Table of contents 目次

  1. About 600...001 600...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 600...001 600...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 600...001 600...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 600...001 600...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

60w1 = { 61, 601, 6001, 60001, 600001, 6000001, 60000001, 600000001, 6000000001, 60000000001, … }

1.3. General term 一般項

6×10n+1 (1≤n)

2. Prime numbers of the form 600...001 600...001 の形の素数

2.1. Last updated 最終更新日

July 17, 2015 2015 年 7 月 17 日

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

  1. 6×101+1 = 61 is prime. は素数です。
  2. 6×102+1 = 601 is prime. は素数です。
  3. 6×108+1 = 600000001 is prime. は素数です。
  4. 6×109+1 = 6000000001<10> is prime. は素数です。
  5. 6×1015+1 = 6(0)141<16> is prime. は素数です。
  6. 6×1020+1 = 6(0)191<21> is prime. は素数です。
  7. 6×1026+1 = 6(0)251<27> is prime. は素数です。
  8. 6×1038+1 = 6(0)371<39> is prime. は素数です。
  9. 6×1045+1 = 6(0)441<46> is prime. は素数です。
  10. 6×1065+1 = 6(0)641<66> is prime. は素数です。
  11. 6×10112+1 = 6(0)1111<113> is prime. は素数です。
  12. 6×10244+1 = 6(0)2431<245> is prime. は素数です。
  13. 6×10303+1 = 6(0)3021<304> is prime. は素数です。
  14. 6×10393+1 = 6(0)3921<394> is prime. は素数です。
  15. 6×10560+1 = 6(0)5591<561> is prime. は素数です。
  16. 6×10839+1 = 6(0)8381<840> is prime. は素数です。
  17. 6×101009+1 = 6(0)10081<1010> is prime. は素数です。
  18. 6×101019+1 = 6(0)10181<1020> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1984 1984 年 12 月 31 日)
  19. 6×101173+1 = 6(0)11721<1174> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1984 1984 年 12 月 31 日)
  20. 6×101334+1 = 6(0)13331<1335> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1984 1984 年 12 月 31 日)
  21. 6×102236+1 = 6(0)22351<2237> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1990 1990 年 12 月 31 日)
  22. 6×102629+1 = 6(0)26281<2630> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1984 1984 年 12 月 31 日)
  23. 6×104426+1 = 6(0)44251<4427> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1990 1990 年 12 月 31 日)
  24. 6×108848+1 = 6(0)88471<8849> is prime. は素数です。 (Makoto Kamada / PFGW / January 1, 2005 2005 年 1 月 1 日)
  25. 6×1020812+1 = 6(0)208111<20813> is prime. は素数です。 (Herman Jamke / December 27, 2007 2007 年 12 月 27 日)
  26. 6×1037744+1 = 6(0)377431<37745> is prime. は素数です。 (Jason Earls / March 7, 2008 2008 年 3 月 7 日)
  27. 6×1072926+1 = 6(0)729251<72927> is prime. は素数です。 (Peter Benson / NewPGen, OpenPFGW, Proth.exe / April 19, 2005 2005 年 4 月 19 日)
  28. 6×1086287+1 = 6(0)862861<86288> is prime. は素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  29. 6×10231617+1 = 6(0)2316161<231618> is prime. は素数です。 (Edward Trice / OpenPFGW / February 8, 2012 2012 年 2 月 8 日)
  30. 6×10522127+1 = 6(0)5221261<522128> is prime. は素数です。 (Edward Trice / OpenPFGW / March 11, 2012 2012 年 3 月 11 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≤200000 / Completed 終了 / Bob Price / July 17, 2015 2015 年 7 月 17 日

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

  1. 6×106k+1 = 7×(6×100+17+54×106-19×7×k-1Σm=0106m)
  2. 6×1013k+11+1 = 53×(6×1011+153+54×1011×1013-19×53×k-1Σm=01013m)
  3. 6×1015k+10+1 = 31×(6×1010+131+54×1010×1015-19×31×k-1Σm=01015m)
  4. 6×1016k+3+1 = 17×(6×103+117+54×103×1016-19×17×k-1Σm=01016m)
  5. 6×1018k+5+1 = 19×(6×105+119+54×105×1018-19×19×k-1Σm=01018m)
  6. 6×1022k+5+1 = 23×(6×105+123+54×105×1022-19×23×k-1Σm=01022m)
  7. 6×1028k+4+1 = 29×(6×104+129+54×104×1028-19×29×k-1Σm=01028m)
  8. 6×1032k+3+1 = 353×(6×103+1353+54×103×1032-19×353×k-1Σm=01032m)
  9. 6×1041k+34+1 = 83×(6×1034+183+54×1034×1041-19×83×k-1Σm=01041m)
  10. 6×1046k+13+1 = 139×(6×1013+1139+54×1013×1046-19×139×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 24.96%. 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 24.96% です。

3. Factor table of 600...001 600...001 の素因数分解表

3.1. Last updated 最終更新日

June 10, 2015 2015 年 6 月 10 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=203, 204, 206, 208, 213, 217, 218, 219, 222, 227, 228, 231, 233, 237, 238, 239, 240, 243, 245, 246, 249 (21/250)

