Table of contents 目次

  1. About 400...001 400...001 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
    4. Algebraic factorization 代数的因数分解
    5. Related sequences 関連する数列
  2. Prime numbers of the form 400...001 400...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 400...001 400...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 400...001 400...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

40w1 = { 41, 401, 4001, 40001, 400001, 4000001, 40000001, 400000001, 4000000001, 40000000001, … }

1.3. General term 一般項

4×10n+1 (1≤n)

1.4. Algebraic factorization 代数的因数分解

  1. 4×104k+1 = (2×102k-2×10k+1)×(2×102k+2×10k+1)

1.5. Related sequences 関連する数列

2. Prime numbers of the form 400...001 400...001 の形の素数

2.1. Last updated 最終更新日

July 8, 2018 2018 年 7 月 8 日

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

  1. 4×101+1 = 41 is prime. は素数です。
  2. 4×102+1 = 401 is prime. は素数です。
  3. 4×103+1 = 4001 is prime. は素数です。
  4. 4×1013+1 = 4(0)121<14> is prime. は素数です。
  5. 4×10229+1 = 4(0)2281<230> is prime. は素数です。
  6. 4×10242+1 = 4(0)2411<243> is prime. は素数です。
  7. 4×10309+1 = 4(0)3081<310> is prime. は素数です。
  8. 4×10957+1 = 4(0)9561<958> is prime. は素数です。
  9. 4×101473+1 = 4(0)14721<1474> is prime. は素数です。
  10. 4×101494+1 = 4(0)14931<1495> is prime. は素数です。
  11. 4×103182+1 = 4(0)31811<3183> is prime. は素数です。
  12. 4×103727+1 = 4(0)37261<3728> is prime. は素数です。
  13. 4×104177+1 = 4(0)41761<4178> is prime. は素数です。
  14. 4×1023210+1 = 4(0)232091<23211> is prime. は素数です。 (Hugo Pfoertner)
  15. 4×1025719+1 = 4(0)257181<25720> is prime. は素数です。 (Hugo Pfoertner)
  16. 4×1032835+1 = 4(0)328341<32836> is prime. は素数です。 (Ray Chandler / srsieve, PFGW / August 30, 2010 2010 年 8 月 30 日)
  17. 4×1036990+1 = 4(0)369891<36991> is prime. は素数です。 (Peter Benson / NewPGen, PRP, OpenPFGW / August 23, 2003 2003 年 8 月 23 日)
  18. 4×10103958+1 = 4(0)1039571<103959> is prime. は素数です。 (Peter Benson / NewPGen, OpenPFGW, Proth.exe / December 31, 2004 2004 年 12 月 31 日)

2.3. Range of search 捜索範囲

  1. n≤50000 / Completed 終了 / Ray Chandler / September 7, 2010 2010 年 9 月 7 日
  2. n≤150000 / Completed 終了 / Ray Chandler / February 20, 2012 2012 年 2 月 20 日
  3. n≤200000 / Completed 終了 / Predrag Kurtovic / February 7, 2015 2015 年 2 月 7 日
  4. n≤250000 / Completed 終了 / Predrag Kurtovic / June 27, 2017 2017 年 6 月 27 日
  5. n≤300000 / Completed 終了 / Predrag Kurtovic / June 17, 2018 2018 年 6 月 17 日
  6. n≤400000 / Completed 終了 / Predrag Kurtovic / July 7, 2018 2018 年 7 月 7 日

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

  1. 4×104k+1 = (2×102k-2×10k+1)×(2×102k+2×10k+1)
  2. 4×105k+1+1 = 41×(4×101+141+36×10×105-19×41×k-1Σm=0105m)
  3. 4×106k+4+1 = 13×(4×104+113+36×104×106-19×13×k-1Σm=0106m)
  4. 4×106k+5+1 = 7×(4×105+17+36×105×106-19×7×k-1Σm=0106m)
  5. 4×1013k+7+1 = 53×(4×107+153+36×107×1013-19×53×k-1Σm=01013m)
  6. 4×1016k+4+1 = 17×(4×104+117+36×104×1016-19×17×k-1Σm=01016m)
  7. 4×1018k+11+1 = 19×(4×1011+119+36×1011×1018-19×19×k-1Σm=01018m)
  8. 4×1022k+17+1 = 23×(4×1017+123+36×1017×1022-19×23×k-1Σm=01022m)
  9. 4×1028k+20+1 = 29×(4×1020+129+36×1020×1028-19×29×k-1Σm=01028m)
  10. 4×1032k+11+1 = 641×(4×1011+1641+36×1011×1032-19×641×k-1Σm=01032m)

Read more続きを読むHide more続きを隠す

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 14.86%. 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 14.86% です。

3. Factor table of 400...001 400...001 の素因数分解表

3.1. Last updated 最終更新日

August 24, 2018 2018 年 8 月 24 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=211, 213, 215, 219, 222, 225, 226, 231, 233, 237, 239, 243, 246, 247, 250 (15/250)

