773425759<57>
7×10103+1 = 7(0)1021<104> = 1259 × 2189639 × 1084487141<10> × 5118387310405609<16> × 54119446405814219<17> × 84525722518020314554799292267603061355961625076981291<53>
7×10104+1 = 7(0)1031<105> = 107 × 193 × 197 × 359 × 4951 × 373276191289916587<18> × 259342123229793379601513864522935022071345647264756418005901008032940784501<75>
7×10105+1 = 7(0)1041<106> = 19 × 6793 × 10059622147<11> × 4868902060907309917<19> × 1107312283062255288305948744024504672397484495735935683620222498413006197<73>
7×10106+1 = 7(0)1051<107> = 29 × 71 × 38677 × 2297189887169<13> × 25483902450521<14> × 15015025815375250460003131008522648759390248687445270890050110546562303343<74>
7×10107+1 = 7(0)1061<108> = 1009 × 3614887589<10> × 718466531357219922722261<24> × 107332746631731595459206997027<30> × 2488704264616083541639494383491405517168483<43> (Makoto Kamada / Msieve 1.17 for P30 x P43 / 2.6 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 1, 2007 2007 年 4 月 1 日)
7×10108+1 = 7(0)1071<109> = 463 × 21211 × 41941 × 676363 × 184385670043<12> × 195710949330785987011597433<27> × 696297751445264707829860395468478578666765855808932841<54>
7×10109+1 = 7(0)1081<110> = 829 × 954067 × 24398641671217086891103<23> × 3627429547287681541354288847808015802890765120425766657908550155246373222376169<79>
7×10110+1 = 7(0)1091<111> = 4139 × 169122976564387533220584682290408311186276878473061125875815414351292582749456390432471611500362406378352259<108>
7×10111+1 = 7(0)1101<112> = 17 × 411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882353<111>
7×10112+1 = 7(0)1111<113> = 43 × 67 × 63421 × 602579979031719044717<21> × 635780199408547170771151786827616042986701340502855247631626697770161565979510377353<84>
7×10113+1 = 7(0)1121<114> = 3779 × 58211 × 958787 × 9300697050713007875573999<25> × 2683449002182317784858528004222630179<37> × 132979625824198218520351735945182440927<39> (Makoto Kamada / Msieve 1.17 for P37 x P39 / 5.4 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 1, 2007 2007 年 4 月 1 日)
7×10114+1 = 7(0)1131<115> = 53 × 55127 × 2395840000328572342902204207026588005535074926473381704202063776576283032216175958703932702907967913541664171<109>
7×10115+1 = 7(0)1141<116> = 661 × 2879 × 8447 × 297546427300992344521<21> × 19564766569232601804888102765823<32> × 748036881256401812942007445925303222764775511468137579<54> (Makoto Kamada / Msieve 1.17 for P32 x P54 / 47 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 1, 2007 2007 年 4 月 1 日)
7×10116+1 = 7(0)1151<117> = 2699 × 19134803 × 259968494214599<15> × 30811056406169099<17> × 1692169458708502808995926188152381385415283020990663737179982049144249631733<76>
7×10117+1 = 7(0)1161<118> = 317 × 353 × 83014772529111787429408381<26> × 119793224689648388450802900474095381<36> × 6290373519699002449341406920469699944412118490423541<52> (Makoto Kamada / Msieve 1.17 for P36 x P52 / 53 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 1, 2007 2007 年 4 月 1 日)
7×10118+1 = 7(0)1171<119> = 233 × 2053 × 3761 × 68777 × 573478493821804383126117265442725302450908591<45> × 986482696674090871440722049772557294942194567424256350401987<60> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 1.23 hours on Core 2 Duo E6300@2.33GHz / April 1, 2007 2007 年 4 月 1 日)
7×10119+1 = 7(0)1181<120> = 228281899010583296767945037279<30> × 3066384163763888902949592988428636997602230211082647655130845684522014813451773825877452319<91> (Makoto Kamada / GMP-ECM 6.1.2 B1=50000, sigma=2781698972 for P30 / March 24, 2007 2007 年 3 月 24 日)
7×10120+1 = 7(0)1191<121> = 38528183 × 104817829 × 2761462141<10> × 58058856079593791465851800829<29> × 10811271738685902783389387496655065729541894101615562151663724263587<68>
7×10121+1 = 7(0)1201<122> = 2702603 × 14226607 × 24654257 × 4813855525596240239<19> × 11411793943210051785369918203<29> × 1344236113850473402608905646586208972724256388984102249<55>
7×10122+1 = 7(0)1211<123> = 23 × 163 × 277 × 46559 × 13868681 × 179176771 × 695948269 × 2888354505059136268957<22> × 2898376950410756486631189477453625810045121535972483258696394672621<67>
7×10123+1 = 7(0)1221<124> = 19 × 47 × 2029 × 1130793109766280907<19> × 111126294019581567532427817147389<33> × 1299891867398249140896400816452691<34> × 23651425575341536609870582458796781<35> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1122879459 for P34 / March 29, 2007 2007 年 3 月 29 日) (Makoto Kamada / Msieve 1.17 for P33 x P35 / 35 seconds on Pentium 4 3.06GHz, Windows XP and Cygwin / April 1, 2007 2007 年 4 月 1 日)
7×10124+1 = 7(0)1231<125> = 78294553894460255262812761337<29> × 894059631457365799463320070816535742477048704910755885627890918729562543989238260932341535315273<96>
7×10125+1 = 7(0)1241<126> = 894964537 × 4541136451<10> × 5846891135784131<16> × 29457959035603347204270465483050784873777468902669317754729056254546383817531217101681848833<92>
7×10126+1 = 7(0)1251<127> = 75679 × 630273181421687406409<21> × 146755311049399059157331290833994884894158824078691244501068729135129736367738511280481415418414796391<102>
7×10127+1 = 7(0)1261<128> = 17 × 53 × 61 × 96640340758217911<17> × 32026256230584280039<20> × 42343594919387034629<20> × 9718316999838019926867981506356760002003495074574166243273092803901<67>
7×10128+1 = 7(0)1271<129> = 463752403 × 23173252175870603<17> × 769395054618273598877816227<27> × 77869118298827494691063374224943<32> × 1087201972155263714852297993406422614113372949<46> (Makoto Kamada / Msieve 1.17 for P32 x P46 / 9.4 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 1, 2007 2007 年 4 月 1 日)