3.4. Factor table 素因数分解表

6×101+1 = 61 = definitely prime number 素数
6×102+1 = 601 = definitely prime number 素数
6×103+1 = 6001 = 17 × 353
6×104+1 = 60001 = 29 × 2069
6×105+1 = 600001 = 19 × 23 × 1373
6×106+1 = 6000001 = 72 × 122449
6×107+1 = 60000001 = 151 × 397351
6×108+1 = 600000001 = definitely prime number 素数
6×109+1 = 6000000001<10> = definitely prime number 素数
6×1010+1 = 60000000001<11> = 31 × 293 × 6605747
6×1011+1 = 600000000001<12> = 53 × 11320754717<11>
6×1012+1 = 6000000000001<13> = 7 × 4513 × 4903 × 38737
6×1013+1 = 60000000000001<14> = 139 × 34759 × 12418501
6×1014+1 = 600000000000001<15> = 1567 × 3967 × 96520609
6×1015+1 = 6000000000000001<16> = definitely prime number 素数
6×1016+1 = 60000000000000001<17> = 15467 × 3879226740803<13>
6×1017+1 = 600000000000000001<18> = 467 × 1284796573875803<16>
6×1018+1 = 6000000000000000001<19> = 7 × 340335059 × 2518526477<10>
6×1019+1 = 60000000000000000001<20> = 17 × 167 × 21134202183867559<17>
6×1020+1 = 600000000000000000001<21> = definitely prime number 素数
6×1021+1 = 6000000000000000000001<22> = 47 × 2333 × 54719063209637851<17>
6×1022+1 = 60000000000000000000001<23> = 6271 × 2650266823<10> × 3610146697<10>
6×1023+1 = 600000000000000000000001<24> = 19 × 31578947368421052631579<23>
6×1024+1 = 6000000000000000000000001<25> = 7 × 53 × 16172506738544474393531<23>
6×1025+1 = 60000000000000000000000001<26> = 31 × 773 × 2503860117681425531027<22>
6×1026+1 = 600000000000000000000000001<27> = definitely prime number 素数
6×1027+1 = 6000000000000000000000000001<28> = 23 × 361754506133<12> × 721123194859339<15>
6×1028+1 = 60000000000000000000000000001<29> = 4801 × 12497396375755051031035201<26>
6×1029+1 = 600000000000000000000000000001<30> = 278581 × 6075673039<10> × 354491121990739<15>
6×1030+1 = 6000000000000000000000000000001<31> = 7 × 59 × 399796009 × 36338144226746427053<20>
6×1031+1 = 60000000000000000000000000000001<32> = 1051 × 57088487155090390104662226451<29>
6×1032+1 = 600000000000000000000000000000001<33> = 29 × 317 × 27697 × 14706583 × 160232083892316607<18>
6×1033+1 = 6000000000000000000000000000000001<34> = 17207 × 348695298425059568780147614343<30>
6×1034+1 = 60000000000000000000000000000000001<35> = 83 × 1361401 × 16294553140421<14> × 32587019298007<14>
6×1035+1 = 600000000000000000000000000000000001<36> = 17 × 353 × 562789 × 58641017 × 3029566777980005477<19>
6×1036+1 = 6000000000000000000000000000000000001<37> = 7 × 439 × 138577 × 12242047 × 1150915641512450972623<22>
6×1037+1 = 60000000000000000000000000000000000001<38> = 53 × 113 × 4099 × 21061 × 116048633486792236701987331<27>
6×1038+1 = 600000000000000000000000000000000000001<39> = definitely prime number 素数
6×1039+1 = 6000000000000000000000000000000000000001<40> = 2179 × 56659 × 2309994469<10> × 21038471059992518119189<23>
6×1040+1 = 60000000000000000000000000000000000000001<41> = 31 × 2825470447<10> × 27466192401587<14> × 24940222831319339<17>
6×1041+1 = 600000000000000000000000000000000000000001<42> = 19 × 109 × 84405537443<11> × 3432418325247921334256483117<28>
6×1042+1 = 6000000000000000000000000000000000000000001<43> = 7 × 5431 × 12611 × 64783 × 193180295584722199571106305381<30>
6×1043+1 = 60000000000000000000000000000000000000000001<44> = 13997 × 43651 × 9395926339974827<16> × 10451592942449592229<20>
6×1044+1 = 600000000000000000000000000000000000000000001<45> = 141773 × 1978299179<10> × 2139270735658099657022956290703<31>
6×1045+1 = 6000000000000000000000000000000000000000000001<46> = definitely prime number 素数
6×1046+1 = 60000000000000000000000000000000000000000000001<47> = 107 × 121591 × 187183537 × 530372671 × 97554764141<11> × 476177392039<12>
6×1047+1 = 600000000000000000000000000000000000000000000001<48> = 2657 × 3412861 × 7095600047<10> × 9325067142016844694550010779<28>
6×1048+1 = 6000000000000000000000000000000000000000000000001<49> = 72 × 1087 × 2537895020703233808083<22> × 44386609518255148449269<23>
6×1049+1 = 60000000000000000000000000000000000000000000000001<50> = 23 × 1160567 × 79918334330375449<17> × 28125922333383127880650489<26>
6×1050+1 = 600000000000000000000000000000000000000000000000001<51> = 53 × 6139787 × 1843835090204453684707905683569730866854391<43>
6×1051+1 = 6(0)501<52> = 17 × 1159657247701<13> × 304349562916359881714040088241074414253<39>
6×1052+1 = 6(0)511<53> = 71983 × 42544643 × 538230961 × 1760325991<10> × 25575186779<11> × 808529429401<12>
6×1053+1 = 6(0)521<54> = 1697 × 269719 × 86687632287383<14> × 15121703768958887835334579829329<32>
6×1054+1 = 6(0)531<55> = 7 × 751 × 13297 × 55807 × 56123 × 1804287570049<13> × 15188828999489696506752821<26>
6×1055+1 = 6(0)541<56> = 31 × 233 × 421 × 272341 × 72450020365565062097204434945389647844594767<44>
6×1056+1 = 6(0)551<57> = 97 × 821 × 183543234976677913<18> × 41048564778833682869028261529146821<35>
6×1057+1 = 6(0)561<58> = 394510951 × 16609273738277543<17> × 915675395184108237016902511266257<33>
6×1058+1 = 6(0)571<59> = 37718022522533<14> × 30362036251597397<17> × 52392779681534623367518913401<29>
6×1059+1 = 6(0)581<60> = 19 × 139 × 31413541 × 7232125525589724872156509017849096384597203614621<49>
6×1060+1 = 6(0)591<61> = 7 × 29 × 1427 × 20712438855154463012762314407917674959697046061011940721<56>
6×1061+1 = 6(0)601<62> = 61 × 30175681 × 79822797269482085863664027<26> × 408354543900247203214977743<27>
6×1062+1 = 6(0)611<63> = 227 × 948799 × 78639923 × 35424856144656390091844500707594811445488827319<47>
6×1063+1 = 6(0)621<64> = 53 × 113207547169811320754716981132075471698113207547169811320754717<63>
6×1064+1 = 6(0)631<65> = 10687 × 313365290753887<15> × 17916144227131827201852468716406014412728509729<47>
6×1065+1 = 6(0)641<66> = definitely prime number 素数
6×1066+1 = 6(0)651<67> = 7 × 34301 × 687684769 × 766609859 × 236954946916397<15> × 200039998745866188690389568389<30>
6×1067+1 = 6(0)661<68> = 17 × 47 × 353 × 19514377061177<14> × 10901219223968945662565276355575405434276865620279<50>
6×1068+1 = 6(0)671<69> = 32696453 × 39987656127484812945413<23> × 458906976273972267247081993747004432809<39>
6×1069+1 = 6(0)681<70> = 181 × 443 × 36345923 × 63717801782714753<17> × 4504187740385421017<19> × 7173580535919808948789<22>
6×1070+1 = 6(0)691<71> = 31 × 16661 × 557329 × 208437977492853009591329927228441927726791535728566959311859<60>
6×1071+1 = 6(0)701<72> = 23 × 10782263 × 48914360697607819366223<23> × 49462619410288208457262695434014159560863<41>
6×1072+1 = 6(0)711<73> = 7 × 2939 × 291644388275895591308997229378311378991882564526320906041899577115637<69>
6×1073+1 = 6(0)721<74> = 199 × 10717141 × 7987068823361803464866907998419<31> × 3522344282723659121878623661414681<34>
6×1074+1 = 6(0)731<75> = 71713 × 115133 × 677749129 × 5610899309<10> × 19109621937767939368004201654255332549309559329<47>
6×1075+1 = 6(0)741<76> = 83 × 72289156626506024096385542168674698795180722891566265060240963855421686747<74>
6×1076+1 = 6(0)751<77> = 53 × 6793 × 187393 × 34863869 × 2078513971403<13> × 5504690659859<13> × 22708640191786349<17> × 98176563304319309<17>
6×1077+1 = 6(0)761<78> = 19 × 11813 × 653722299549164948784877973<27> × 4089254551558801036157589009223360059576611971<46>
6×1078+1 = 6(0)771<79> = 7 × 1664867 × 3961039 × 14625232591<11> × 370787449092414981629<21> × 23968272859703472959773937285158849<35>
6×1079+1 = 6(0)781<80> = 285031 × 210503418926362395669242994621637646431440790650841487417158133676687798871<75>
6×1080+1 = 6(0)791<81> = 5113 × 117347936632114218658321924506160766673185996479561901036573440250342264815177<78>
6×1081+1 = 6(0)801<82> = 111949 × 35737634987<11> × 126145676809<12> × 699274404521801727955091123<27> × 17001420921467775458006288461<29>
6×1082+1 = 6(0)811<83> = 151 × 34613 × 25862357294843<14> × 4493360119456930454809<22> × 98786074257911359306215236531947566825721<41>
6×1083+1 = 6(0)821<84> = 17 × 25171 × 2600783 × 17366897 × 308604441953<12> × 44059979703527<14> × 2283121624258682255324277559118476008803<40>