3.4. Factor table 素因数分解表

4×101+1 = 41 = definitely prime number 素数
4×102+1 = 401 = definitely prime number 素数
4×103+1 = 4001 = definitely prime number 素数
4×104+1 = 40001 = 13 × 17 × 181
4×105+1 = 400001 = 7 × 57143
4×106+1 = 4000001 = 41 × 97561
4×107+1 = 40000001 = 53 × 754717
4×108+1 = 400000001 = 19801 × 20201
4×109+1 = 4000000001<10> = 47 × 127 × 670129
4×1010+1 = 40000000001<11> = 13 × 3076923077<10>
4×1011+1 = 400000000001<12> = 7 × 193 × 41 × 317 × 641
4×1012+1 = 4000000000001<13> = 277 × 7213 × 2002001
4×1013+1 = 40000000000001<14> = definitely prime number 素数
4×1014+1 = 400000000000001<15> = 7333 × 54547933997<11>
4×1015+1 = 4000000000000001<16> = 173 × 23121387283237<14>
4×1016+1 = 40000000000000001<17> = 13 × 41 × 457 × 569 × 821 × 351529
4×1017+1 = 400000000000000001<18> = 72 × 23 × 2687 × 132089534249<12>
4×1018+1 = 4000000000000000001<19> = 12056437 × 331772977373<12>
4×1019+1 = 40000000000000000001<20> = 922367 × 43366685928703<14>
4×1020+1 = 400000000000000000001<21> = 17 × 29 × 53 × 1129 × 5953 × 35933 × 63389
4×1021+1 = 4000000000000000000001<22> = 41 × 97560975609756097561<20>
4×1022+1 = 40000000000000000000001<23> = 13 × 273773 × 11238957373163449<17>
4×1023+1 = 400000000000000000000001<24> = 7 × 26249 × 2176953679868076607<19>
4×1024+1 = 4000000000000000000000001<25> = 1999998000001<13> × 2000002000001<13>
4×1025+1 = 40000000000000000000000001<26> = 733 × 1847 × 4219 × 2447761 × 2860952089<10>
4×1026+1 = 400000000000000000000000001<27> = 41 × 293 × 33297261300258053775077<23>
4×1027+1 = 4000000000000000000000000001<28> = 797 × 31557220333<11> × 159038740554601<15>
4×1028+1 = 40000000000000000000000000001<29> = 13 × 15384616923077<14> × 199999980000001<15>
4×1029+1 = 400000000000000000000000000001<30> = 7 × 19 × 131 × 35343237863<11> × 649577122635449<15>
4×1030+1 = 4000000000000000000000000000001<31> = 1199481995446957<16> × 3334772856269093<16>
4×1031+1 = 40000000000000000000000000000001<32> = 41 × 659 × 1613 × 752459 × 1474663 × 827143245899<12>
4×1032+1 = 400000000000000000000000000000001<33> = 593 × 877 × 3089 × 3121 × 3989 × 19999999800000001<17>
4×1033+1 = 4000000000000000000000000000000001<34> = 53 × 75471698113207547169811320754717<32>
4×1034+1 = 40000000000000000000000000000000001<35> = 13 × 78517 × 39187985747329583696230409681<29>
4×1035+1 = 400000000000000000000000000000000001<36> = 7 × 472477 × 1342739 × 277543751143<12> × 324532520167<12>
4×1036+1 = 4000000000000000000000000000000000001<37> = 17 × 41 × 881 × 267713 × 8479780817<10> × 2869440456241033<16>
4×1037+1 = 40000000000000000000000000000000000001<38> = 59 × 11161 × 60744207660148306983002252091499<32>
4×1038+1 = 400000000000000000000000000000000000001<39> = 89 × 21929 × 710777042881<12> × 288348545377013952641<21>
4×1039+1 = 4000000000000000000000000000000000000001<40> = 23 × 450493 × 26255689 × 14703498742403429328114331<26>
4×1040+1 = 40000000000000000000000000000000000000001<41> = 13 × 15384615383076923077<20> × 200000000020000000001<21>
4×1041+1 = 400000000000000000000000000000000000000001<42> = 7 × 41 × 18287 × 28607 × 8232503 × 323617065960441802399049<24>
4×1042+1 = 4000000000000000000000000000000000000000001<43> = 345997 × 405788401 × 244759045477<12> × 116399007761442929<18>
4×1043+1 = 40000000000000000000000000000000000000000001<44> = 379 × 641 × 18867364133062891<17> × 8726729622988730725849<22>
4×1044+1 = 400000000000000000000000000000000000000000001<45> = 541 × 42767521 × 467644594134881<15> × 36968576709426987061<20>
4×1045+1 = 4000000000000000000000000000000000000000000001<46> = 22013 × 64997 × 2795679912153810318713513708145726641<37>
4×1046+1 = 40000000000000000000000000000000000000000000001<47> = 13 × 41 × 53 × 5849 × 2494117169<10> × 888265814281<12> × 109273660408134809<18>
4×1047+1 = 400000000000000000000000000000000000000000000001<48> = 7 × 19 × 251 × 273641 × 49043851 × 892830248999542574297475458717<30>
4×1048+1 = 4000000000000000000000000000000000000000000000001<49> = 29 × 157 × 997 × 1093 × 196277 × 2346997 × 27736601 × 39336709 × 1604034898237<13>
4×1049+1 = 40000000000000000000000000000000000000000000000001<50> = 6047 × 9198701017619<13> × 719107005037030071155743700669957<33>
4×1050+1 = 400000000000000000000000000000000000000000000000001<51> = 20832397 × 19200862963585035365829481840231827379249733<44>
4×1051+1 = 4(0)501<52> = 41 × 127 × 2699 × 340957 × 834775929756340659346435744705824635801<39>
4×1052+1 = 4(0)511<53> = 13 × 172 × 15473 × 2717549 × 9730969 × 4596227727257<13> × 5661209930204358073<19>
4×1053+1 = 4(0)521<54> = 7 × 2887 × 19793161462714632094611311791775941412242070364689<50>
4×1054+1 = 4(0)531<55> = 397 × 5569 × 18513601 × 97724029689006262970120726321857649103557<41>
4×1055+1 = 4(0)541<56> = 47 × 311792317 × 3546491561<10> × 769658009527008787510356671896509059<36>
4×1056+1 = 4(0)551<57> = 41 × 61 × 941 × 622549 × 526655496128047225409<21> × 518389881029517119825821<24>
4×1057+1 = 4(0)561<58> = 2383 × 309519429257646847<18> × 5423105248953848825200534252128523601<37>
4×1058+1 = 4(0)571<59> = 13 × 173 × 10252493 × 1734766609991044971257473234202380382148194988893<49>
4×1059+1 = 4(0)581<60> = 72 × 53 × 1721 × 7172369 × 561815797 × 22210104408309019466753678280866226961<38>
4×1060+1 = 4(0)591<61> = 229 × 76597 × 69336888435401<14> × 28844674820724601<17> × 114020450593997974882777<24>
4×1061+1 = 4(0)601<62> = 23 × 41 × 231611 × 151054394039690896708813<24> × 1212427431602724544074830260849<31>
4×1062+1 = 4(0)611<63> = 5881 × 242593794022971299662713397<27> × 280368440058228030693613482669893<33>
4×1063+1 = 4(0)621<64> = 57463303 × 92412075452419139957<20> × 753252673202065154243392276401159931<36>
4×1064+1 = 4(0)631<65> = 13 × 113 × 3061 × 5233 × 697935976337<12> × 37277079488149<14> × 65338124795818366546880104541<29>
4×1065+1 = 4(0)641<66> = 7 × 19 × 2204550857157326593682271383927<31> × 1364231987313074370799674019902811<34>
4×1066+1 = 4(0)651<67> = 41 × 677 × 956647082893<12> × 15916078812572232654253<23> × 9464542666233135185372313917<28>
4×1067+1 = 4(0)661<68> = 164117 × 1742051 × 139908969084878224421852702990639345649008391006902174303<57>
4×1068+1 = 4(0)671<69> = 17 × 97 × 9929 × 91453 × 126085681 × 165300869 × 5685054840613<13> × 2254552250995694797203588661<28>
4×1069+1 = 4(0)681<70> = 1441373 × 2775131766725198820846512318463021022316915885062367617542440437<64>
4×1070+1 = 4(0)691<71> = 132 × 1493 × 214426983624269161<18> × 739322702995632778091948645116533136331014788973<48>
4×1071+1 = 4(0)701<72> = 7 × 41 × 54059 × 623599681 × 206158145486328458561<21> × 200541243562919356138928178827285917<36>
4×1072+1 = 4(0)711<73> = 53 × 2861 × 23173 × 41729 × 39024189068687294863375801<26> × 699056274030059420482348829080741<33>
4×1073+1 = 4(0)721<74> = 383 × 24733 × 4222643524750338840751339185002352540273726532526653589843444435659<67>
4×1074+1 = 4(0)731<75> = 1877 × 819374245465341477001<21> × 260083864515468281071095575684487609275500129561813<51>
4×1075+1 = 4(0)741<76> = 223 × 641 × 296554471805228957<18> × 700580501444791801<18> × 134689758945851757063416146149285251<36>
4×1076+1 = 4(0)751<77> = 13 × 29 × 41 × 7537 × 205929062893<12> × 3295105303424261<16> × 51048013082528437769<20> × 9912209782592943898697<22>
4×1077+1 = 4(0)761<78> = 7 × 167 × 27179 × 160481 × 905917 × 1631579 × 53075227971470436723416564853216129170625280592743997<53>
4×1078+1 = 4(0)771<79> = 661152529 × 1490111265532794649<19> × 32601096982344030022369<23> × 124539585518612667972527269049<30>
4×1079+1 = 4(0)781<80> = 10399301453<11> × 44286505549343<14> × 86852917252842856443203096773392846999695124656258528219<56>