7×10129+1 = 7(0)1281<130> = 20339094283792370330464042356579607994600801891<47> × 344164784445593301152541755553359867327580661913692995263470054136783938426510011211<84> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 3.36 hours on Core 2 Duo E6300@2.33GHz / April 1, 2007 2007 年 4 月 1 日)
7×10130+1 = 7(0)1291<131> = 5703267238439297<16> × 365538164758125101<18> × 27761662426981271125283255479<29> × 7215493164143024352001386544961<31> × 167621646582705309569926513219943139907<39> (Makoto Kamada / Msieve 1.17 for P31 x P39 / 2 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 1, 2007 2007 年 4 月 1 日)
7×10131+1 = 7(0)1301<132> = 16573 × 827182080526619<15> × 60570823643539584765292420545299<32> × 843009197215127294834358695906019746493107625259983272341093175391722476971875477<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 6.67 hours on Athlon XP 3000+ / April 2, 2007 2007 年 4 月 2 日)
7×10132+1 = 7(0)1311<133> = 3917 × 8731 × 14638283495713663736241157708855869290229636409<47> × 13982677029538623333501754987296211103374639783010627959614701454655065820539607<80> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 5.29 hours on Cygwin on AMD XP 2700+ / April 2, 2007 2007 年 4 月 2 日)
7×10133+1 = 7(0)1321<134> = 43 × 31938787737893<14> × 2453625078680201566748816367059723<34> × 20773178568202312946561506523760891062078565941949791090519972188145838947872363815413<86> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 5.53 hours on Core 2 Duo E6300@2.33GHz / April 3, 2007 2007 年 4 月 3 日)
7×10134+1 = 7(0)1331<135> = 29 × 347 × 23753 × 1619918959<10> × 2906434717<10> × 7704541993<10> × 48751543478733853<17> × 236142858679332973<18> × 7012747867264861258628432471574510309408105143540607498174295309<64>
7×10135+1 = 7(0)1341<136> = 425027 × 16469541934982954024097292642585059302114924463622311053180150908059958543810157942907156486529091093036442390718707282125606137963<131>
7×10136+1 = 7(0)1351<137> = definitely prime number 素数
7×10137+1 = 7(0)1361<138> = 401 × 819319 × 94462361101393<14> × 15300445053292681<17> × 78763062104760693596513<23> × 258787878652319024306477498105531<33> × 72322138322265272755297913721084726006639421<44> (Makoto Kamada / Msieve 1.17 for P33 x P44 / 7.2 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 1, 2007 2007 年 4 月 1 日)
7×10138+1 = 7(0)1371<139> = 683 × 323565643 × 5455759339741710826253913205440113<34> × 5805768712228287085116276448327387554343755401317995474938232335903884659779580329249392645433<94> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 10.45 hours on Core 2 Duo E6300@2.33GHz / April 2, 2007 2007 年 4 月 2 日)
7×10139+1 = 7(0)1381<140> = 868451 × 4230765977679406827389503051<28> × 19051699252422062688206066138557556924036559617662919866782206797311788639804341499722390566839227421856001<107>
7×10140+1 = 7(0)1391<141> = 53 × 19597 × 61541309707039<14> × 52143054355223185883<20> × 10854524950314912484667997912049<32> × 19349001352421860990031887892254003455517463005159744816652778091636397<71> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P32 x P71 / 7.73 hours on Athlon XP 3000+ / April 3, 2007 2007 年 4 月 3 日)
7×10141+1 = 7(0)1401<142> = 192 × 71 × 288313621751<12> × 3053463834919049029013<22> × 3345092274004510611419<22> × 92148925276609062141707715311<29> × 1006412843425557458231103085699176491026342350208974913<55>
7×10142+1 = 7(0)1411<143> = definitely prime number 素数
7×10143+1 = 7(0)1421<144> = 17 × 419 × 22881959 × 1082531743<10> × 474685933669<12> × 255559769903549<15> × 39487949562433818587<20> × 828204943303538804294799840975534200719003469254996500030706812644159131312633<78>
7×10144+1 = 7(0)1431<145> = 23 × 809940785427965343526229739355042505157936405047381591533420897433<66> × 375765527014597615163944861799356289186159071363960150031523628164542872741439<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 14.94 hours on Core 2 Duo E6300@2.33GHz / April 3, 2007 2007 年 4 月 3 日)
7×10145+1 = 7(0)1441<146> = 67 × 599 × 412457 × 466747 × 1141698744217337<16> × 2434518084465653<16> × 1795008466954729168800209414936453<34> × 1815955371841082430332694563327821684185611841419005671789292422271<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 4.36 hours on Core 2 Duo E6300@2.33GHz / April 2, 2007 2007 年 4 月 2 日)
7×10146+1 = 7(0)1451<147> = 1611773 × 184985242269227057794527421<27> × 2347778282697900525301150769488586939894677015640579123650376087635529935797615271526247988318046013093790614783097<115>
7×10147+1 = 7(0)1461<148> = 283183 × 1902961 × 4224729381223999559<19> × 1257698080821893649965656268769551561386291<43> × 2444700608743657571446769617615111125524512245960929287873490693266909697683<76> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 15.32 hours on Core 2 Duo E6300@2.33GHz / April 5, 2007 2007 年 4 月 5 日)
7×10148+1 = 7(0)1471<149> = 3684925389750999011<19> × 22029725720760974922384230516355618304117854041<47> × 862303702875318574684178933529694530368164638218030948135135277879348224342523674051<84> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 23.53 hours on Cygwin on AMD XP 2700+ / April 10, 2007 2007 年 4 月 10 日)
7×10149+1 = 7(0)1481<150> = 353 × 4957 × 2883242209<10> × 27592287833712963754580710491390334851359<41> × 5028466680407615659824747536024164572850397380074196151582478698822339725661178413486182331051<94> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 18.01 hours on Core 2 Duo E6300@2.33GHz / April 10, 2007 2007 年 4 月 10 日)