6×1084+1 = 6(0)831<85> = 7 × 197 × 9221 × 31177 × 7568527 × 39290123 × 108401984385654685133<21> × 469507629407253139906085225665498575799<39>
6×1085+1 = 6(0)841<86> = 31 × 6827 × 876677 × 12147559 × 966625438653914723<18> × 27540562330104221469572957255891172036635636735957<50>
6×1086+1 = 6(0)851<87> = 1327 × 76753 × 12337057 × 17415121 × 3705060199<10> × 7400339291663857765484830291991875052756503510426252057<55>
6×1087+1 = 6(0)861<88> = 453451 × 505643 × 18622367 × 180045788879165581<18> × 7804750743261622757311259350760834146985607834180691<52>
6×1088+1 = 6(0)871<89> = 292 × 59 × 3581 × 34033 × 1786637 × 12971069 × 3326205203<10> × 73699717159<11> × 1746512648577745608670770637652515241481683<43>
6×1089+1 = 6(0)881<90> = 53 × 593 × 19090648763880492538738108116707499443189411053485634286805179929364599573642177606669<86>
6×1090+1 = 6(0)891<91> = 72 × 2383 × 1454612251783<13> × 38583854261803063891061<23> × 915542013048253542684782683675913912809936371430181<51>
6×1091+1 = 6(0)901<92> = 229 × 5449 × 3936971760167<13> × 12213402240021839572649954565734941302776408893963263345101942272443728243<74>
6×1092+1 = 6(0)911<93> = 509 × 174990711565745028168904901757395757001<39> × 6736254254849041911313042640073220109096970044505389<52>
6×1093+1 = 6(0)921<94> = 23 × 3889 × 12421 × 122243852122547<15> × 44177575990804917577240031942529437755601646590367341215467242111773609<71>
6×1094+1 = 6(0)931<95> = 1229 × 81139505539820154437<20> × 601681988108295251598063284083437223829862273056653086908294981183123137<72>
6×1095+1 = 6(0)941<96> = 19 × 15527 × 299146613 × 14953622366592442973291661206155279<35> × 454652514628133701293284270253908633856234072151<48> (Makoto Kamada / GGNFS-0.70.8 / 0.27 hours)
6×1096+1 = 6(0)951<97> = 7 × 377183428187<12> × 18860663840080796999105381<26> × 120487954732241877019878624151198513351556109280299078280369<60>
6×1097+1 = 6(0)961<98> = 56207 × 2080630904836525863529<22> × 513057215195251896718766661771109556220731994182841655274064438564486167<72>
6×1098+1 = 6(0)971<99> = 576897077 × 463697380804547191<18> × 2242943165869171747348094295096124663610560630080590487050517465963032843<73>
6×1099+1 = 6(0)981<100> = 17 × 107 × 353 × 9344237019686750027643367849906635498444963222640463349566349533644704075800450703698916224243<94>
6×10100+1 = 6(0)991<101> = 31 × 10988671 × 256470851428667<15> × 6445130741893997272288850119<28> × 106555198029917904757934072544719944133911203314837<51>
6×10101+1 = 6(0)1001<102> = 349 × 362549619674618223167<21> × 4741965277137344047882581864905450007182542675222783233872004976836277282239947<79>
6×10102+1 = 6(0)1011<103> = 7 × 53 × 659 × 529687 × 46331100053136927844437500771763677444507250136372992673418064800026514466955569321510517807<92>
6×10103+1 = 6(0)1021<104> = 243629701591<12> × 40304843805077<14> × 51901639078658911183463<23> × 117728795678308022566270071685994524524193885160094796861<57>
6×10104+1 = 6(0)1031<105> = 37370640967135726343267<23> × 9203784399467016788249685113729690619419<40> × 1744432892227357395735142027143932533665937<43> (Makoto Kamada / Msieve 1.17 for P40 x P43 / March 28, 2007 2007 年 3 月 28 日)
6×10105+1 = 6(0)1041<106> = 139 × 738929844829893537529<21> × 28570752196990754353494572179370181595997<41> × 2044615119347519919559849474950280720223543<43> (Makoto Kamada / Msieve 1.17 for P41 x P43 / March 28, 2007 2007 年 3 月 28 日)
6×10106+1 = 6(0)1051<107> = 29401 × 6685671247<10> × 369696101861<12> × 51940802628894500623<20> × 15896100624996536948021898679570060061241584509024461214768661<62>
6×10107+1 = 6(0)1061<108> = 3301 × 188417 × 164052409 × 5880348011941284246615854413500342753034392574740915407786860158576275770540964336501180117<91>
6×10108+1 = 6(0)1071<109> = 7 × 727 × 269089 × 116960511029<12> × 6063254605249<13> × 669060346041879059651<21> × 9234481200250125127176894322385720240709107656511138911<55>
6×10109+1 = 6(0)1081<110> = 7822741 × 12580929070333423746767<23> × 609648605752542018869682610829436145583707994320866899932711993373999617005237683<81>
6×10110+1 = 6(0)1091<111> = 17713 × 33075221 × 13415324383775158973<20> × 76340534197621381168700453218973975001163815611335044871304764485517103259263569<80>
6×10111+1 = 6(0)1101<112> = 317 × 2136234618410849156029<22> × 842291613546434840273761021908166265719<39> × 10519147937640716926880457101711532119600907985103<50> (Makoto Kamada / Msieve 1.17 for P39 x P50 / March 28, 2007 2007 年 3 月 28 日)
6×10112+1 = 6(0)1111<113> = definitely prime number 素数
6×10113+1 = 6(0)1121<114> = 19 × 47 × 557 × 1193 × 1759 × 4021 × 4217 × 33900073442377684574112498516882213832532833600600564042656027111525885319259392813402783988539<95>
6×10114+1 = 6(0)1131<115> = 7 × 49599570081656020724913841661<29> × 17281255779671851243059588271315196225145084333965975289768881624112485132674005882563<86>
6×10115+1 = 6(0)1141<116> = 17 × 23 × 31 × 53 × 10193 × 694401711828655092792949<24> × 1281308932338524719016033<25> × 40539413087936983301001961<26> × 254034564641855352598667465918297<33>
6×10116+1 = 6(0)1151<117> = 29 × 83 × 131 × 685813586041<12> × 1844456395138388719546644007583570020351357048013<49> × 1504282446191996744686075825671917165322581155319641<52> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 1.68 hours on Pentium 4 2.80GHz / March 29, 2007 2007 年 3 月 29 日)
6×10117+1 = 6(0)1161<118> = 19249 × 104513 × 84949547191298834829861938440359659209<38> × 35108453167910401652183651057262560059278692771200689617890345494466697<71> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 2.30 hours on Pentium 4 2.80GHz / March 29, 2007 2007 年 3 月 29 日)
6×10118+1 = 6(0)1171<119> = 2411 × 987542448413<12> × 52015854024587<14> × 4130272925600541901178462189<28> × 117296157088580226224056755910106397663849713852624571466192849<63>
6×10119+1 = 6(0)1181<120> = 57543559 × 10426883745581325618041803775119297018107621740949321539183907620312466248394542297948585349057050850817204406839<113>
6×10120+1 = 6(0)1191<121> = 7 × 21247 × 801463667 × 27355202177207582747<20> × 8471936362176685853698170750873328576488389<43> × 217194658091737425168747728304628592086097429<45> (Makoto Kamada / Msieve 1.17 for P43 x P45 / March 28, 2007 2007 年 3 月 28 日)
6×10121+1 = 6(0)1201<122> = 61 × 252471385973041681<18> × 3895913010443395142052463046808468849591523951821310370343831754337081720480312214147822474048551205061<103>
6×10122+1 = 6(0)1211<123> = 1951 × 154619 × 1988983227431523625230622190849179449444735386649339263584065100428785335666892435047821737006964580574537628776429<115>
6×10123+1 = 6(0)1221<124> = 677 × 85482211 × 46731777018239824577493857223667185843576140952323<50> × 2218577168058000218769466780291988857687020303171346242507278821<64> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 1.95 hours on Core 2 Duo E6300@2.33GHz / March 28, 2007 2007 年 3 月 28 日)
6×10124+1 = 6(0)1231<125> = 344209 × 56280827 × 3097195063457860009522337786495159196439749744481215793546730363286460601958790340899822844604035083233374808707<112>
6×10125+1 = 6(0)1241<126> = 2237 × 3668449819<10> × 8271163308755950427286499111<28> × 51476248134260390790050421143<29> × 171723290681284284232336757421737754290876953562908401679<57>
6×10126+1 = 6(0)1251<127> = 7 × 785261756545781<15> × 11994069018834818454367125998411<32> × 91006459628890919464580217746794559086729129284436424507130614642478391402153873<80> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=4054558047 for P32 / March 25, 2007 2007 年 3 月 25 日)
6×10127+1 = 6(0)1261<128> = 263 × 1553 × 821897 × 80977097 × 123689475752141401<18> × 17844800569550782026356258864473158644358187707400859825983068391046935363574684890879023151<92>
6×10128+1 = 6(0)1271<129> = 53 × 367 × 382800053 × 639224669 × 126061886020057845203330929768004199056650509960559266998271417668976313280156469855945817424565152822528243<108>