4×1080+1 = 4(0)791<81> = 709 × 958682189 × 3901200066397<13> × 5347577827006842697<19> × 28208744710860366713399153737658674189<38>
4×1081+1 = 4(0)801<82> = 41 × 263 × 277 × 82613 × 6607585172530757<16> × 7457700591622276977648263<25> × 328961073500403971350916708317<30>
4×1082+1 = 4(0)811<83> = 13 × 89 × 8320453 × 127095503602181369<18> × 32692601016761314157119495004047542663458645548499540849<56>
4×1083+1 = 4(0)821<84> = 7 × 19 × 23 × 61331 × 2132065135506677737272745109390372272910797502215335604455310419649103760569<76>
4×1084+1 = 4(0)831<85> = 17 × 109 × 853425905273368333<18> × 21499961203232518024633<23> × 117647058823529411764823529411764705882353<42>
4×1085+1 = 4(0)841<86> = 53 × 971 × 2991889 × 3116849 × 829547000162864046944367046259459<33> × 100476073473841019014510202342341373<36>
4×1086+1 = 4(0)851<87> = 41 × 197 × 733 × 7986133 × 65307413 × 5076336961<10> × 1187792304317<13> × 576148187135201<15> × 37289088323622219708408124357<29>
4×1087+1 = 4(0)861<88> = 150893 × 409597 × 2164979 × 4035102268771272917<19> × 7408425138353516758928742273260814998297567120698567<52>
4×1088+1 = 4(0)871<89> = 13 × 309929 × 7230701 × 11817812485849<14> × 482836088598383929<18> × 7551796575516578981<19> × 31863018833731140278508013<26>
4×1089+1 = 4(0)881<90> = 7 × 186806046659<12> × 181062640643378909404647518804407631099<39> × 1689437662993745555909697934943056683623<40>
4×1090+1 = 4(0)891<91> = 317 × 773 × 845166009699652159666515021017148258333637<42> × 19314310664570004537506940810390365837495453<44>
4×1091+1 = 4(0)901<92> = 41 × 52562142481636817481601<23> × 18561072856541213939514050581011188369320296717040037332455429879961<68>
4×1092+1 = 4(0)911<93> = 2293 × 9076746840853577<16> × 2203432611999477182878829995513<31> × 8722197993894461404273789795028347143480157<43>
4×1093+1 = 4(0)921<94> = 127 × 2081291 × 176869847757581148834467117<27> × 85559780579232529861792445700437376029567083586972454614129<59>
4×1094+1 = 4(0)931<95> = 13 × 1361 × 225721 × 1939265163533<13> × 5164750569576816620964067538335815709623314583988191852709325014543362449<73>
4×1095+1 = 4(0)941<96> = 7 × 59 × 1607 × 26921 × 2181259 × 8726647 × 2050333674467557<16> × 573619207734231410765653214023473131490255218752669688731<57>
4×1096+1 = 4(0)951<97> = 41 × 653 × 21347052697<11> × 1948217037997<13> × 39654833524613<14> × 631411766525927033401<21> × 143475878369122834469397183454904461<36>
4×1097+1 = 4(0)961<98> = 251 × 691 × 53077 × 157211 × 2224367 × 543367039097502667247<21> × 22867526479928742063772216587242930120801823067098947687<56>
4×1098+1 = 4(0)971<99> = 53 × 7547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754717<97>
4×1099+1 = 4(0)981<100> = 5340514614533165278697161411<28> × 748991490279753729991982536795069576765844598816949515716785117147315691<72>
4×10100+1 = 4(0)991<101> = 13 × 17 × 3677 × 54829 × 267581 × 1729468241<10> × 530526767289696833<18> × 1976577034596636110381<22> × 1850013310736271697135674572900561429<37>
4×10101+1 = 4(0)1001<102> = 72 × 19 × 41 × 47 × 173 × 4517179 × 6579538699<10> × 43363042523148153702266204810980480699687116865954056179861696866240783475881<77>
4×10102+1 = 4(0)1011<103> = 463049479397<12> × 8638385697375033388477501655442812500798005297363031687909266430467188209717273606396266733<91>
4×10103+1 = 4(0)1021<104> = 75691460528272051<17> × 1023246397461943840048249<25> × 39556096425362661005215663<26> × 13056279985721006726424982182157633373<38>
4×10104+1 = 4(0)1031<105> = 29 × 1153 × 1229 × 4073 × 44773 × 136573 × 380321041 × 11586215577990829<17> × 3031758035603884709<19> × 29254915858051818526570428231358748733761<41>
4×10105+1 = 4(0)1041<106> = 232 × 3329 × 92623529 × 10065112367161<14> × 61374787300570333<17> × 1770038185341029783677361<25> × 22427348776522401264947020870679665813<38>
4×10106+1 = 4(0)1051<107> = 13 × 41 × 2237 × 236672805169<12> × 236806432528979638909578742022011126001<39> × 598583780294530529081821283615359397949289067281249<51> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 0.94 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 22, 2007 2007 年 3 月 22 日)
4×10107+1 = 4(0)1061<108> = 7 × 641 × 739 × 211511398519689785054417917<27> × 570329330270045351436503539535108189841256840826470291937286786510642047521<75>
4×10108+1 = 4(0)1071<109> = 14282353 × 449624801 × 4448153205854852299395290701502028576933415201<46> × 140032948352417840393666225586218181275872400017<48>
4×10109+1 = 4(0)1081<110> = 73637 × 85645489596205447<17> × 504566703184287260002689525090090859<36> × 12570160427975508498024126528760502161684857548395201<53>
4×10110+1 = 4(0)1091<111> = 2797 × 11813 × 12106185410285130629221105282016464351627060726230087557078015981435891044452369287927188316344672904641<104>
4×10111+1 = 4(0)1101<112> = 41 × 53 × 419 × 954263 × 4603818109825557387601129945008576400336570077856109340401190640622283958065767097101108400901358321<100>
4×10112+1 = 4(0)1111<113> = 13 × 409 × 5897 × 803237 × 882851476915327188602341<24> × 93926450809509114392492557<26> × 19153270310774260418014378549639674313960981532321<50>
4×10113+1 = 4(0)1121<114> = 7 × 503 × 1597 × 27693103 × 1921587721428489822984360074527<31> × 1336771611781129939139846137350975094986672392926838753978751165909733<70> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.48 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 22, 2007 2007 年 3 月 22 日)
4×10114+1 = 4(0)1131<115> = 1481 × 10284099811172636668173569<26> × 19239826379011231330142545758809249<35> × 13650152431907201963179891116352788668531001597230041<53> (Makoto Kamada / Msieve 1.17 / March 22, 2007 2007 年 3 月 22 日)
4×10115+1 = 4(0)1141<116> = 205327 × 194811203592318594242354877829023947167201585763197241473357132768705528254929941020908112425545593127060737263<111>
4×10116+1 = 4(0)1151<117> = 17 × 41 × 61 × 193 × 6197 × 53653 × 415721 × 8418828519021619133<19> × 1041409915758482772813621281597<31> × 40224367811668375803852835183908505200564069461<47>
4×10117+1 = 4(0)1161<118> = 4164125225093709812091452961256189013773247773370698915379<58> × 960585905509117746404238452290739780153822354353075575508219<60> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.55 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 23, 2007 2007 年 3 月 23 日)
4×10118+1 = 4(0)1171<119> = 13 × 2521 × 1917014041<10> × 32794004557<11> × 19414403288312435820668470666126269499692898656496134681162055945274405314730287544170314937001<95>
4×10119+1 = 4(0)1181<120> = 7 × 19 × 663127 × 1049565721<10> × 100814601578535670801<21> × 17915709037898119173692619891853<32> × 2392459322134858608657877987740046002908201967261647<52>
4×10120+1 = 4(0)1191<121> = 509 × 18797 × 471749 × 3696899840127421<16> × 1332399407553263054444728109<28> × 3181885712427202864515492961<28> × 56543929648956861705455421014649847997<38>
4×10121+1 = 4(0)1201<122> = 41 × 179 × 35407 × 1677282149548946503<19> × 91775729995559202309480860055465558152596719087388419932408692990597402155192941860585945575179<95>
4×10122+1 = 4(0)1211<123> = 1693 × 2081 × 34301081 × 250868621552100821173<21> × 237061104674256043241201<24> × 55656577748792728734500686238834161290097068307476037683753452569<65>
4×10123+1 = 4(0)1221<124> = 151007 × 488636333 × 537902543 × 100779815274977560127837755663970009211033146759104806586600787111420881878953212789248848361924885397<102>
4×10124+1 = 4(0)1231<125> = 13 × 53 × 10253 × 14281 × 90620549 × 41641602785482764604422844952478401980473629079093433<53> × 105069597079303499041538586981063998401693897581284689<54>