7×10150+1 = 7(0)1491<151> = 12583 × 7011677 × 48703953167<11> × 565102429506584132764175102442628047540137331998418471757<57> × 2882707341673302681845839339823884543514446084956768454184275090583469569<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 15.03 hours on Cygwin on AMD 64 3400+ / April 10, 2007 2007 年 4 月 10 日)
7×10151+1 = 7(0)1501<152> = 3319 × 9029 × 20543 × 1049778553<10> × 5575410493<10> × 10983502889<11> × 1768772004902478309893971384441205809591822385192631640941577176302280245653996748505868572705067900666570182697<112>
7×10152+1 = 7(0)1511<153> = 121386524700439541<18> × 5766702702194301289915542121264216675448468498235675287504272647229475254071295684910157483266006251101179901778543432381439265648468061<136>
7×10153+1 = 7(0)1521<154> = 53 × 167 × 569 × 173483 × 58181687021<11> × 240810772871<12> × 438563879448152243<18> × 20339748706129911647205888791801144203<38> × 64105581640209598722446044764182036063686833229677824048410717867<65> (Robert Backstrom / GMP-ECM 6.0.1 B1=477500, sigma=1974761456 for P38 / April 4, 2007 2007 年 4 月 4 日)
7×10154+1 = 7(0)1531<155> = 43 × 5623 × 12401 × 79861933 × 1575233648179<13> × 193370246682439687632641395275617696499919070409857<51> × 959688618561589603204660736875782818852796083063317811556994979114317575491<75> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 28.11 hours on Cygwin on AMD 64 3400+ / May 3, 2007 2007 年 5 月 3 日)
7×10155+1 = 7(0)1541<156> = 1129 × 1193 × 55130793260966415361235729756577932205405829083406166227977587<62> × 9426911131444313172543736731542159160773688947699429609478209619825750212976152411926859<88> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 27.19 hours on Athlon XP 3000+ / April 3, 2007 2007 年 4 月 3 日)
7×10156+1 = 7(0)1551<157> = 421 × 5579837 × 2979850197200760481438850057555189304248982827177376528452273550927508874773969476203341379500713217992302967761753767199093514926176273846380507313<148>
7×10157+1 = 7(0)1561<158> = 107 × 131 × 257 × 44701 × 36067159 × 412688953 × 11433124763162139881<20> × 50150999103831809543<20> × 58723657563182981121109730736410322969118927<44> × 867361611497461809778725449710059255808380370747<48> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P44 x P48 / 4.26 hours on Athlon XP 3000+ / April 1, 2007 2007 年 4 月 1 日)
7×10158+1 = 7(0)1571<159> = definitely prime number 素数
7×10159+1 = 7(0)1581<160> = 173 × 19 × 59 × 461 × 124753 × 8695702266873779<16> × 3614107149313696436903098527751<31> × 173125876189407980940183608574563<33> × 4061870467967602945551870950350685652940570551689772588617215412107<67> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1329172899 for P31 / March 30, 2007 2007 年 3 月 30 日) (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=472219747 for P33 / March 30, 2007 2007 年 3 月 30 日)
7×10160+1 = 7(0)1591<161> = 94514160553<11> × 1036143335433866880995009<25> × 714794695072678527154522192706524446062218435179592437787846626018548054950234092183347409551014373062624055379118229312253913<126>
7×10161+1 = 7(0)1601<162> = 229 × 242467 × 1517671 × 32593933 × 46943545972117<14> × 638839674622067064620477103409<30> × 8498215560590040816704776139546515219193719251278278781985430547992584465308428088850076281224633<97> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=4012320279 for P30 / March 30, 2007 2007 年 3 月 30 日)
7×10162+1 = 7(0)1611<163> = 29 × 331 × 40665431 × 1645805022353<13> × 2473251925797485004201944893565647<34> × 4405547920203456458779052457232424346149863777109139414484987392817028714950420487387989307793267723460519<106> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1594068802 for P34 / March 30, 2007 2007 年 3 月 30 日)
7×10163+1 = 7(0)1621<164> = 2621 × 637097 × 6177922939<10> × 156791141329<12> × 402780568113496127134113047287312945816114000773181<51> × 107446665123360825440701365404164787206317314310967090805791720700790075639081056243<84> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs / 46.82 hours on Msieve 1.33 / April 4, 2008 2008 年 4 月 4 日)
7×10164+1 = 7(0)1631<165> = 1493 × 4603 × 119429 × 79514415457<11> × 4011137403054399824497281514214954974908736320403030763817761<61> × 2674077881194096559726374285341983014251581688108917524458192840920208139039746043<82> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 51.39 hours on Cygwin on AMD 64 X2 6000+ / January 23, 2008 2008 年 1 月 23 日)
7×10165+1 = 7(0)1641<166> = 1090967 × 11436012877<11> × 1934565819362618078884501610509<31> × 290020221573261953762717502067915448761963064267460125187429746035634212740848140784915846874690427361518315806184905871<120> (Makoto Kamada / GMP-ECM 5.0.3 B1=91890, sigma=2976108834)
7×10166+1 = 7(0)1651<167> = 23 × 53 × 31327 × 34726262056239405863392591<26> × 1913290242196232539268012066652201280412112493917178819<55> × 27589042770237067407217839796789774556735213612294539601853969868354417611828713<80> (Justin Card / GGNFS / 93.42 hours on AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ 3 GB RAM Running Ubuntu Linux 8.04 64-bit / September 24, 2008 2008 年 9 月 24 日)
7×10167+1 = 7(0)1661<168> = 94126111912362384454419640507<29> × 45944168788570289296719424358942927<35> × 161866703314530544206931137643404221120769747950795429104385791774237543764981165611916824698958062426909<105> (Robert Backstrom / GMP-ECM 6.0 B1=1160000, sigma=3892956357 for P35 / February 9, 2008 2008 年 2 月 9 日)