6×10129+1 = 6(0)1281<130> = 46441 × 18431290643<11> × 1214943511927468592389<22> × 15906743128195327845877493<26> × 563762750909587173399187190635729<33> × 643369114600182232260522769188169819<36> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1640166223 for P33 / March 25, 2007 2007 年 3 月 25 日)
6×10130+1 = 6(0)1291<131> = 31 × 325910589480211013<18> × 80533406104775313809314886144551<32> × 73742017814548265755028178719963181032292046951828193081508776580982918009049717<80> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 2.49 hours on Core 2 Duo E6300@2.33GHz / March 29, 2007 2007 年 3 月 29 日)
6×10131+1 = 6(0)1301<132> = 172 × 19 × 353 × 7577 × 40853363102957510445201825139711551633716795076125752017311613159589753090587746005643771867608180363065555099012489640531<122>
6×10132+1 = 6(0)1311<133> = 72 × 347 × 36596493239037447170949018613664094139517120346108317971376267<62> × 9642423972646013466783289114801468750815943389674239701142494172201<67> (suberi / GGNFS-0.77.1-20060513-pentium4 / 6.36 hours on Pentium 4 2.26GHz, Windows XP and Cygwin / March 29, 2007 2007 年 3 月 29 日)
6×10133+1 = 6(0)1321<134> = 4390696903639<13> × 206718352549405901933<21> × 366262675924266703046624692745658752739944862649<48> × 180487069279920119803199143358086060304773059562666427<54> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 7.67 hours on Pentium 4 2.80GHz / March 29, 2007 2007 年 3 月 29 日)
6×10134+1 = 6(0)1331<135> = 13183 × 56512788861073<14> × 4433404553816215317147736447963746529<37> × 95562856740921441632025329178966092257<38> × 1900919699476513791402495760985135475898063<43> (suberi / GGNFS-0.77.1-20060513-pentium4 / 8.00 hours on Pentium 4 2.26GHz, Windows XP / March 31, 2007 2007 年 3 月 31 日)
6×10135+1 = 6(0)1341<136> = 6880668114947944749317742283818949380447951589<46> × 872008342760387973294859623740096978369380316479863520578687666785407351034250325563331309<90> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 4.93 hours on Cygwin on AMD 64 3200+ / March 29, 2007 2007 年 3 月 29 日)
6×10136+1 = 6(0)1351<137> = 287271635614354961093<21> × 41930632229393576833881200665999<32> × 4981121010552314579673023411353830652553041863694028008692298895946066995164432699043<85> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 5.30 hours on Core 2 Duo E6300@2.33GHz / March 29, 2007 2007 年 3 月 29 日)
6×10137+1 = 6(0)1361<138> = 23 × 48323971 × 4272684397523<13> × 14655169765563672253443781435081771<35> × 8621228002824546712512779722593849212894060284244445369802723033429410273152233309<82> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 6.19 hours on Core 2 Duo E6300@2.33GHz / March 29, 2007 2007 年 3 月 29 日)
6×10138+1 = 6(0)1371<139> = 7 × 149 × 313 × 1667 × 63551171 × 231479951514173<15> × 749462771129028187179501577300325243967405287612534956934150011882051100389202685246684753100633759671351799<108>
6×10139+1 = 6(0)1381<140> = 2277647 × 1508867401072225998121996787<28> × 323196751600306705639682362661998583<36> × 54019028760861303562927364638531753025925788771571944925497170577303123<71> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 7.00 hours on Athlon XP 3000+ / March 29, 2007 2007 年 3 月 29 日)
6×10140+1 = 6(0)1391<141> = 6553 × 36947 × 37307 × 73951 × 1557224920267273<16> × 2362708497035574005050811627<28> × 244138366996402871314657154147600629479440536453368969093870526132980050402458013<81>
6×10141+1 = 6(0)1401<142> = 53 × 1787 × 63350613973033755318811964819292373641921212953088870352968504186419740051313997318157341808237691503626822649956182492001984985904488391<137>
6×10142+1 = 6(0)1411<143> = 179 × 193 × 1949 × 20250697 × 168722167314338241440719151552099503<36> × 260805622756239731875686742670995926907630708041156681530524921153215720747176911819093845937<93> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 9.01 hours on Core 2 Duo E6300@2.33GHz / March 29, 2007 2007 年 3 月 29 日)
6×10143+1 = 6(0)1421<144> = 34979851 × 17152731725472472710075294488818720239831782016452843095300777581928522222693287058312512537574845587535521520660565420933325302043167651<137>
6×10144+1 = 6(0)1431<145> = 7 × 29 × 9419 × 8690737773132673400046895125462569162199460287601619<52> × 361071965016480062594290480035242393015221651315524279120702561149015142886111978824947<87> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 8.84 hours on Cygwin on AMD 64 3200+ / March 29, 2007 2007 年 3 月 29 日)
6×10145+1 = 6(0)1441<146> = 31 × 647 × 736071551375499639200941<24> × 2620389743008896032383787<25> × 1550955553437612011205718195563558193552672293790742620592000665671583464243332425988643526279<94>
6×10146+1 = 6(0)1451<147> = 59 × 7901 × 5214659 × 346417145671<12> × 286908163723179938475463307<27> × 2483413159054730378337215283022999229010263978375223753982805831421347502775406769232845620736793<97>
6×10147+1 = 6(0)1461<148> = 17 × 2543 × 115760644183242053581470522727778242831221097437922034717<57> × 1198933330911430747361811027483210008562962708283177147904000051570352016647574586611563<88> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 13.08 hours on Athlon XP 3000+ / March 30, 2007 2007 年 3 月 30 日)
6×10148+1 = 6(0)1471<149> = 45413 × 1021518389977<13> × 61418399131257487532861<23> × 4713973367965261212205092299<28> × 43077009313549326145069669110361<32> × 103703570011344634621906538130450202423763726827619<51> (Makoto Kamada / Msieve 1.17 for P32 x P51 / March 28, 2007 2007 年 3 月 28 日)
6×10149+1 = 6(0)1481<150> = 19 × 109 × 113 × 10579907627<11> × 5679856078924981<16> × 22501049938160881627846852996382188283<38> × 1896141385290142214720833871694818954129695297495385547007001852440390777837062947<82> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 16.31 hours on Core 2 Duo E6300@2.33GHz / March 30, 2007 2007 年 3 月 30 日)
6×10150+1 = 6(0)1491<151> = 7 × 2287 × 274691407 × 106052555431<12> × 12865327147663768523973250151725082408362339117847704977202467479029658749866722758755177966327179672272580078220625196472106417<128>
6×10151+1 = 6(0)1501<152> = 139 × 498255827 × 85355460087173921743066987368891301<35> × 4059984657865523211612358150944087268984576395068423<52> × 2499932966831125928910143611140847400709468157774550779<55> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 17.90 hours on Cygwin on AMD 64 3200+ / March 30, 2007 2007 年 3 月 30 日)
6×10152+1 = 6(0)1511<153> = 97 × 107 × 4413797 × 146950709 × 312531144238105714806234223<27> × 298164910200576610275597713265821141<36> × 956449101954012566944100844383139842704712531307907202661451759300471921<72> (Jo Yeong Uk / GMP-ECM 6.1.1 B1=1000000, sigma=23251224 for P36 / March 29, 2007 2007 年 3 月 29 日)
6×10153+1 = 6(0)1521<154> = 21617 × 1541654209<10> × 984429390961917259297755699215421271<36> × 182887609531191459362098716133019089012168238316933698590744176357181073877813369466618012759402594754327<105> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 27.14 hours on Athlon XP 3000+ / March 31, 2007 2007 年 3 月 31 日)
6×10154+1 = 6(0)1531<155> = 53 × 110164333547<12> × 238374791151267475667638647382887847013<39> × 43109605018575408648854020726186133527988347085935528901089943775031879035223884740987728777643420089547<104> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 21.24 hours on Core 2 Duo E6300@2.33GHz / March 31, 2007 2007 年 3 月 31 日)
6×10155+1 = 6(0)1541<156> = 15679 × 5838172087029064235976796069<28> × 6554747975404540742365128375128746950110811434716985062195497790142313250580415385937683038666601418715210100773572817781651<124> (Jo Yeong Uk / GMP-ECM 6.1.1 B1=1000000, sigma=273397416 for P28 / March 30, 2007 2007 年 3 月 30 日)
6×10156+1 = 6(0)1551<157> = 7 × 293 × 34589 × 3080875249<10> × 27451967147179722860574811764507770588509908035860564022334209651903010584803289607053853581663398484714009288847560755778089982663689650391<140>