4×10125+1 = 4(0)1241<126> = 7 × 3465927964099<13> × 18646352828611<14> × 40406937613934921<17> × 21882280681486971925481937485784203208914088263175996664282980555648871573032498247<83>
4×10126+1 = 4(0)1251<127> = 41 × 89 × 157 × 2333 × 43969 × 37132169765645505210537037<26> × 1833052150971326717676530757844097982202256630343703419817263946327914048885728723324893<88>
4×10127+1 = 4(0)1261<128> = 23 × 2544761 × 16180327 × 35832931081<11> × 54093077531<11> × 21790833172315990738253233519382438490953607919672593208341683869485576176214437220110961811<92>
4×10128+1 = 4(0)1271<129> = 373 × 761 × 2633 × 5817901501<10> × 34078691320501<14> × 1513015890063439996908593<25> × 862917513178823378823631229<27> × 2067538466388206817464922662772364909800768017<46>
4×10129+1 = 4(0)1281<130> = 2571557 × 3993481 × 389504261589723049023540667029763241272203254578966125062684058985602519974144182176885796920166971006571953362133253<117>
4×10130+1 = 4(0)1291<131> = 13 × 24329 × 26293188445622053<17> × 10943887203994016693<20> × 439518862738820048374800235746739067905044179173052197766563183577009727868501488261896597<90>
4×10131+1 = 4(0)1301<132> = 7 × 41 × 39983 × 6117344564173<13> × 13540374519737783<17> × 914330696485126819<18> × 460262717377104473504549506528838721203624141138015878165033860155386374302161<78>
4×10132+1 = 4(0)1311<133> = 17 × 29 × 433 × 701 × 3373 × 4254113 × 30223181 × 88380821229433<14> × 378879178609013<15> × 35917654067934382596442843652221<32> × 51247760017521254232765394554789953067443953049<47>
4×10133+1 = 4(0)1321<134> = 18650253859<11> × 656859394409<12> × 3004948379353932636885592567<28> × 1215103598620682615274146445588556223<37> × 894236732175920580152377822028339767396828303931<48> (Makoto Kamada / Msieve 1.17 / March 23, 2007 2007 年 3 月 23 日)
4×10134+1 = 4(0)1331<135> = 2521769 × 6482122769<10> × 498771505631914848917<21> × 339732985011027186094197732510445277293910533<45> × 144410272621457596142773322790127495868916847945915681<54> (Shaopu Lin / Msieve v. 1.17 / March 24, 2007 2007 年 3 月 24 日)
4×10135+1 = 4(0)1341<136> = 127 × 214556798183205397<18> × 146795921913563321819395980538666834042505147352976071774890915399867927840476992392706923237735278878621927216090179<117>
4×10136+1 = 4(0)1351<137> = 13 × 41 × 149 × 4481 × 11122527809<11> × 16596601969<11> × 1637757436921<13> × 2972939782892017<16> × 82473787923605350135609<23> × 410588190710389639144589153<27> × 3693097747722714009348879879577<31>
4×10137+1 = 4(0)1361<138> = 7 × 19 × 53 × 1009 × 3823 × 218117 × 1603681 × 23055346723785830899288317321960983887657807<44> × 1824138707895749513832021600956777695371243638120294559951871173502726613<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 7.70 hours on Cygwin on AMD XP 2700+ / March 26, 2007 2007 年 3 月 26 日)
4×10138+1 = 4(0)1371<139> = 6961 × 9998845837<10> × 27181130477<11> × 92639850016760801<17> × 21243739982186736081596209<26> × 1074340998593730730892428867826432317325432888260258081212279529347431801<73>
4×10139+1 = 4(0)1381<140> = 641 × 27851 × 7102095496029555951338486428062736055043334947960741098720689<61> × 315482054875753501037036269251586513863489506091455405288439226913423699<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 8.58 hours on Core 2 Duo E6300@2.33GHz / March 24, 2007 2007 年 3 月 24 日)
4×10140+1 = 4(0)1391<141> = 63377 × 83561 × 500467433 × 679233377 × 4899244937<10> × 23696426502493<14> × 3839802081892921<16> × 66052631879764390352533<23> × 7546035908518137699673476947473361898516667544440801<52>
4×10141+1 = 4(0)1401<142> = 41 × 3167 × 1385099246529648770253437136267455844731<40> × 41102459480233672086378912659093765960173<41> × 541102285545511773447658741193840771596059733459284964441<57> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 7.40 hours on Core 2 Duo E6300@2.33GHz / March 25, 2007 2007 年 3 月 25 日)
4×10142+1 = 4(0)1411<143> = 13 × 3250517 × 70502989264785613<17> × 13426309871176552568186516301787835466311568281191496953878958627394634905531548898527727705393436465260263421649042037<119>
4×10143+1 = 4(0)1421<144> = 72 × 7874219 × 10763828209<11> × 96314054182771268977482219619348989633785487937642420968781693916432139510787929323379246182872041692533059858697565965894819<125>
4×10144+1 = 4(0)1431<145> = 173 × 8317 × 25621 × 33113 × 319133 × 503249 × 579112895164952297<18> × 67704575690756412277<20> × 127833457376629982084572450664243129<36> × 4070728657304927469734608391624183892984329021<46>
4×10145+1 = 4(0)1441<146> = 3527 × 3016133 × 9386330623739<13> × 75701171851442047<17> × 431900725161775951764678157<27> × 12252413917377543644136805930318944909387796884332369139786560301466153041715531<80>
4×10146+1 = 4(0)1451<147> = 41 × 2729 × 2184156109565083400994331504190413<34> × 185296227258331476479382730913150879294782961<45> × 8833287103024449941246276528945173645345205610821578498935895813<64> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 11.10 hours on Core 2 Duo E6300@2.33GHz / March 26, 2007 2007 年 3 月 26 日)
4×10147+1 = 4(0)1461<148> = 47 × 251 × 733 × 863 × 6442862514461602713781483216855754068454488467466706327<55> × 83194530963377483428159654973172315536690121265505564170886744203220844329565112601<83> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 12.48 hours on Cygwin on AMD XP 2700+ / March 27, 2007 2007 年 3 月 27 日)
4×10148+1 = 4(0)1471<149> = 132 × 17 × 138549833 × 1693109461<10> × 2976415801<10> × 796769450569<12> × 162214004147497<15> × 1070055437699459212912601513126490566842954733<46> × 144182457504055569482879143621295762376248991721<48>
4×10149+1 = 4(0)1481<150> = 7 × 23 × 13259 × 207877 × 2614971570401<13> × 344706864796710622005213145364745706122291413413780429853772014962334522600966629386228064440103850507036806595831441440265287<126>
4×10150+1 = 4(0)1491<151> = 53 × 277 × 61357 × 2304158963285019721<19> × 5047235270038343639185708957<28> × 381833693783494213482826202929761765045615299273179467013156591317268744276402346427879154651849<96>
4×10151+1 = 4(0)1501<152> = 41 × 1601 × 980423 × 670961329 × 479516387641<12> × 1931836501146231929868971910071660171111512618650385393945865617903542995026941985367517437264335727157861561970857469063<121>
4×10152+1 = 4(0)1511<153> = 543661 × 4675861 × 14926753 × 52223864333161118057243878862623357<35> × 382966681140453190759201610136931180705493<42> × 527077985383865837122630444188680560669184029075046608177<57>
4×10153+1 = 4(0)1521<154> = 59 × 397 × 13063 × 167318969 × 606641514185778295831468249<27> × 3183635597702264953513076409369407360357<40> × 40455156645999949292666657280615001667447267467607551015375410772491397<71> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P40 x P71 / 26.67 hours on Athlon XP 3000+ / March 29, 2007 2007 年 3 月 29 日)
4×10154+1 = 4(0)1531<155> = 13 × 25707428533<11> × 622744718528007083089<21> × 192197594968209977118057036742684208332916351564626023278876166757315566433401247957901720654599642233127888813956068110721<123>
4×10155+1 = 4(0)1541<156> = 7 × 19 × 90173 × 63329687397592132145980877526417873030946686466430656344663544587463<68> × 526652909060236900579923203193911048657743442112564846958614597680814721066334503<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 25.81 hours on Cygwin on AMD XP 2700+ / April 3, 2007 2007 年 4 月 3 日)
4×10156+1 = 4(0)1551<157> = 41 × 117647489 × 601895033 × 454356957312809<15> × 5341058207367813588605221<25> × 5288095175146719223160893179452720213<37> × 107361595370695238400797719157921129302056548074664130232322929<63>