7×10168+1 = 7(0)1671<169> = 39874420514155621405930029196213<32> × 175551140549239192504522004124894766597610705708295751211644739831183679452961360088433039867758405935282447575807483052676447787480773277<138> (Jo Yeong Uk / GMP-ECM 6.1.1 B1=1000000, sigma=1122796349 for P32 / April 6, 2007 2007 年 4 月 6 日)
7×10169+1 = 7(0)1681<170> = 47 × 151 × 13679 × 69581271307931<14> × 39537414818425401700082179<26> × 262100745709398798485248290413230243877973456030393217395713586895123047106795590404763309503410957879426068029019824408023<123>
7×10170+1 = 7(0)1691<171> = 499 × 384941 × 3687989 × 27612726356486912972395700594939<32> × 35785279872327545208647282141323368359931221872796464844278919978115969773916536537918582989981782789362311769452347991469809<125> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3105718241 for P32 / March 30, 2007 2007 年 3 月 30 日)
7×10171+1 = 7(0)1701<172> = 191 × 11351 × 200087 × 199743193690849<15> × 503783621180657<15> × 640757244242093195737825269513973688101421<42> × 250266153200200437607062854749076319929624557778915248618363969037755267406743304872865851<90> (Robert Backstrom / GMP-ECM 6.2.1 B1=7574000, sigma=1044013304 for P42 / August 13, 2008 2008 年 8 月 13 日)
7×10172+1 = 7(0)1711<173> = 2221 × 13553 × 40608976450967<14> × 1250211931636399<16> × 1729886492471252763870965272592750279236691610626561<52> × 26478339906294335929258650981294604168689957012271868771914007551648773172005815302429<86> (Sinkiti Sibata / Msieve 1.40 snfs / March 15, 2010 2010 年 3 月 15 日)
7×10173+1 = 7(0)1721<174> = 62473 × 1835807801<10> × 3510906612731053298436347<25> × 992595949608553727415223604789713<33> × 1626878119033344343859043164870647<34> × 1076543722683910823425060595208148712881299436943475382391159481127061<70> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=3918156657 for P34, pol51+Msieve 1.36 gnfs for P33 x P70 / 4.00 hours on Opteron-2.6GHz; Linux x86_64 / August 7, 2008 2008 年 8 月 7 日)
7×10174+1 = 7(0)1731<175> = 9404860453<10> × 744295998327876518892565858680263822942658179598191216245577184642146226217908562518466109983014332769919728228422657277677312922486591625348383039958328236558259117<165>
7×10175+1 = 7(0)1741<176> = 17 × 43 × 16106554067<11> × 546424038802294846052914856058998495168369<42> × 50847756028512910420533268455094582971422236487293<50> × 213981604431953258247908719407251822585834319843385691315588724389559589<72> (matsui / GGNFS-0.77.1-20060722-nocona / April 22, 2009 2009 年 4 月 22 日)
7×10176+1 = 7(0)1751<177> = 71 × 8573471 × 805581827 × 284095648103<12> × 8413635332369<13> × 1772201439222433182847040694601969<34> × 5991250959750702185019813412247610703<37> × 56246368184668911475605266297942702738852214410521358324628735307<65> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=2065754217 for P34 / August 6, 2008 2008 年 8 月 6 日)
7×10177+1 = 7(0)1761<178> = 19 × 1979 × 516977 × 9303190260631<13> × 1144423847222026461367968957138227525885867288802638771749<58> × 33822727063690530921073941085820990588251786480748806377471603628050005835995594966694479465627627<98> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / April 9, 2010 2010 年 4 月 9 日)
7×10178+1 = 7(0)1771<179> = 67 × 557 × 38661967709<11> × 36637648795722647<17> × 5818134233320100182457<22> × 1662167533338508964204747<25> × 1783080582215628427498691<25> × 76793947157016219502762538117085488564563018478796006649288560115315417360157<77>
7×10179+1 = 7(0)1781<180> = 53 × 4944817 × 243957911 × 215486917894351463<18> × 50808471665857893437517964208287426218431300280849428134175259933029146285367548593237918762046686401653261335756691370412456767128823237057384557<146>
7×10180+1 = 7(0)1791<181> = 2151725922138758923261663<25> × 7087520924662674679818007<25> × 7661490366139566446798966070947300571261638662078538221<55> × 59910573124188012800381184539160322443650207109608875457020039287966758514941<77> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / April 12, 2010 2010 年 4 月 12 日)
7×10181+1 = 7(0)1801<182> = 353 × 321719196896439418987<21> × 1163758540886892142057804574557793566313774324590007<52> × 15290044086607599920811066936958074079383149382493153<53> × 34639749264300926764106750653359853464270168546755427221<56> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / April 15, 2010 2010 年 4 月 15 日)
7×10182+1 = 7(0)1811<183> = 109 × 11621 × 84792619 × 8678619303260101422863539087<28> × 750964406660170807841205276154203602906351985572563625545734283586039282401294289072997102053862402904598025459534302886442020907461631823053<141>
7×10183+1 = 7(0)1821<184> = 183343 × 20379849399125231<17> × 1873409578113106928328966276808224641434894106903238236146532586172224571192149315108338077096513679903851828807831202801279484505307072253390163416596493461284897<163>
7×10184+1 = 7(0)1831<185> = 149 × 1873 × 31839019 × 22998826951<11> × 10720385743213976744960363751202582332539223737226730163789310098069<68> × 31952012548531934919441863659102516564697183016636115618338798373100704924878111429176293511933<95> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / April 20, 2010 2010 年 4 月 20 日)
7×10185+1 = 7(0)1841<186> = 219465968201<12> × 2982379230977<13> × 5719598275459<13> × 124799843126040139853583973137905993<36> × 1498264268835317638740861311886614620581341911339706843765757747502239267429695244435778601442079954910294221994299<115> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=3255657909 for P36 / March 28, 2010 2010 年 3 月 28 日)