6×10157+1 = 6(0)1561<158> = 83 × 151 × 72179234791<11> × 72357737078330308558694680661590216271249223389638162975859539<62> × 916640329258611436341178406620060063987449880780814068401233780150914565592579353<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 34.58 hours on Cygwin on AMD XP 2700+ / April 19, 2007 2007 年 4 月 19 日)
6×10158+1 = 6(0)1571<159> = 23571451973426463027469189039<29> × 25454520182991554071457193472923624023655677192163090199587296650880130688226908716630410700752359541445351753329666094641222465359<131>
6×10159+1 = 6(0)1581<160> = 23 × 47 × 3167 × 36887 × 48599731 × 306920722151401391534780179<27> × 767698777607940194265527635370316671942213<42> × 4149093592080265396266679279339449692918936093049417612900424150237843877<73> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P42 x P73 / 25.89 hours on Core 2 Quad Q6600 / June 2, 2007 2007 年 6 月 2 日)
6×10160+1 = 6(0)1591<161> = 31 × 670853 × 27432596289301964073885280181487235430291<41> × 105170824355437139403715973975995678497668642440971399521069843399452536718803322806044637013799975195072495150977<114> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 33.19 hours on Cygwin on AMD 64 3200+ / June 10, 2007 2007 年 6 月 10 日)
6×10161+1 = 6(0)1601<162> = 1187 × 505475989890480202190395956192080876158382476832350463352990732940185341196293176074136478517270429654591406908171861836562763268744734625105307497893850042123<159>
6×10162+1 = 6(0)1611<163> = 7 × 409 × 461 × 1297 × 71355177903228522649<20> × 105440523536650831469<21> × 2635929378062082616090181215642985097332592374330359<52> × 176734845085883901472849673672121748213269636335439399849960889<63> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 25.27 hours on Core 2 Quad Q6600 / May 9, 2007 2007 年 5 月 9 日)
6×10163+1 = 6(0)1621<164> = 17 × 353 × 383 × 5215147241069255739103596758994562191897609456843465301<55> × 5005670690155230684429614037038784632521687552228111599112073609027731095334283017297356948767263632947<103> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 63.28 hours on Cygwin on AMD XP 2700+ / July 26, 2007 2007 年 7 月 26 日)
6×10164+1 = 6(0)1631<165> = 127301 × 9028519 × 731813929840206967957739<24> × 369270152835869755547632504844697137215152321611<48> × 1931781669601575696400721360944887567321529473091599594216511185010148045718575651<82> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 109.83 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / May 25, 2008 2008 年 5 月 25 日)
6×10165+1 = 6(0)1641<166> = 108649 × 1383530154323<13> × 10418259026881<14> × 12198214958645406697515956553865609339286480946779228031841<59> × 314083740589948806536874133179020940182628645393194584520163117078481245780803<78> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs / 73.33 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / August 13, 2008 2008 年 8 月 13 日)
6×10166+1 = 6(0)1651<167> = 511873 × 1672952309429<13> × 10374402770189235705553<23> × 6753709287929355035146226664320891176106045884127335781481288525048429003589981557630847342869747421590160530223111979292489101<127>
6×10167+1 = 6(0)1661<168> = 19 × 53 × 151888273037<12> × 285222132532084029211<21> × 11344553699289079283476154821341898793<38> × 1212346876153485600056159157453359594304541020922218903516315067388636750613885280058055706162793<97> (Robert Backstrom / GMP-ECM 6.2.1 B1=5466000, sigma=2706353897 for P38 / October 3, 2008 2008 年 10 月 3 日)
6×10168+1 = 6(0)1671<169> = 7 × 192463 × 782311 × 76228657 × 7328634264783832045460771<25> × 10190258598918290646665763144046669701615740101386780018710605032958701422540550897580384388016235363077372155509748597910533<125>
6×10169+1 = 6(0)1681<170> = 1163 × 50207 × 409692145250436913282056636020822590790365187<45> × 2508127593417771961783639597835041387496768657625863183136324428934170806705227815812321776714203987196208985026667903<118> (matsui / GGNFS-0.77.1-20060513-prescott snfs / 153.02 hours / May 30, 2008 2008 年 5 月 30 日)
6×10170+1 = 6(0)1691<171> = 2036522480469412757<19> × 15289860020412201132871070965187<32> × 19268971414983811114353408295498404565964742578518175921195273229007773017207159266351520463816824536907817669941020019839<122> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2501685443 for P32 / March 27, 2007 2007 年 3 月 27 日)
6×10171+1 = 6(0)1701<172> = 154699561095803788960811837883435548718183965521<48> × 38784854704818871237674570715604655076738950339421849949486353744053423298050903282396196418361477719330298221232535393256881<125> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 121.74 hours on Core 2 Duo E6300@2.33GHz / April 22, 2007 2007 年 4 月 22 日)
6×10172+1 = 6(0)1711<173> = 29 × 199 × 16071179 × 19040639559853345070153144890519<32> × 33975895006073920745483829891601971700743187759442035498563591928892715199253724062640060946711525430463604441778590052394140275231<131> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1259013039 for P32 / March 27, 2007 2007 年 3 月 27 日)
6×10173+1 = 6(0)1721<174> = 21541129 × 27853693276708012843709352467087495738965213940272118513379684045344141432884042428788203255270417813291030381926592612671322844777541604249248031521467607384923974969<167>
6×10174+1 = 6(0)1731<175> = 72 × 26739999478904985595633<23> × 2530871633323057178390377682713<31> × 1809354470273988391909928868065730996169303489059876315412862866428943687873409338301708886637922973447152338599360182281<121> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1641265231 for P31 / March 27, 2007 2007 年 3 月 27 日)
6×10175+1 = 6(0)1741<176> = 31 × 227 × 18229 × 142965322616087752221825023<27> × 78834246190375597401811445588639063<35> × 41500681309919383885445995508284685803042892144778268185725040022437427106594917277468373401274522948400313<107> (Nechaev Sergey / Msieve v. 1.39 for P35 x P107 / 6.91 hours on Intel Celeron 1200 MHz, Windows XP / December 11, 2008 2008 年 12 月 11 日)
6×10176+1 = 6(0)1751<177> = 1030061 × 759763843008042511<18> × 766672144559061628890362809860246401749327549579192810118560668328581190184331587072870045980078093533295409943121533471797139072738514272272184421422731<153>
6×10177+1 = 6(0)1761<178> = 1711983023<10> × 130909460131276140628552263669024355006100394847355624263188932213877563<72> × 26771996829082488321535109586807695003489696065663320871538381541557110996579284791617298469559549<98> (Tyler Cadigan / GGNFS and Msieve snfs / 97.06 hours on C2Q Q6600 2.4 GHz, 3 Gb RAM, Windows Vista / July 7, 2009 2009 年 7 月 7 日)
6×10178+1 = 6(0)1771<179> = 223 × 23027 × 104789 × 1426643 × 40644591731<11> × 1922982159835701962150458941690226028839255940333920593187848701699883509225282546417481896412237304915230566990618028032839551868545552478944916472713<151>
6×10179+1 = 6(0)1781<180> = 17 × 751 × 112771 × 518476220445751<15> × 7132513818777656481169<22> × 112692106264930656963353447779273751723066822219291723251430616150893819819926889355130216345663562021311482951308997824134576583591747<135>
6×10180+1 = 6(0)1791<181> = 7 × 53 × 5189 × 1530654942827<13> × 77961257465282390200811842235367085099161175733216672157092688181205275825630537<80> × 26117856802019915612096483598867398142659189050194588384216401897862531400938257621<83> (Tyler Cadigan / GGNFS, Msieve snfs / 143.05 hours on C2Q Q6600 2.40 GHz, 3 Gb RAM, Windows Vista / July 5, 2009 2009 年 7 月 5 日)
6×10181+1 = 6(0)1801<182> = 23 × 61 × 22921 × 1872699346433998020537767237<28> × 3221817407318169274057683443449767963151785037276817<52> × 309236703947623304730799733324982576204663378968922310111028745418217199315661984343512735564463<96> (Tyler Cadigan / GGNFS, Msieve snfs / 223.86 hours on C2Q Q6600 2.4GHz, 4 Gb RAM, Windows Vista / July 2, 2009 2009 年 7 月 2 日)