4×10157+1 = 4(0)1561<158> = 1321757 × 46712194341161070054665870112933244096080435997557581817007450649<65> × 647855429982898406721265781990638069224565341233236221727068040304877394852504476748157<87> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 28.48 hours on Cygwin on AMD 64 3200+ / April 17, 2007 2007 年 4 月 17 日)
4×10158+1 = 4(0)1571<159> = 25263414276699562450578618285557<32> × 15833172651129734691753638260959425453361976485639459624681318174193891148379882892150660341586988134980814335626714549512537693<128> (Makoto Kamada / GMP-ECM 5.0.3 B1=85070, sigma=3599089489)
4×10159+1 = 4(0)1581<160> = 131 × 52009 × 17330918709002002575539<23> × 33875725650758540850207863307029935526293568365103392584123312512205435389144906177579530015230347839191982884839325363901546049921<131>
4×10160+1 = 4(0)1591<161> = 13 × 29 × 853 × 249517493 × 519168493069<12> × 1092173329376508437<19> × 160550853845011584389826077<27> × 82739149005614537671026137265110876506013<41> × 66182786292580938056857269476000328045369018340249<50>
4×10161+1 = 4(0)1601<162> = 7 × 41 × 24481 × 1793611 × 6778769 × 51739157 × 24543891373<11> × 7075521653495357<16> × 365498852272237776807460331845037<33> × 1425813087563283653143535013962362288561660254770001654328238688640363615813<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P33 x P76 / 20.75 hours on Cygwin on AMD XP 2700+ / March 28, 2007 2007 年 3 月 28 日)
4×10162+1 = 4(0)1611<163> = 2497329853<10> × 75396687085921<14> × 376268494658838666197<21> × 7033585355523255976857977544415093<34> × 8027072786280128866004929270459039253458495879153981797095597384581952824282996219837<85> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=1124441233 for P34 / April 3, 2007 2007 年 4 月 3 日)
4×10163+1 = 4(0)1621<164> = 53 × 73978717 × 19915232337028022644423<23> × 512261774037057670967542856493977494372940799796521098095418261503423667203083915141568831529293379787730027819780685726100536178487<132>
4×10164+1 = 4(0)1631<165> = 17 × 97 × 937 × 262253 × 6891629 × 6639016981<10> × 4809423279366120261605554143564035809924606662417867200996041<61> × 4486013842492913780384052131069660841652414226854579805176904834375247431701<76>
4×10165+1 = 4(0)1641<166> = 23743 × 80900761 × 513790423 × 61142992571<11> × 7779120398579544883895822513251508700047607501669183213883240931<64> × 8521353913589854424771282379603548481995888227244581651836279018886769<70> (Kenji Ibusuki / GGNFS-0.77.1 snfs / 51.86 hours on Core 2 Quad Q6700 (2.66GHz), Windows XP and Cygwin / March 2, 2008 2008 年 3 月 2 日)
4×10166+1 = 4(0)1651<167> = 13 × 41 × 4517 × 152421337841<12> × 941160476969540120952877<24> × 338717486802811900673981008844119653096357974239957<51> × 341928753479598700237304527485927308118819144008567869244980664981674968409<75> (Serge Batalov / Msieve 1.36 snfs / 23.50 hours on Opteron-2.6GHz; Linux x86_64 / August 22, 2008 2008 年 8 月 22 日)
4×10167+1 = 4(0)1661<168> = 7 × 1171 × 321850576013<12> × 452834568437<12> × 334819846493942686654911244234336665685732640496966982512267869273961723073832542974680534405433160996863130567626286114687860700987297851293<141>
4×10168+1 = 4(0)1671<169> = 457 × 108533 × 409730312389<12> × 93411933000652685441898259747177<32> × 52255203297194322487918784669188516128517<41> × 40322921276290620277618877465920528643175473599262864740732386428828904824821<77>
4×10169+1 = 4(0)1681<170> = 317 × 769 × 145112173 × 741131087 × 1525722368634215200183830631475295084172954111987708688260657091635320684718502089815481557958855197157252102548295224312605614793133357560373856487<148>
4×10170+1 = 4(0)1691<171> = 89 × 809 × 12037 × 389533 × 50122020190096192578898087923762046470485403737718517<53> × 23639069626409130088066491289529080774163216816334627185245521359044363228829638540915634190946573122893<104> (Kenji Ibusuki / GGNFS-0.77.1 snfs / 78.39 hours on Core 2 Quad Q6700 (2.66GHz), Windows XP and Cygwin / March 20, 2008 2008 年 3 月 20 日)
4×10171+1 = 4(0)1701<172> = 23 × 41 × 641 × 55305917 × 571780967537331426467595011<27> × 983788565105385106532942023<27> × 3392183977152881040429986688657533088590419<43> × 62705813661270651499429351472678860702534232323580249870005333<62> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P43 x P62 / 10.75 hours on Cygwin on AMD XP 2700+ / March 26, 2007 2007 年 3 月 26 日)
4×10172+1 = 4(0)1711<173> = 13 × 293 × 6317 × 10821849037<11> × 1421625392482859915483832616008001758580123586608198873632381915389763080921<76> × 108056649779213250338622526245609523248658330816513865559158044196250326196011521<81>
4×10173+1 = 4(0)1721<174> = 7 × 19 × 19081 × 1380947158352491<16> × 1031387844700915926546275570854626898299232457527<49> × 4950984722498265333902822196208270860948138231881<49> × 22352008973784616122462526641600512964655392476154917761<56> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 92.56 hours on Core 2 Quad Q6700 / October 16, 2008 2008 年 10 月 16 日)
4×10174+1 = 4(0)1731<175> = 21669802129<11> × 90895849637269554525310385291775885388075787009<47> × 2030771183197325350577624750920707697746469994254856700264575730266390155389375430973873995208761043763694185654787441<118> (matsui / GGNFS-0.77.1-20060513-pentium-m snfs / 105.95 hours / July 14, 2008 2008 年 7 月 14 日)
4×10175+1 = 4(0)1741<176> = 16811 × 33374333358396914109100082498630504183786129383<47> × 105371111708302205780401868932937382113312422601077<51> × 676600448832315856534571187702619060715236193076202145589311912099919790801<75> (matsui / GGNFS-0.77.1-20060513-prescott snfs / February 8, 2008 2008 年 2 月 8 日)
4×10176+1 = 4(0)1751<177> = 41 × 53 × 61 × 113 × 1013 × 430121 × 11426141 × 80884901 × 6252736601<10> × 18689267390859149292717056482637255317654199244915941552355138149<65> × 567495530173653267529874247825892220316564875841726498015299495959356337<72>
4×10177+1 = 4(0)1761<178> = 127 × 6659 × 9739 × 69371 × 1058602893359918430986584487<28> × 6613355335599340569623394994644333734548049640883060507455398558497289708022568396139682510787269921256324528401245789362207525550004619<136>
4×10178+1 = 4(0)1771<179> = 13 × 566167021042476149422414249581680453<36> × 6061095723787709816177996585617442722607441719998843595973408858077<67> × 896645819043518706309661143084647289327440781070529452934200366627156144117<75> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=531751960 for P36 / March 26, 2007 2007 年 3 月 26 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 59.57 hours on Core 2 Quad Q6700 / March 8, 2009 2009 年 3 月 8 日)
4×10179+1 = 4(0)1781<180> = 7 × 18457340200388066441<20> × 6004231495142581556980974994915411<34> × 515626709759236369230555350134883854087864590105169849025864162520888571350730707352467835084057429485986388639654825004337893<126> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=2723994585 for P34 / March 26, 2007 2007 年 3 月 26 日)
4×10180+1 = 4(0)1791<181> = 17 × 233 × 11113 × 60107617 × 5525523109177<13> × 18966827428229747257<20> × 84774463712793346273<20> × 470115515406025639190126858917694761<36> × 361956680025158803047826849991830275331755207987544646460405310663321715919113<78>
4×10181+1 = 4(0)1801<182> = 41 × 1619 × 39293 × 30576859493<11> × 241401448929077<15> × 2077692861147390086533008886417768067467725384178251411463577449555727370531714620689079810440916876471502278084657087636963275443748788347824202503<148>
4×10182+1 = 4(0)1811<183> = 1160317 × 413745536263432081<18> × 30385872315370452048023578488339493475461704437<47> × 27420685405397558932205897020211411740511536898793314180500096877831147046352018738909437880962687052207823325649<113> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 87.22 hours on Core 2 Quad Q6700 / March 12, 2009 2009 年 3 月 12 日)