7×10186+1 = 7(0)1851<187> = 337 × 1382021 × 2637072207006861879397652165594950129472178505487241969697937369829151<70> × 5699430672501051047902541639580244876448692243705493980775805037402308092806940908138307601033399740413046563<109> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / April 26, 2010 2010 年 4 月 26 日)
7×10187+1 = 7(0)1861<188> = 61 × 97 × 13477 × 11051321 × 1250700283367<13> × 63509076905737709607773998521570759812813213872065422716685196728502463710090990822013222977121418889253667306124842970619057148376308515425352173304503501688127<161>
7×10188+1 = 7(0)1871<189> = 23 × 1607 × 2521 × 61075211 × 123003227052651152950005200833711850969402456441204373766640629730402381369407452911904359537763602419186641694035978494527928170552400569670237539931553001319142163758580411<174>
7×10189+1 = 7(0)1881<190> = 126751 × 442961 × 407211125311<12> × 306169214480545484095401530789754572073207974170533359013961672659299954901090426329959390170917046029755821875856455791456029698311298216039897481418256760523924811281<168>
7×10190+1 = 7(0)1891<191> = 29 × 18168419302228497779<20> × 102557119002802823101<21> × 73316966906831314464051823<26> × 355098879311614202406460897590438184483<39> × 49758043313543013512337916205691953866857075376389549242886554315519833104914284256879<86> (Robert Backstrom / GMP-ECM 6.0 B1=1540000, sigma=898811196 for P39 / January 27, 2008 2008 年 1 月 27 日)
7×10191+1 = 7(0)1901<192> = 17 × 277 × 4177 × 6818267 × 73528321631<11> × 41697361934200639<17> × 500881825913992314314860812685238515894838537806105643255432993<63> × 3398852862293089914345296433984518611686392712942554926958953192271806981140902754230183<88> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / May 5, 2010 2010 年 5 月 5 日)
7×10192+1 = 7(0)1911<193> = 53 × 60342221562520298675808271913387<32> × 2188773768650039140461457627089616957466162048627827553532370714156265666695112700205642303636943536844392668804225938184082442940320634356324063411380105589591<160> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=103207662 for P32 / April 1, 2007 2007 年 4 月 1 日)
7×10193+1 = 7(0)1921<194> = 9241 × 219293 × 6936938890086167066622757<25> × 416799264204760872538311419626193147745097254548873427679161241223<66> × 11947017190738494041966249432399123577044765342551316421496675140896193359494307125720749979007<95> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / May 16, 2010 2010 年 5 月 16 日)
7×10194+1 = 7(0)1931<195> = 44402740939<11> × 4350604316543<13> × 3229114677266322853<19> × 142681828165844793819666383<27> × 7864779302790260093837923822449676279939337792435192801017306821724144034045223318387861266653023159472973073168992395224536087<127>
7×10195+1 = 7(0)1941<196> = 19 × 1172079999382367<16> × 27345778536021534559891834827169314256710931648974916905148450411<65> × 11494680164184052663991007499150815250455971265649181086139724662638358173031963613986904051922820749271724449479567<116> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / May 23, 2010 2010 年 5 月 23 日)
7×10196+1 = 7(0)1951<197> = 43 × 317 × 1372963 × 155958192256776607461677914766427083<36> × 594199120193077001645309055358241879<36> × 40361871151463849042790718793758421235896740788692674390815928089148405647260192809195875203996485372867989826323481<116> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=6156168597 for P36(5941...) / March 28, 2010 2010 年 3 月 28 日) (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=2237009929 for P36(1559...) / March 29, 2010 2010 年 3 月 29 日)
7×10197+1 = 7(0)1961<198> = 653 × 2819 × 21323 × 39733 × 350290855167544918210905040724772517249847051<45> × 6649862800656602065695357765877549945685231793320527<52> × 192685322413049850087575204207648665571479543825609940246715415270238306453252156307101<87> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=11000000, sigma=8526517687 for P52 / May 25, 2010 2010 年 5 月 25 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P45 x P87 / June 3, 2010 2010 年 6 月 3 日)
7×10198+1 = 7(0)1971<199> = 23549 × 131245193 × 15232681991<11> × 148684531570815410532680649579255676722504892797241305592208580365871104569745716862242777344488021346683252216593937137486891010964381392274126000451717972340113579633503929323<177>
7×10199+1 = 7(0)1981<200> = 725090659 × 9164565419785211353947485730559067633598909453060553091<55> × 12601421708673267908518642679052842255542705603661102143494833<62> × 835938463122991700708024721076119775411047328115374627215348137414234571113<75> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / June 21, 2010 2010 年 6 月 21 日)
7×10200+1 = 7(0)1991<201> = 118799 × 6220943 × 3123018700066548676649<22> × 303287456024033375811688864745842636310948539879346801763295868948372563194612386405922432317470705052355289515702782896341928269340989242839814851203707940413910774457<168>
7×10201+1 = 7(0)2001<202> = 223 × 1031 × 29205221 × 168536293 × 6185582126784729953345591238789488809610648564335378231562125446493136738665677193171516688211981203791887044531146436338622925129281495144420814833996734962954806193040209368851409<181>