6×10182+1 = 6(0)1811<183> = 197 × 145547 × 1137803 × 3697766213694124457129202150295765873<37> × 4973650241959479991177377391777452977902057601073658068611396750923243720787211361706581622604893959178219884712767066984209658142981<133> (Serge Batalov / GMP-ECM 6.2.1 B1=11000000, sigma=1250300280 for P37 / February 13, 2009 2009 年 2 月 13 日)
6×10183+1 = 6(0)1821<184> = 20333 × 10194940864693489<17> × 28944435148578785733104660113465072797152479367601174647170452255255351712646305441136563428992615113626275537468635220759236152222648647988056301400691764608750773<164>
6×10184+1 = 6(0)1831<185> = 587 × 6203 × 325333469 × 713020687 × 71036326324885719916006924101251043260542849380055405036227243025556824832034153023040670401241782980289641135898120243779064840152646514058646245571449472789347<161>
6×10185+1 = 6(0)1841<186> = 19 × 167 × 3149035144740077<16> × 30217523095511560432976100709<29> × 123251687544331276107061304469530687861827519667502885428574726923<66> × 16123225707827282939353513239821935387962162632669892472730626095154698983<74> (Tyler Cadigan / GGNFS, Msieve snfs / 216.99 hours on C2Q Q6600 2.40 GHz, 4Gb RAM, Windows Vista / June 24, 2009 2009 年 6 月 24 日)
6×10186+1 = 6(0)1851<187> = 7 × 10163 × 62671630591<11> × 1345737301505097687201439347428036846138371098114174304318480099980843850210046146833023361562269414714787790594720740673267590241197928585436790524132914144562207600247571<172>
6×10187+1 = 6(0)1861<188> = 4547 × 6536834037833420095985946925674276836560136508795702561667702266167<67> × 2018639826103785865286631933082975605890545795355024440916114945745465813061205948102752034943266139296166842862791149<118> (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / 777.86 hours / August 27, 2008 2008 年 8 月 27 日)
6×10188+1 = 6(0)1871<189> = 1637 × 57366058831<11> × 91095427949217511<17> × 22030613152866699260353<23> × 3183643221139836301633704566827700114389439812117447115877607563174062544857782710167851006811747130033335416499676921705100923728652101<136>
6×10189+1 = 6(0)1881<190> = 42589 × 5780291335866737<16> × 107788304148617970061487122159<30> × 174013302696433020274845304681<30> × 18309085696764041534162136664724986762411<41> × 70971393580825121102733841341176453634821357709829428898091709401554553<71> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=4096400016 for P30 / March 27, 2007 2007 年 3 月 27 日) (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2803236752 for P30, Msieve+pol51select gnfs for P41 x P71 / 16.0 hours on Opteron-2.2GHz; Linux x86_64 / August 3, 2008 2008 年 8 月 3 日)
6×10190+1 = 6(0)1891<191> = 31 × 317 × 607 × 4014704477167<13> × 2505463157764540601632715230028063963509462985755629687871628272822482673435884812516654525020188175592347477023966102366980522080623114977847924939420382160579296254327227<172>
6×10191+1 = 6(0)1901<192> = 131635826256638403650836189<27> × 4558029656988930544160466050975243216804086899733582752815935681533569740973520942156018486465079186654037838635878625973621820618371568810759829632545572174289678709<166>
6×10192+1 = 6(0)1911<193> = 7 × 99079 × 687912079 × 2915419952598811618594940160413805922953111384734672751972710929408139<70> × 4313576840393877505883357285400035595676725490320331778252232358628296531245916896568438767438261380374823357<109> (Tyler Cadigan / GGNFS, Msieve snfs / 386.28 hours on C2Q Q6600 2.4 GHz, 4 GB RAM, Windows Vista / May 13, 2009 2009 年 5 月 13 日)
6×10193+1 = 6(0)1921<194> = 53 × 1009 × 500066384184503<15> × 419477943340664305459<21> × 5348689947030520136369877611008157028910945064205692570927331747738290069137351398562510725948141270187377372256033232564725133808464233517898734873007769<154>
6×10194+1 = 6(0)1931<195> = 153817 × 33881245227068299278185531<26> × 901361069267656452128353133474957<33> × 266634767326292612283152421868647275640368024889323<51> × 479040217579134298529209937599938953347103505261874490787658533513714122044192133<81> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=3175350205 for P33 / July 13, 2008 2008 年 7 月 13 日) (Tyler Cadigan / ggnfs, msieve gnfs for P51 x P81 / 172.66 hours on C2Q Q6600 2.4 GHz, 3 GB RAM, Windows Vista / April 27, 2009 2009 年 4 月 27 日)
6×10195+1 = 6(0)1941<196> = 17 × 353 × 421 × 53984968629707<14> × 5444649381690383<16> × 450367983155898302933<21> × 154154162540960500400074342123380051113966965013<48> × 116380439153233275654538630432091976492720690680968724771611953842197614880172185920433608769<93> (Tyler Cadigan / GGNFS, Msieve snfs / 357.78 hours on C2Q Q6600 2.4 GHz, 3 Gb RAM, Windows vista / April 5, 2009 2009 年 4 月 5 日)
6×10196+1 = 6(0)1951<197> = 4526985911422555852980453461875447673693370404671619628486604463189<67> × 13253851718117155717822280766012995701858464863771693748201984239161431357726436028994453405662098135543550990120795749232748691709<131> (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / 2601.57 hours / July 21, 2008 2008 年 7 月 21 日)
6×10197+1 = 6(0)1961<198> = 139 × 407899 × 1342591 × 861735247427<12> × 14372479836996783727118873851<29> × 636406362238420386067405897142966505290908179596403443220782248012253741879671512661660594487605220807515330784453069807282234525943730437109463<144>
6×10198+1 = 6(0)1971<199> = 7 × 83 × 827 × 1671913865053753682774008058984727775285847092318926307764219314568321887709471774615950144902657<97> × 7468883908162308115227893005644186201669945225303700140432172123968956930897287431172882486068439<97> (matsui / GGNFS-0.77.1-20060722-nocona / March 14, 2009 2009 年 3 月 14 日)
6×10199+1 = 6(0)1981<200> = 100827365033<12> × 21583541164043<14> × 10056670285225909<17> × 2683916005958404450397<22> × 479403087032713635428088886452712241517044136079900092034489<60> × 2130718979593492245520692728000484684740606068588764504461505725233767054216707<79> (Tyler Cadigan / GGNFS, Msieve gnfs for P60 x P79 / 729.05 hours on C2Q Q6600 2.40 Ghz, 4 GB RAM, Windows Vista / July 10, 2008 2008 年 7 月 10 日)
6×10200+1 = 6(0)1991<201> = 29 × 367530286683762818311653969900003494345257271270268514080948164981978980653079960969<84> × 56293742099725151227484967667076511849333661046901547637197489587498221199711228253147257513850471263698402737741901<116> (Serge Batalov / Msieve 1.36 / 13 CPU-days on Opteron-2.8GHz; Linux x86_64 / July 4, 2008 2008 年 7 月 4 日)
6×10201+1 = 6(0)2001<202> = 2225563489<10> × 61606411986233<14> × 118262220048541<15> × 564256026646829812845655621474346967186364866619<48> × 13689148278628213736253934043379291331904196376743122587373<59> × 47905644251948833734888937404536696715074656053242700517219<59> (Daniel Morel / GGNFS-0.77.1 for P48 x P59(1368...) x P59(4790...) / June 10, 2015 2015 年 6 月 10 日)
6×10202+1 = 6(0)2011<203> = 113761 × 244393 × 660429923798209<15> × 135180804513951511904761<24> × 5164634473621039289825138497<28> × 1664792180982452240067957261454638056603<40> × 2811432753405739343413857814027793980466733704390188713337746638191403396481943299125843<88> (Wataru Sakai / GMP-ECM 6.2.1 [powered by GMP 4.2.4] B1=3000000, sigma=2090088941 for P40 / April 29, 2009 2009 年 4 月 29 日)
6×10203+1 = 6(0)2021<204> = 19 × 23 × 8747 × 40099 × 294001 × 110099638731542339689<21> × [120932336311005545217438828723296762314979253137175536923058070093950074987740428648151640404375291883342041532643463387992645778112870514906506745223897415122959454469<168>] Free to factor
6×10204+1 = 6(0)2031<205> = 7 × 59 × 269 × 173189 × 2924524113403271554277<22> × 1734660937911648308100611<25> × [61469376594875039285339745941562553088275938523221973444637371499240824867009628082697711902012802021710169239870884627641364181080164857616797060251<149>] Free to factor
6×10205+1 = 6(0)2041<206> = 31 × 47 × 107 × 321588220688443027059385703<27> × 52608200965763511019049070037321<32> × 22748582359849985239621437062492301500654660877058842699222608390850103339364205134046046593760422318845790606886535630528076929599435895212973<143> (Andreas Tete / Syd`s Database workers / June 24, 2009 2009 年 6 月 24 日)