4×10183+1 = 4(0)1821<184> = 571331 × 17022010645669213<17> × 411302495331540351096624737709336167001799823065120271742613631066484339478569900893608595236556946204914561093603844242212191786134503556784400139088557339624167<162>
4×10184+1 = 4(0)1831<185> = 13 × 181 × 197 × 269 × 1945721 × 714653561 × 74953971409<11> × 404456814671197<15> × 6235763129526027221<19> × 2760112522862723807812664721033907942981<40> × 442140427088359732723919401655352200442156534928655623582787212323205365610813<78>
4×10185+1 = 4(0)1841<186> = 72 × 11387136743730658714583956573<29> × 716884805183080328390151232007836066382576126466769923060288875148399148124935727379700456665628633735390872417050473157442542103739431462713157977652619013<156>
4×10186+1 = 4(0)1851<187> = 41 × 1277 × 10302637 × 18930161 × 391726120432932548967124005640017420299524591508036017422310707844564674476058001102379920105794482705962546997707950441216394877921057009240485597529605804457857401649<168>
4×10187+1 = 4(0)1861<188> = 173 × 466357 × 17220341786228465534537012038573242088381604649445961<53> × 28790792619619581217940562985478392520067468106423516010341011616813295711690892727971687568687842629056533596007927442531799081<128> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 123.18 hours on Core 2 Quad Q6700 / March 17, 2009 2009 年 3 月 17 日)
4×10188+1 = 4(0)1871<189> = 29 × 3121 × 87442273 × 47981418968173<14> × 741548670319163677<18> × 469477203241985275180141<24> × 887855725323927778428067905829036736061102263034655095257<57> × 3407823789490258686400384521327420200673346836273759228105068009<64>
4×10189+1 = 4(0)1881<190> = 53 × 18077 × 2643247 × 96964568413<11> × 3643105412001703<16> × 13506270059310058545933600271041349759458769588496747569910410889<65> × 331054716915185039351115638053193982176316954185352183355312068630530447500029226468933<87> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 141.02 hours on Core 2 Quad Q6700 / March 23, 2009 2009 年 3 月 23 日)
4×10190+1 = 4(0)1891<191> = 13 × 3929 × 749212249 × 29090728066409<14> × 35931483680231802283901933540889672060081039517709758737692657346760870151470055777789795773004731558783470983290996179404117750527088920858749286063304888393298893<164>
4×10191+1 = 4(0)1901<192> = 7 × 19 × 41 × 647 × 46903543 × 4164599914798824246547757<25> × 765226605021062082766257793518013247<36> × 758492370060731172732749892408126693839219951872236949815340112500285954615089467270693873387494136665940937734088263<117> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=3120847556 for P36 / April 14, 2007 2007 年 4 月 14 日)
4×10192+1 = 4(0)1911<193> = 109 × 6581 × 26096209 × 6867491821<10> × 59570268209<11> × 273203515315421<15> × 24631420088448566099321<23> × 26230629738266686917601<23> × 1649861139458928415606764241<28> × 1793513415513160594803114592713415561157304692799480329352881941524270449<73>
4×10193+1 = 4(0)1921<194> = 23 × 47 × 9641387878495279411<19> × 3837909611610355848177122629200006844797882368715559135086528572099369204241254419822350508391343985371943871062052253656604854487110794376292596221461942865984755780601811<172>
4×10194+1 = 4(0)1931<195> = 721324202162977116296517293557<30> × 230366834312643340988031253121778481<36> × 4539551603725680577678687090612374940158174209<46> × 530269411486144259272416902466941069870793165414892485082648513501276740375531374317<84> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=2362285868 for P30 / March 26, 2007 2007 年 3 月 26 日) (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=2436293813 for P36 / April 21, 2007 2007 年 4 月 21 日) (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=632711195 for P46 / July 27, 2007 2007 年 7 月 27 日)
4×10195+1 = 4(0)1941<196> = 161971 × 4235420235990630674411<22> × 1782770591401940738293939<25> × 3270625053699212080692362493772858750666560394798793476886954585597967393938023443092469894332061712616542478561422647444539097061183051509475339<145>
4×10196+1 = 4(0)1951<197> = 13 × 17 × 412 × 25889 × 118801 × 553769 × 33209893 × 1013068290246913<16> × 18806089121412281873<20> × 14213662795471783729249<23> × 142851133452691513013398945489<30> × 49208667527925948973221056694552522133283274195899584254244124598255278818709511593<83>
4×10197+1 = 4(0)1961<198> = 7 × 251 × 5093190443767<13> × 1918281337544801<16> × 23301614476086791174193268524783637900374553651086479598676942509371151606132217635609620426691548453826094285457806633452456767854973084897460444026604823399971309779<167>
4×10198+1 = 4(0)1971<199> = 601 × 929931633094791878075356891588302829966299262696914473414281<60> × 7157057364649085307661377430067986943422261055343880321564902746003515911775225750122658781467332419066410898034428685018858357725799521<136> (Wataru Sakai / Msieve / 598.43 hours / March 3, 2009 2009 年 3 月 3 日)
4×10199+1 = 4(0)1981<200> = 14092207 × 27329994207449<14> × 103858354572756598961544410066501676256846583840753041387052260431908902185135719697115097666505659907583087248314673208582579183479386989196198354232004355351786310608896508872807<180>
4×10200+1 = 4(0)1991<201> = 31541 × 51001 × 329257 × 1593797 × 18155779891740157<17> × 596998838337353504040649<24> × 173113057012428875682266741<27> × 3955770714637851776058805084888354384537087623653<49> × 63839354599755592537240016160672526653527833995247027347015572381<65>
4×10201+1 = 4(0)2001<202> = 41 × 5121931 × 103849329299<12> × 13503675809573<14> × 587861201947289<15> × 1860750042755447209<19> × 2795453108496978738236562037<28> × 1684776046154235009517333610464790582051<40> × 2636510377862930365366650606354695539107142487471106263373162893880619<70> (Robert Backstrom / GGNFS 0.77.1-20051202-athlon, Msieve-1.38 gnfs for P40 x P70 / 13.15 hours / November 4, 2008 2008 年 11 月 4 日)
4×10202+1 = 4(0)2011<203> = 13 × 53 × 401 × 57046808129<11> × 4352160109233622287476004876885802806219798409446401497170469759529369422418203133<82> × 583123015262945556349244647056353780728267122790222566698427071203798962005200699046348941121122402068437<105> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P82 x P105 / August 24, 2018 2018 年 8 月 24 日)
4×10203+1 = 4(0)2021<204> = 7 × 641 × 3996493212534098134156111341457064136963014957402517508990780184800320983<73> × 22306161491827264164393810143013170259394176192731199083359389215809287265225238597639960484443643575958988629141966737446379681<128> (Wataru Sakai / Msieve / 858.79 hours / May 8, 2009 2009 年 5 月 8 日)
4×10204+1 = 4(0)2031<205> = 157 × 977 × 1097 × 117757 × 119929 × 130729 × 14788601 × 112700188358977<15> × 1011168875778642564121<22> × 1145752847230341104854444689755408827131862665943263929<55> × 6668219558002128682158806103505276064352507360154596086811797813918493447153374881817<85>
4×10205+1 = 4(0)2041<206> = 49048739 × 1340576829415582072376659<25> × 608331683217417163805795747590704069377173907054777153930489027864772074508375822311131626385934663449597573367164604502335486269650432180157579535254123979829571693432017001<174>
4×10206+1 = 4(0)2051<207> = 41 × 8489980721<10> × 161526918197<12> × 8620981820393556165598209791935039169<37> × 9614845316674752971125223167274964585506988001<46> × 85827308286463291545643661160043563366431087143222524276657149458595022132599515717888654971338922437<101> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2709458539 for P37 / March 13, 2011 2011 年 3 月 13 日) (Jo Yeong Uk / GMP-ECM 6.3 B1=11000000, sigma=5407201763 for P46 / April 27, 2013 2013 年 4 月 27 日)