7×10202+1 = 7(0)2011<203> = 197 × 4327 × 706923507729536474071232987<27> × 1178444579138691834797246652349<31> × 98574216065071930107349981798201895094656280748425636584792892050810619755899291964036739441047581060611708600290153928841373984753022227333<140> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3326811782 for P31 / November 11, 2010 2010 年 11 月 11 日)
7×10203+1 = 7(0)2021<204> = 163 × 2663 × 88947356043536642176654277<26> × 7342174264627978992997154461<28> × 2469343674961373256345362706804394650371359896725419671086664147890548652863307713721245169933367831358545000422329643809331139061257457043174957<145>
7×10204+1 = 7(0)2031<205> = 218527 × 241534907923<12> × 3260699035026944417<19> × 196111313915686475978431<24> × 53777904637353086218640483293339<32> × 3856521786160803640690544065730090348140212555829192120277270933053775455523420956866958793848702569300311829907777<115> (Dmitry Domanov / November 15, 2010 2010 年 11 月 15 日)
7×10205+1 = 7(0)2041<206> = 53 × 47461109 × 417152000935751155416755619152059727<36> × [66709848964815759202156595466644097737481139983634577335404822249747000762497038734315266313600746536051326289263045669577067644557455081778699625226486641079719<161>] (Serge Batalov / GMP-ECM B1=4000000, sigma=1295074837 for P36 / November 15, 2010 2010 年 11 月 15 日) Free to factor
7×10206+1 = 7(0)2051<207> = 4373821304351<13> × [160043118200474352418041425841769474249544904255743169384460556266487640838118437695053219844355195868932858042067958894196777278337782584293580530082157474886441480078093981612877756574638493151<195>] Free to factor
7×10207+1 = 7(0)2061<208> = 17 × 269 × 368243 × 1417415988991662763961289953<28> × 2932682253621565551038172600503139175513084138231336518857873531344217824484202502381370937418160222920854917678447738930119798800860770550384474165852862317383359026806103<172> (Serge Batalov / GMP-ECM B1=2000000, sigma=666130825 for P28 / November 14, 2010 2010 年 11 月 14 日)
7×10208+1 = 7(0)2071<209> = 113 × 3527819 × 13997279 × 268021289 × 110265990881<12> × 80370775171134947036778363140241781703336788459<47> × 157421792428752365365763743706104500987740262954270733<54> × 33550252746945825953313415264113494427781075811237214122147424170503448299<74> (Dmitry Domanov / November 18, 2010 2010 年 11 月 18 日) (Erik Branger / GGNFS, Msieve gnfs for P54 x P74 / December 20, 2010 2010 年 12 月 20 日)
7×10209+1 = 7(0)2081<210> = 7121 × 431115365267584905520305468152137<33> × 1783917673245708457469229208927597<34> × 127817036639248008722067016095671734243759299767871392978999220392871549636868734201929321040421590323880828005510404659535924858586713043629<141> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=1420889416 for P34 / November 12, 2010 2010 年 11 月 12 日) (Dmitry Domanov / November 15, 2010 2010 年 11 月 15 日)
7×10210+1 = 7(0)2091<211> = 23 × 107 × 373 × 11867 × 19729870764078520909588859<26> × [32569599007361899567079864120584144323423349030760352116741117184754927801687184850999490943132045235215743970686674842696866250793849249005718936880470206909458224251134201289<176>] Free to factor
7×10211+1 = 7(0)2101<212> = 67 × 71 × 13356510362839349608365680487750571733737046201101<50> × 1101721648212121478714405730779404200931268648572143559312472462431416591754792212986578202191524979642406693382680891087439429777288573822184244873326308884593<160> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs / July 14, 2012 2012 年 7 月 14 日)
7×10212+1 = 7(0)2111<213> = 751 × 1147718497<10> × 5991304308220291<16> × 535946401441503011042167079<27> × [252918142839932780165339870424403997004000076408742793014378799975608851876970962925327610894916805573810309394698043065851198131915804608586787549961575940947<159>] Free to factor
7×10213+1 = 7(0)2121<214> = 19 × 353 × 1043685701505889369315640375726852542120172953630535261666915163262263306992694200089458774414790517369912032205158789324586253168331593857164156851051140599373788579096466378410615774563888474727896227821678843<211>
7×10214+1 = 7(0)2131<215> = 379 × 293194973 × 451231481 × [1396056255115913740035180757171670218705774118625238671437132549222915968867626430936257261167135522510197635627410548455313525193736849918619065775731679194042076867267250539692485137185888729863<196>] Free to factor
7×10215+1 = 7(0)2141<216> = 47 × 383 × 102715184594445396778765847<27> × 20912625264198459845976352155351133<35> × 18103318898263437971241516394207395730673429252031422051259604133262539637695014194312548640522965469814750973629373972283191172162961310272253845274851<152> (Dmitry Domanov / November 15, 2010 2010 年 11 月 15 日)
7×10216+1 = 7(0)2151<217> = 4817 × 34297 × 97667039138051742991<20> × 1398482982892631110306664611<28> × [310213041803497240940303475385940745003504507125957938895528409418236436784971316913277954398203898436574481837505207184332892916465128502140470163574306661560349<162>] Free to factor
7×10217+1 = 7(0)2161<218> = 43 × 59 × 307120292082125004338721170713355714702878191829303<51> × [89839858794651618726230218748922466885882896885672936418293839392553459688939999940266350324207825510592213229520647090569552250660838473379052918472600578031281391<164>] (steinrar / GMP-ECM B1=110000000, sigma=948868638 for P51 / November 12, 2011 2011 年 11 月 12 日) Free to factor
7×10218+1 = 7(0)2171<219> = 29 × 53 × 11299 × 15902399 × 781107297449257<15> × 8296125915237033141913<22> × 4030584577683355044611539<25> × 97043722871827232176009971021856700716877536886603599879848036916685565242246400989296269948049876359456080554436682694691365943991097303459927<143>