6×10206+1 = 6(0)2051<207> = 53 × 4574867761<10> × [2474553431574288530669443783559353284181479263246617180652420545039052014506919716133564757945814528582635726057474956448419781325594489783919704691885447005671549227755073481668599013567760077997<196>] Free to factor
6×10207+1 = 6(0)2061<208> = 513423499698584619487313<24> × 79618697596892077071138483321192894737071<41> × 146777821844486557389040483960612504449998876641972816252309655923845838222171851166658021925077821429691049478851087369411295798187375235312287<144> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3743416835 for P41 / October 21, 2011 2011 年 10 月 21 日)
6×10208+1 = 6(0)2071<209> = 2647 × 3821 × 850753 × 6755761 × 971934673 × 21283182711527263<17> × [49896359055227933118610317314146247306293714743503905351208213773843602035116122826852286798123479165041143667670534060051856340657949231563840707868910418698998269<164>] Free to factor
6×10209+1 = 6(0)2081<210> = 14606547715813294792570148783<29> × 78248562896776458346290111772194889535027<41> × 524961312088981240761706813162724768225758601667592541510525842405874187614578364712638573542900687344493022787724045392478559560366855673461<141> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=368381219 for P41 / June 23, 2011 2011 年 6 月 23 日)
6×10210+1 = 6(0)2091<211> = 7 × 4421 × 19622139371<11> × 252809993911<12> × 9268407889573397<16> × 4827473644273332098647024801834676314904186877557<49> × 112660341051730378022841041426578603660447154319481<51> × 7753467841745894609952521327357873711653244823140906637011225288209207<70> (Jarekcz / GMP-ECM B1=110000000, sigma=2789305117 for P49 / February 9, 2012 2012 年 2 月 9 日) (Warut Roonguthai / Msieve 1.48 gnfs for P51 x P70 / February 11, 2012 2012 年 2 月 11 日)
6×10211+1 = 6(0)2101<212> = 17 × 3137 × 1934993 × 197187806811077<15> × 2735647194507440043171527<25> × 1077874674487459041321780056497445099308196526362518107059676445510932744355786130014254635238238193900381920634361431912800286992413856080171934813272242432699627<163>
6×10212+1 = 6(0)2111<213> = 30310182479923312155099860956849<32> × 71462050059312788558061849474665255505891120211095721<53> × 277004757824786859739574561746447571367623701884925334566659905599249423169467669692331048224981488052053000278285698065610052969<129> (Luca Dentis / GMP-ECM B1=110000000, sigma=1720472598 for P53 / February 17, 2012 2012 年 2 月 17 日)
6×10213+1 = 6(0)2121<214> = 887 × 710379914267074902446340727571899<33> × [9522192505057989196554921686963471449090843139265281936834912784663455668678513277670521436604345942154664018593294330166634222414359055518446450597428054285995444333986164085477<178>] (Dmitry Domanov / ECMNET / June 29, 2009 2009 年 6 月 29 日) Free to factor
6×10214+1 = 6(0)2131<215> = 14966220127<11> × 4009028297783502192370232534934035986600319232361909519573913186770809548443574085351283835222718423671091310549450934185100269706864241420227775592706274511954463918195982845976484279997654480576784316063<205>
6×10215+1 = 6(0)2141<216> = 27743 × 2608618741<10> × 2762769781<10> × 130348155258427691832199143115088842224118243369<48> × 23021712823674463610604725762720121163464475786421833593613070410954740853473218308017685931816166156557222385360810464398466464467405038012828543<146> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1829096944 for P48 / October 17, 2011 2011 年 10 月 17 日)
6×10216+1 = 6(0)2151<217> = 73 × 3559 × 4057 × 18461 × 8865690481<10> × 75489457323208605217787830670233307<35> × 83978197266462101076064089967720589<35> × 11134874088796811548989085386956025402377404670627767<53> × 104862011886701842859867678154061045329791078617618960948431616167852869<72> (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=1144671962 for P35 / April 27, 2009 2009 年 4 月 27 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=862339009 for P35 / June 22, 2011 2011 年 6 月 22 日) (Warut Roonguthai / Msieve 1.47 gnfs for P53 x P72 / June 24, 2011 2011 年 6 月 24 日)
6×10217+1 = 6(0)2161<218> = 257 × 349 × 6461393 × 809911656979<12> × [127828853422059537003472317965694266321463860425142827561508522098008664069098486916507550465809801978757093612412749321256468501907725458430073251293462025007845075292622242824462589338838792231<195>] Free to factor
6×10218+1 = 6(0)2171<219> = 773 × 3360557628479311451<19> × [230972571308791767079660398588940172682674244652603150512637261643251127081200372333147802374543750072565549539549438844421098731540456164788424191023126992805869669114418432392670388290991549245687<198>] Free to factor
6×10219+1 = 6(0)2181<220> = 53 × 34003565881<11> × 494973402126704928209657394401416382082437<42> × [6726188830424553957034050930323117633464279117529765442480040261457293421363839323101511248843846029484797845424675131183704410465632954687105721729614190663095365761<166>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2881583422 for P42 / October 18, 2011 2011 年 10 月 18 日) Free to factor
6×10220+1 = 6(0)2191<221> = 31 × 11562157632455563451<20> × 4724959633308048901807<22> × 47608461509345259544598383222613395095037977779<47> × 744163595831850770524650122231893527065008676611309268372786950965724605002909874364184528641303749037408203154616808217304514717457<132> (Liuqyn / GMP-ECM B1=110000000, sigma=2561761274 for P47 / February 17, 2012 2012 年 2 月 17 日)
6×10221+1 = 6(0)2201<222> = 19 × 13547461 × 16726782991<11> × 3349384721392093940733381409<28> × 3849322964951777452392095093<28> × 694683008640191018051495572579<30> × 2106663983424484976725368044339228518607232620507<49> × 7385773499148755352472981597178105724655405297506528416547206510108989<70> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=2976623049 for P30 / April 25, 2009 2009 年 4 月 25 日) (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 gnfs for P49 x P70 / 88.83 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / May 1, 2009 2009 年 5 月 1 日)
6×10222+1 = 6(0)2211<223> = 7 × 337 × 6053 × 13757 × 246247 × 328787 × 2619177251<10> × [144038444453453329574500213335144414500762145327079867935224833493301308448860309970418483001096065719783607979333452602014533516564320416462824684134685434787889528135769064809669572762597881<192>] Free to factor
6×10223+1 = 6(0)2221<224> = 42023 × 2048279561630094413940242246970488263454250075107126516663<58> × 4487087514500719652610502868943979821190063207053724258161633999469<67> × 155349702434172729239694378089117934482361267066359337694151534312046853369486165859085416527621<96> (RSALS + Rich Dickerson / ggnfs-lasieve4I14e on the RSALS grid + msieve for P58 x P67 x P96 / May 26, 2012 2012 年 5 月 26 日)
6×10224+1 = 6(0)2231<225> = 12893 × 456587 × 5234914814974827841<19> × 19469917292117625378372454307740577683777572293324023736069492063795887600699869853539709332305042399546624874863957940518852410480205669600935052587176978380108070012514004659219771434223235406271<197>
6×10225+1 = 6(0)2241<226> = 23 × 36379877 × 167906990293368652928728873261<30> × 42706444003089520713978269973163684708080590638366819749334561938215780974654681734405888760198272741801801164400514926098114885040973707174419364829994643860289586117344843093917829015271<188> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=784847885 for P30 / April 25, 2009 2009 年 4 月 25 日)
6×10226+1 = 6(0)2251<227> = 16993 × 853230859912925311<18> × 1182152605259529083<19> × 23328829225931296935726363124384539817061<41> × 150054198203333894416412386736518052903362043117297361103189602498212076728503882348175799862828310083290295350842104744376323742647819954320828649<147> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2397751228 for P41 / June 14, 2011 2011 年 6 月 14 日)
6×10227+1 = 6(0)2261<228> = 17 × 353 × 17997054941964696824701<23> × [5555538749704637838636056885361687030218278147127919593369097015272101270279286520883876392076389277937907573983740176346326219501356061869390862382923304585478834763645330358076583391112333703954459301<202>] Free to factor