4×10207+1 = 4(0)2061<208> = 2137537151086140780378598137246884887064851<43> × 2812726946992196303955780250469663669810710081<46> × 4510386964277796118081223118223701478503227449062032837<55> × 147504388817832250629782059406052001349839987803889705588283463583<66> (Robert Backstrom / GMP-ECM 6.2.1 B1=3628000, sigma=3845259699 for P43, GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 101.97 hours, 17.25 hours / January 6, 2009 2009 年 1 月 6 日)
4×10208+1 = 4(0)2071<209> = 13 × 733 × 4513 × 46589 × 218233 × 8623123641424928553601<22> × 275759473220416681288561<24> × 36106110373082818812350759763661<32> × 1060615417762646572618195239987309218160726413<46> × 1004638515256209055038246038744545150819657528797448156508330342617613<70> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=696637667 for P32 / October 31, 2008 2008 年 10 月 31 日)
4×10209+1 = 4(0)2081<210> = 7 × 19 × 3868312352905881234614717303045694938316220300630823137841921435236696906862947702213074172986063797<100> × 777475685161057172420107889087596154100076593781412039785204592057085537200948941303744478811373723078515001<108> (Serge Batalov / Msieve-1.39 snfs / 1000.01 hours on Opteron-2.6GHz; Linux x86_64 / February 17, 2009 2009 年 2 月 17 日)
4×10210+1 = 4(0)2091<211> = 5717 × 3771013 × 233278222252612529180268961<27> × 911781382426316231653996553754721<33> × 872305985302314642837664533768067528978848533430533241529384958629887457539688700015453948305990321439785340542663401455101411284361180402201<141> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2914364967 for P33 / March 13, 2011 2011 年 3 月 13 日)
4×10211+1 = 4(0)2101<212> = 41 × 59 × 148721 × 1332356352410729241381459477648619855405009<43> × [83450977684793282694551706981476556088621921512009377560353348583288515960273808416054497177857020031325682869956011963367750061419815803842510520381026012953211<161>] (Serge Batalov / GMP-ECM 6.2.1 B1=43000000, sigma=1854358772 for P43 / February 17, 2009 2009 年 2 月 17 日) Free to factor
4×10212+1 = 4(0)2111<213> = 17 × 2857 × 2131693 × 70842509 × 663053414577744687381599917<27> × 139893211207942643736922745313159710321<39> × 23474613840481557853118432748582756807946049343049856395181<59> × 25046014308160060753652965557111998610872516551741092521547633774020201<71> (Makoto Kamada / Msieve-1.38 snfs for P39 x P59 / 1.62 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / November 2, 2008 2008 年 11 月 2 日)
4×10213+1 = 4(0)2121<214> = 1091 × 34361 × 4269047 × 2836927429276991352710729<25> × [8810291618252846318741362925342329396537080601641446794149478971401796137928306301441229305771806124478694771112148333660490759809147040407405323752228466732260965957031088877<175>] Free to factor
4×10214+1 = 4(0)2131<215> = 13 × 89 × 997 × 17503955120237<14> × 1485058612125103453932281<25> × 1333987279362861290496004852240598783809970645042807264538099579389277668813962496788930262902451506668191857384961859976223548132387811966426431129896290637992370007605877<172>
4×10215+1 = 4(0)2141<216> = 7 × 23 × 53 × 1297201 × 280709138925610745225627616235368407<36> × [128734342401119972983581009935100049656649334653400039391667634128613012584259319294236788779710630652264467617853270939946120791315424107847649862903165446035555727219771<171>] (Ignacio Santos / GMP-ECM 6.2.3 B1=1000000, sigma=2323201769 for P36 / June 22, 2010 2010 年 6 月 22 日) Free to factor
4×10216+1 = 4(0)2151<217> = 29 × 41 × 1373 × 688512200950880259397<21> × 50573650464010212230513357749<29> × 995113252657683337996926110413<30> × 41833433897402299416847516692008758830906126644136052429<56> × 1690346080592033636898907143447681168419065457194335326431482594037873908193<76> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=2673524017 for P30 / November 1, 2008 2008 年 11 月 1 日)
4×10217+1 = 4(0)2161<218> = 18686807 × 578022421484392833484314349887736849483921909178334750733<57> × 3703225908027418809075172754492065279505406206615636647652312656725745127646139680370212557167658670799266733808441570447351849092965953387204337084674371<154> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 174.05 hours, 56.83 hours / April 17, 2009 2009 年 4 月 17 日)
4×10218+1 = 4(0)2171<219> = 1049 × 3529 × 108052008673334736208579275462658441387593090182097348916954197563913438455331704809475945056634109696019985299524219992809138822789573305319049217960080725655679848381421429576698152121560670797675044929375856481<213>
4×10219+1 = 4(0)2181<220> = 127 × 277 × 491 × 5081 × 391976229133<12> × [116274929177068394034445168029117678023767598280205360680402098732576928860666573423761231407315435416561191203122321241025448557314927842681535803476850418852033848061983277157659261544982402004533<198>] Free to factor
4×10220+1 = 4(0)2191<221> = 13 × 1181 × 6589057 × 124219769 × 1249376837<10> × 607021466763300821<18> × 444449141043266291533<21> × 42291256679033137134771637121479530755891442059584525827865339970574160993<74> × 223296850841264041346286705754966008069735102697303194855843986237022783354244973<81>
4×10221+1 = 4(0)2201<222> = 7 × 41 × 55493239095428870021395686757<29> × 25115279729838673041822990404411304580037176086385392155823273909673771694393791630240491096085374125051037065829934662353778187686075644790068872620199820114451706178407000835125992731217139<191>
4×10222+1 = 4(0)2211<223> = 6097015972179447612468707229921763686040066157<46> × [656058638890223304734304814532016364046521353594428916682596906758480771159191063541717990626390717402033424938857168466764328812593445093132882486910603381621639064614968488293<177>] (Serge Batalov / GMP-ECM 6.2.1 B1=11000000, sigma=2238052366 for P46 / November 7, 2008 2008 年 11 月 7 日) Free to factor
4×10223+1 = 4(0)2221<224> = 36796872653<11> × 1087048901606556863064837913903682960358560556067373250856900749347493740122437246841211878354460222448730825298921361571286572781237165318077336771872867018887307504469080947469940958626280897382760524021100973317<214>
4×10224+1 = 4(0)2231<225> = 257 × 459834665137<12> × 80139003431254841<17> × 1117554729596171621<19> × 14062325122689483593<20> × 2767593820315607196395314730016666048255527051377982687119041941<64> × 971075360824875755457217544245461262021767508202022480923000915283508183947227086253070744073<93>
4×10225+1 = 4(0)2241<226> = 31237 × 609641 × 3910997 × [53706768769429363793482678416871438245556988417973753812346805832702342873602425939717837859237868760949667888190502096723565700869017553283380850238323411769596938288424660294475642510961192383548068546243249<209>] Free to factor
4×10226+1 = 4(0)2251<227> = 132 × 41 × 797 × 7672476084343263227874361<25> × [944051236095625745605914377984667843452266499332174506062342859837045027395377946743564230504319254831003037392991414235483922896812610601139178907120628322515230507074953238453161918168433330957<195>] Free to factor
4×10227+1 = 4(0)2261<228> = 73 × 19 × 2274638262341070593950100717451021126508724154034353396727<58> × 26983602469312680130580985847029543470319676934990817496724014747605720259827010445557677689524276607304620925751442325052907279775178255048557619638932527039814094539<167> (RSALS + Jeff Gilchrist / ggnfs-lasieve4I14e on the RSALS grid + msieve 1.48 for P58 x P167 / February 24, 2011 2011 年 2 月 24 日)
4×10228+1 = 4(0)2271<229> = 17 × 53 × 2381 × 21089 × 240017 × 249089 × 11728313 × 34665109 × 636573841 × 725488909 × 886678473578749<15> × 16755502705377552397<20> × 1214464431029862275147439736082080827831090257987254979629<58> × 436523024418824031180581936516007205843771593262444864684074629830283990147587370053<84>
4×10229+1 = 4(0)2281<230> = definitely prime number 素数