7×10219+1 = 7(0)2181<220> = 39045823 × 609417979528764089657778747586539132988865504417<48> × 294176648490820789057573108591943912590875309786072461096416890513841222330750935088901852144263146018239165068381753823067935741802840349435272162138730720957586911<165> (Dmitry Domanov / November 19, 2010 2010 年 11 月 19 日)
7×10220+1 = 7(0)2191<221> = 6098331851078413<16> × 11478548840798387137451053755288833087461074071207168027047800671333964899700354107594102479970341588129177328537942632557690620230114762476525649986299539311119114469455790997607119734374165483614072769477<206>
7×10221+1 = 7(0)2201<222> = 5453813 × 16678940063369088847<20> × [7695367222850007446939155120698103502243726756367553626404036709423752904985885514746794465968333153799799893580631574634463721926560299185891570806201957364704460298630450543531431010475762937491<196>] Free to factor
7×10222+1 = 7(0)2211<223> = 9949 × 3168774904387<13> × 222037955222887910951458491900319816104093672950131124212907578301474941072635950751527414485505064548326887684731527169822037100028883770218338276378153408534237585230642633404035326307699021150639703844327<207>
7×10223+1 = 7(0)2221<224> = 17 × 6669557559828565337201286595902169703354432202743<49> × [617379342165744744109799966482118844711196884975928259583020464199573759732663570662779076969433118076186181804226417458232437350311559939675815199894074893634818398170973271<174>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3323799218 for P49 / June 11, 2011 2011 年 6 月 11 日) Free to factor
7×10224+1 = 7(0)2231<225> = 224793275557<12> × [3113972151816007447013189571679372563857123759292096554375580048881808909865441647242111680103169430591438410070625135875002485361822392833882273353273463106165791880854326813665310782933439151620858731415260027693<214>] Free to factor
7×10225+1 = 7(0)2241<226> = 1201 × 478874853525562275936252215723<30> × [12171188833293089290292479931908456261787097498248706696450413909245100902250661655365377888287607217151976052121506333457499333048019262560336124739567945376970290664634422008182727869653798387<194>] (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=1801561398 for P30 / November 12, 2010 2010 年 11 月 12 日) Free to factor
7×10226+1 = 7(0)2251<227> = 2269 × 3381666480297327860425114235631204129434179290396503053428265259<64> × 9122896996349490787144837178265322695297702492214967336086263058588890631244327583177808077554177644936587233481871642192919744426627371055805113066090259403231<160> (RSALS + Mathew / ggnfs-lasieve4I14e on the RSALS grid + presumably msieve for P64 x P160 / June 19, 2012 2012 年 6 月 19 日)
7×10227+1 = 7(0)2261<228> = 59203222577021<14> × 37649924970181133083937974730563<32> × 598594278748117459436527048313419398053<39> × 524633497131945389250424608128573206971763184590640963225054416635206212027490536041980802924352652716665178446272166652268960773241763362833979<144> (Dmitry Domanov / November 15, 2010 2010 年 11 月 15 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1572601963 for P39 / October 13, 2011 2011 年 10 月 13 日)
7×10228+1 = 7(0)2271<229> = 20353 × 251287 × 21065899 × 35393857 × 1835657683061918419356417259782729499671965314146827684029436312068112445435380118859580457463464087004610735168442344583488248913112493500186612368961935987440158173340638028519457709004534723259178822837<205>
7×10229+1 = 7(0)2281<230> = 1759 × 195299165021773<15> × 203766044037815600043537052978080411310551628555710745434321154360471741477663965708306063128879288959369507712458719675936841159256936081921175568544731937914357747888143977124275697722801434320932304353847170843<213>
7×10230+1 = 7(0)2291<231> = 180419 × 39429349 × 2056291084747<13> × 58266600850017604186783<23> × 1681088351546026291926710209<28> × 488541371719672581270794320183023544635515441959668303962747823092563280654021582052113512382872862873527700620405625842831545195079781843000153328428779219<156>
7×10231+1 = 7(0)2301<232> = 19 × 53 × 1847 × 2796760898443<13> × 45142570679542361<17> × 93087706217217634429986159809414389733741<41> × [320234205846237904833972629142006344497727907611330818159087737426562946546626881678420824871211995126111540021733078784236635329891281986055023901047144383<156>] (Dmitry Domanov / November 17, 2010 2010 年 11 月 17 日) Free to factor
7×10232+1 = 7(0)2311<233> = 23 × 6016019 × 763882319 × 263322653357<12> × 5317042635101<13> × [473016381636279983288151635048999586848492227119450738708156363427827127528531746556006061462638394612750572140926217301703420017728668238865629608978062229225127796895066825869590129600657931<192>] Free to factor
7×10233+1 = 7(0)2321<234> = 497239 × 22928157919<11> × 54158701857167<14> × 70855963055955691987199<23> × 1903800766466122369324945189<28> × 189543166294795042650073348157<30> × 26547637053502792160054346940797959<35> × 124691387241289665574772668101343859<36> × 13394517787448017514942164469099553692525566325517605509<56> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3456759372 for P30 / November 13, 2010 2010 年 11 月 13 日) (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=3689282462 for P35 / November 14, 2010 2010 年 11 月 14 日) (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=2493959216 for P36 / November 15, 2010 2010 年 11 月 15 日)
7×10234+1 = 7(0)2331<235> = 2060657 × 52011882861871<14> × 247169656628024140765913<24> × 264237590965015885596330282098336735904782708376090098122274921738311838169015585098773580766193517291513968711453714407597064737951433149511957828696426602684550885723579262914909856907461591<192>