6×10228+1 = 6(0)2271<229> = 7 × 29 × 554503 × 4625381172371<13> × 1024270246223771<16> × [11250950835078257092587523087761353502758727110999868384122564107470762528276862320886261278553329280222844251141286045581714145858865460016993980893336885027290226763646180334123589384265058629<194>] Free to factor
6×10229+1 = 6(0)2281<230> = 3331 × 51178651 × 15247364120761080019<20> × 23083040398172312983687660449500916932696614323065102361931902852451991975232985632567773880128053178275361089585717569770869770720152189812790448348845860485937295473801513483593237358685958625713259<200>
6×10230+1 = 6(0)2291<231> = 28580683787911<14> × 966104844865412266835017<24> × 4291261667578816733310217<25> × 7829789442671845101708781187<28> × 646724471904227486287969678475507650807150787626440294302298069606340259318073423579855720775004434559244811093120430417194411350111118189037<141>
6×10231+1 = 6(0)2301<232> = 517189 × 233707958941<12> × 666326798213<12> × 2633861861153993<16> × [28284479737499129152822600564231655496835764653077090817754128651163796472081365298861046682262445285592081935768488045664721912918535404037065424197190461427203294489468499248120754453461<188>] Free to factor
6×10232+1 = 6(0)2311<233> = 53 × 151 × 24433776845411<14> × 3648794765150784943<19> × 9271425880342337957537563139998169933441799916441558373<55> × 9070095576259033901463743258837986832933278101846777357186246457227663780700787488762216946233238419305919628585380317160061445560373475550123<142> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2996709645 for P55 / October 3, 2011 2011 年 10 月 3 日)
6×10233+1 = 6(0)2321<234> = 294510113 × 1778348809<10> × 778008505367081881201<21> × 2561616974580876396755878639763<31> × [574824873435899378320065034350864626543502944955975704501487535802286423132854167632694971627309959241359282121449541103533943009375174285144531117192634556032152531<165>] (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=2878558676 for P31 / April 27, 2009 2009 年 4 月 27 日) Free to factor
6×10234+1 = 6(0)2331<235> = 7 × 631 × 6947 × 29599 × 89983 × 400417 × 33815673323<11> × 34065915203<11> × 42381982012937719996781541707<29> × 17778023228758783526348292647766340722880511004101<50> × 13305879021578738778643983828305010925616630988038713<53> × 15875599519197612600929334930759310129257729865522799741895029<62> ([AF>Le_Pommier>MacBidouille.com]m.o.u.s.t.i.c / GMP-ECM B1=110000000, sigma=1693717372 for P53 / October 17, 2010 2010 年 10 月 17 日) (juno1369 / GGNFS + Msieve gnfs for P50 x P62 / October 18, 2010 2010 年 10 月 18 日)
6×10235+1 = 6(0)2341<236> = 31 × 146807 × 39354311511429882928421207419725036797127964577<47> × 335004371033978170127841893046092684577130764895147712303150389434763619081855345937930512874263549580310312810475308980847179347139683026972304048411026125037229495133539117958188089<183> (Frank Villasenor / GMP-ECM B1=110000000, sigma=1499033456 for P47 / November 6, 2011 2011 年 11 月 6 日)
6×10236+1 = 6(0)2351<237> = 1931 × 4297 × 124447 × 2020530728631977367651683<25> × 287576723692415176064312067280682520949945746249466352463721951457763944003335261921765989752422514216338104289278901900719806333306707513644986758860538144862049585237138318928951944714842328553064743<201>
6×10237+1 = 6(0)2361<238> = 14207 × 30319 × 127247 × 168769 × 294478757 × [2202621105970231633096320716945299937737615144016321880109664447051016331230243862979945994446896802085657981349347119419652804647506547756650174746519529727219895372440161403050334403001641372784744844096265747<211>] Free to factor
6×10238+1 = 6(0)2371<239> = 22851109319452294619<20> × [2625693097049089179102852472133002996435553277937619019278256313518290223610517942128123079019982545066636294331949382226994154385558313972151398260950370569326765626569778411133963460805661320049237911582251832189072979<220>] Free to factor
6×10239+1 = 6(0)2381<240> = 19 × 83 × 3209206549<10> × 21059094549481<14> × 19799792940089117<17> × [284329253122044126126507729304987239671901220746257910658557985655216463118884855064541107365005713589154594373478262599109523624517863380475553575947251619381911189078192142750450431861737084979281<198>] Free to factor
6×10240+1 = 6(0)2391<241> = 7 × 29361243894553<14> × [29193002184143548010722146658005203781686415613396510380928161193735148151520181647487611118921561593227420751593314409161865463194750353232784801436898113035460560948748183599434430406028420522019493313302619407575651965342031<227>] Free to factor
6×10241+1 = 6(0)2401<242> = 61 × 1993457 × 66806086732346187153080093460977<32> × 7385816445095095081672536827873340851880321452808389514070616294708745431771144121371438927806790015808582624263908381754884501004064893018058904330640238898561924274951347352236524448164445185989177269<202> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2896162561 for P32 / April 26, 2009 2009 年 4 月 26 日)
6×10242+1 = 6(0)2411<243> = 25919781365568892722384956852629495634503802901348780782570768063568310293710996482740826565327874208225740749<110> × 23148343403738084574786519719198785959318631918784209019174405368746958342042218577943294663688899880455296243370662891699700923071749<134> (Markus Tervooren / gnfs-lasieve4I14e/gnfs-lasieve4I14e 64bit-binaries, msieve 1.44 for P110 x P134 / January 20, 2010 2010 年 1 月 20 日)
6×10243+1 = 6(0)2421<244> = 17 × 139 × 777082049701<12> × 13604467049460231226367027<26> × 56252487052244287328130032241000503859115369<44> × [4269700282926336274467321549434975508544818185404431152949209397120222893741851919446584122194729796723070708659083819846912912767980629089757807128611131344229<160>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2437190698 for P44 / June 2, 2011 2011 年 6 月 2 日) Free to factor
6×10244+1 = 6(0)2431<245> = definitely prime number 素数
6×10245+1 = 6(0)2441<246> = 53 × 904553907099202855771697<24> × [12515290275275522677447921732793061935758321841029560108679729030434755172127603073693023217299084935355957348545636709883130535820345086270196087344266563979905106610551523765653010191477331581620753298350470259022879661<221>] Free to factor
6×10246+1 = 6(0)2451<247> = 7 × 131 × 16979 × [385362815558355715954977548441229890564025366378879856912217497745466961143803080115066767640287961079383262780894970456480880898290999408275396710144798151131974368491503038939049925229979711290032211835481163690370483314978288337835762607<240>] Free to factor
6×10247+1 = 6(0)2461<248> = 23 × 64502343527451756321326593416153156822188510993<47> × 40443424370521824728099907957468957355291552367752848725941579690299109731436832691693984983805350191875476171634638662389386605140231027674803952914383462009298719698559670626457608130168274688117559<200> (RSALS + Tom Womack / ggnfs-lasieve4I14e on the RSALS grid + msieve for P47 x P200 / June 8, 2010 2010 年 6 月 8 日)
6×10248+1 = 6(0)2471<249> = 97 × 1129 × 907355487952378274363<21> × 88681323985290974670149<23> × 68088840023549764912462202076155166068454341739405596698914195931122921597936876142048454503999951364220813879016235098496103008145032699014206084246146683593865766583245479481473238938126263660282271<200>
6×10249+1 = 6(0)2481<250> = 181 × 2431787 × [13631609705421664004371639057049120417316645483410243519006225117669020549553937720269631331547881754973510408518963614977664823331486939371850471955976752807299950555652469989630684409930339589047907649352113332421545252603690276223146333783<242>] Free to factor
6×10250+1 = 6(0)2491<251> = 31 × 467 × 10819258797103<14> × 150634428107377<15> × 2543026722062724874222761013772549130160652191728112226848569205345587500212581524689828614601617923924327123659806074932013190941461852182458839185936866804855754517808574882484256833179523889435807795775883254316131323<220>
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