4×10230+1 = 4(0)2291<231> = 173 × 9152489 × 252624037933692072393129117016709280794603547867019871028519367412710565127633681619505155525156406852192846468232931112518868386764752050324638404041274228144403616182496393190297506216062340695715876578977682142204499933<222>
4×10231+1 = 4(0)2301<232> = 41 × 209929 × 171045796291<12> × 151665385898395010920361713151614617130219<42> × [17914505220645022132194954402500979428459361638158467906590559309010783910561177699484997168919844042329407282181531626843571647207113173504748854176220229117272439835781521<173>] (Jo Yeong Uk / GMP-ECM 6.3 B1=3000000, sigma=6134707835 for P42 / June 22, 2011 2011 年 6 月 22 日) Free to factor
4×10232+1 = 4(0)2311<233> = 13 × 313 × 337 × 251621 × 469541870881<12> × 30014273848957<14> × 534695718389538267842639037229978253206456308162436414822347550938002366555153353<81> × 15384615384615384615384615384615384615384615384615384615383076923076923076923076923076923076923076923076923076923077<116>
4×10233+1 = 4(0)2321<234> = 7 × 12983 × 12618170294693<14> × [348811271163252370210612734963523254646594918249087302660630940511337621609010871181668602767014545497037982893129583986945293766246967995915927305014200045819794612475555563990563745183513376198670997494006657169197<216>] Free to factor
4×10234+1 = 4(0)2331<235> = 101844481261409<15> × 15083067110761453<17> × 166470474810555341081321<24> × 281722440676563078737805904561<30> × 59520510316289955705069974366831129<35> × 932840774605491827367365884272243625937825837089740051536226422913469229092335449597657018460854220557450573143028437<117> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=2491282100 for P30 / November 2, 2008 2008 年 11 月 2 日) (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3553856087 for P35 / November 21, 2008 2008 年 11 月 21 日)
4×10235+1 = 4(0)2341<236> = 641 × 44263 × 3599263 × 255771973 × 2525595417360720847349418399085176183355724297940127<52> × 606360356715044363553197719386419019822429801044602418979358571249578646327872607361512864562827095184920847571890230832148464068658949833446599287566868039930539<162> (Jo Yeong Uk / GMP-ECM 6.4.4 B1=11000000, sigma=4030962254 for P52 / October 10, 2013 2013 年 10 月 10 日)
4×10236+1 = 4(0)2351<237> = 41 × 61 × 117544433 × 128559502397<12> × 645204292022947594566560089<27> × 6699286506274141797109815307016926080793<40> × 619463214764350244902246724110519391574061961990845426302616569085969<69> × 3952744382511096329705320980593637243303419285421995417863091081509746384257377<79> (Makoto Kamada / Msieve-1.38 snfs for P40 x P69 / 1.62 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / November 2, 2008 2008 年 11 月 2 日)
4×10237+1 = 4(0)2361<238> = 23 × 727 × 1699 × 4241 × 77962531 × 123866097520553272509520813<27> × 5083970348510261759335252157<28> × [676230413605955129605354486014521738526895649311989696184845947638518215716542400947488253388711090435926834770951019457366341947049456598366448537219021549936677729<165>] Free to factor
4×10238+1 = 4(0)2371<239> = 13 × 11728776877<11> × 286265807209<12> × 44874068978343506281<20> × 11885822804057748455895493<26> × 422911528517671635279241199954086672512819330893<48> × 4749360430317354949216389905325606214784731753082957<52> × 855431189865208976114047930253021465132317651100002178476508620983478733<72> (rkillian / GMP-ECM B1=110000000, sigma=3131248890 for P48 / August 31, 2010 2010 年 8 月 31 日) (Erik Branger / GGNFS, Msieve gnfs for P52 x P72 / September 11, 2010 2010 年 9 月 11 日)
4×10239+1 = 4(0)2381<240> = 7 × 47 × 41893 × 1098613 × 520512077 × [50751290197039174977112551431903899323929494349499256480302322628695135287849225834912975184531171005394421043505550569260012632282440159555947336687305498898507812826687595415993327189298091583773830362544443830680533<218>] Free to factor
4×10240+1 = 4(0)2391<241> = 3797 × 24977 × 275729 × 2471393 × 1295852116961<13> × 59021635048978918237423695747967725983412277880123146182396163677350125724605798633485923954941<95> × 809260202646847344797043610627690537279987440281654920929209559143365705090206211638537456406164458667642094964257<114>
4×10241+1 = 4(0)2401<242> = 41 × 53 × 22911583 × 62061919957<11> × 12945533764740055863423747387655263309689836911130140356964096739723898369118609489119010096253343363419508321485034771592993003974361916798079643431814073169713170812165542478032908785099461498126223933439950573612980127<221>
4×10242+1 = 4(0)2411<243> = definitely prime number 素数
4×10243+1 = 4(0)2421<244> = 167 × 499 × 33461534459<11> × 38246818028611<14> × [37506091803232300246153964037751360052070199287344009701430144095005843908692475793239852205548785338336670134733234023324341872177909170724055033663717297751021566608537985327024606478204000425747591569480230901853<215>] Free to factor
4×10244+1 = 4(0)2431<245> = 13 × 17 × 29 × 494041 × 6360593 × 70110421 × 1063728224989<13> × 12148418471901262420361101<26> × 65410771359361952392693793<26> × 2008466708215711599048187312289<31> × 153439118336387104335313493107209665842195972706444429<54> × 108749211544556029830506369336331342119441820820121702905724110978018201289<75> (Makoto Kamada / Msieve 1.38 for P31 x P54 / 51 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / November 3, 2008 2008 年 11 月 3 日)
4×10245+1 = 4(0)2441<246> = 7 × 19 × 367885532726263369<18> × 947255853369650441723806278949229684129<39> × 252848348718738248054735889573081237056927<42> × 60020541527437240963374051468568365819621167111923661277994930871623<68> × 568680468126153435753728167358980072501665559484793347884252370988739251938957<78> (yoyo@home, ECM B1=43000000, sigma=1774910016 for P39 / January 30, 2010 2010 年 1 月 30 日) (Youcef Lemsafer / msieve 1.52 (SVN 942) GPU for polynomial selection, GGNFS (SVN 440), msieve 1.51 (SVN 845) gnfs / December 19, 2013 2013 年 12 月 19 日)
4×10246+1 = 4(0)2451<247> = 41 × 557 × 1597 × 37372533192409<14> × 8727020049799717<16> × [336277270197571194694599167999489364048869681650509232785741533248676206882399428414702744553461554191510107698912625436480348696350938968554576404701771244631046341141003347894755534981647251532984417755325653<210>] Free to factor
4×10247+1 = 4(0)2461<248> = 251 × 18797 × 85093 × 18313975459545581365621451<26> × [5440280160228364168388954886554154956082230667821654009825515137353304533015851832287889842237427177754937406635211474521081167104083163271414973599848661004051886455901155247175357847137327435058370081960353081<211>] Free to factor
4×10248+1 = 4(0)2471<249> = 317 × 4349 × 25633 × 1115580458177<13> × 234046722213975127327184686613228150778995773714719821<54> × 17613153769512112517578753541630628864236833323216296297<56> × 2461338222207399496484039883032285004259961128085456678539752052171509493196922687274302976705525864295840055350573941<118> (Sinkiti Sibata / Msieve snfs / 6.26 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 3, 2008 2008 年 11 月 3 日)
4×10249+1 = 4(0)2481<250> = 1746449 × 26733795833299<14> × 17677918550311046578053131<26> × 4846322688208438969819911619492873330875712349390199687135598584660142832537401299208570433227770123237467674481232936840180075956293104033604008336872481275509793405168852166511016795506306583658406071521<205>
4×10250+1 = 4(0)2491<251> = 13 × 3646063837616479765543282237<28> × 609367039316849421092272000364917<33> × [1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213<190>] (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=3159199225 for P33 / November 2, 2008 2008 年 11 月 2 日) (Wataru Sakai / GMP-ECM 6.2.1 B1=1000000, sigma=1542610798 for P28 / February 17, 2009 2009 年 2 月 17 日) Free to factor
plain text versionプレーンテキスト版

4. Related links 関連リンク