7×10235+1 = 7(0)2341<236> = 7723 × 1833107324923520191156936657<28> × 4944519709200589391448681510975040724382724446868960230835984376766520601376095020250527999874812518679007660569215148961653786236991395594527949505753048300725929769928772863927829222270605355727756547091<205>
7×10236+1 = 7(0)2351<237> = 59189203355853243931061057301042720446445702001<47> × 11826481187650191962966819500530227345838068917545220452621159581797160317624295437266543822896701383581107190421605005223005597439008807544524908954896208472704999275601417951241418358298001<191> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=813633075 for P47 / November 20, 2010 2010 年 11 月 20 日)
7×10237+1 = 7(0)2361<238> = 585149 × 311438359283<12> × 822099059275608758748336031<27> × 1290612229521958876647719039<28> × [36202581738856918551615300539194749838465896816281679154227268019997034156113283859924829519139280407449151737597739781244166722269031425342456226528851536598892160567<167>] Free to factor
7×10238+1 = 7(0)2371<239> = 43 × 1532029 × [1062582351080943015120228081176494822256309526717168372260607672327290786756768994915649708312795766951220654378589924985784545611021055570218348681146314447536036228107710694103534715104290863885067935519527705825351202062223395583<232>] Free to factor
7×10239+1 = 7(0)2381<240> = 17 × 11467 × 25648433 × 3440243441390452951<19> × [40695772206103227264017807784434045711473192813664223910584354791158780966904831417627095017411680278360963450665962031693877514692769353426527883264232875592985031207038620197478361258515670315871066575009173<209>] Free to factor
7×10240+1 = 7(0)2391<241> = 24514526286010756573241467309988425845133218566461228511820653752143043<71> × 285544983342980536453387034329966191768771431300906682064959974685376008253085126961450280256025185961390049564091983998091149743432726045136098367062340029538606477820907<171> (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.53 (SVN 965M) for P71 x P171 / June 15, 2014 2014 年 6 月 15 日)
7×10241+1 = 7(0)2401<242> = 3049 × 123983 × 489707849 × 1373226096173<13> × 275359054695736996442672015011062302993980518319785268500205181844498043298944090864940850815568923557834579513304445117348641651202967375001550863442064575283215745767294573539355751476427535367677571579350290939<213>
7×10242+1 = 7(0)2411<243> = 5366461 × [130439781450009605958191068564553063927977861014922124655336170336465689399401206866126484474591355457535235977676908487735213206617918214629715933834234516937698792556211626246794675299047174665016665545505688013012672597452958290389141<237>] Free to factor
7×10243+1 = 7(0)2421<244> = definitely prime number 素数
7×10244+1 = 7(0)2431<245> = 53 × 67 × 151 × 179 × 2115187 × 10677031187735930721468898731731821119079<41> × [32293722533073525767151757621595371624391272004174995754345894156354618878356094370450651536695514834883159376899880361428245994074290833967933749911115094394124422099230021384106636638084103<191>] (Dmitry Domanov / November 19, 2010 2010 年 11 月 19 日) Free to factor
7×10245+1 = 7(0)2441<246> = 353 × 69088109 × 28702520036569387095248427104597982701022090674069788147872723078848493063923908818664752734629080425443875749874724458252488586998813765891492239525576928713017724950082019454030359575645471813145194535013106259714196460074190625601413<236>
7×10246+1 = 7(0)2451<247> = 29 × 71 × 164789 × 3197521979896292061856819850475614700608163083047<49> × [6452082866915392006294917517770105988858810176348311539607924360603949584569388727504613158416319459284029675494493210762674078325607129339822456456439096296345401457837145572159488683341233<190>] (processing-home / GMP-ECM B1=110000000, sigma=99288629 for P49 / June 18, 2011 2011 年 6 月 18 日) Free to factor
7×10247+1 = 7(0)2461<248> = 61 × 29377459 × 81949081 × 4116237974961476657<19> × [115800227753795263531073322007471921978816404369700216495884850277396090338973913210758230164953381187620584165859013864314700064865090578149219160588854390266801196997653308267301097196866229589369133642962052447<213>] Free to factor
7×10248+1 = 7(0)2471<249> = 863 × 5261 × 35263591889353<14> × 185417334800379161185184893<27> × 938468829714829248723460566887067553<36> × 12889488947484066484526136384923478380292943<44> × 1949335134805180994280966773636774724507063617017380885800382610691210094245517603326531246084831785857576135150100113804977<124> (Dmitry Domanov / November 17, 2010 2010 年 11 月 17 日) (Wataru Sakai / GMP-ECM 6.2.3 B1=11000000, sigma=1019171859 for P44 / November 29, 2010 2010 年 11 月 29 日)
7×10249+1 = 7(0)2481<250> = 19 × 647 × 809 × 6622947448709999788429537193<28> × 5973344053164134769041687383699233929<37> × [17791919205115873842394951154181800349514829424156197534626674151008074168749438528387742024283888159203801632398154304615829370893075417491857904771550768436320132063594024797909<179>] (Dmitry Domanov / November 18, 2010 2010 年 11 月 18 日) Free to factor
7×10250+1 = 7(0)2491<251> = 1038529 × 8261621 × 8158571871906242889860671035352405854424230899264507190044129923915278532863078988039660418710276052322069385737442659674248619959742174238330544597998897635868840617133835801695427759798842959409660160599014442333078109178457895687583389<238>
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4. Related links 関連リンク