Table of contents 目次

  1. About 900...007 900...007 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 900...007 900...007 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 900...007 900...007 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 900...007 900...007 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

90w7 = { 97, 907, 9007, 90007, 900007, 9000007, 90000007, 900000007, 9000000007, 90000000007, … }

1.3. General term 一般項

9×10n+7 (1≤n)

2. Prime numbers of the form 900...007 900...007 の形の素数

2.1. Last updated 最終更新日

October 27, 2015 2015 年 10 月 27 日

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

  1. 9×101+7 = 97 is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  2. 9×102+7 = 907 is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  3. 9×103+7 = 9007 is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  4. 9×104+7 = 90007 is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  5. 9×105+7 = 900007 is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  6. 9×1015+7 = 9(0)147<16> is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  7. 9×1019+7 = 9(0)187<20> is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  8. 9×1020+7 = 9(0)197<21> is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  9. 9×1046+7 = 9(0)457<47> is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  10. 9×1052+7 = 9(0)517<53> is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  11. 9×1053+7 = 9(0)527<54> is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  12. 9×10192+7 = 9(0)1917<193> is prime. は素数です。 (Julien Peter Benney / August 16, 2004 2004 年 8 月 16 日)
  13. 9×10380+7 = 9(0)3797<381> is prime. は素数です。 (discovered by: (発見: Jason Earls / August 18, 2004 2004 年 8 月 18 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 8, 2005 2005 年 1 月 8 日)
  14. 9×10588+7 = 9(0)5877<589> is prime. は素数です。 (discovered by: (発見: Jason Earls / August 18, 2004 2004 年 8 月 18 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 1, 2006 2006 年 6 月 1 日)
  15. 9×10776+7 = 9(0)7757<777> is prime. は素数です。 (discovered by: (発見: Jason Earls / August 18, 2004 2004 年 8 月 18 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 1, 2006 2006 年 6 月 1 日)
  16. 9×10906+7 = 9(0)9057<907> is prime. は素数です。 (discovered by: (発見: Jason Earls / August 18, 2004 2004 年 8 月 18 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 1, 2006 2006 年 6 月 1 日)
  17. 9×101350+7 = 9(0)13497<1351> is prime. は素数です。 (discovered by: (発見: Jason Earls / August 18, 2004 2004 年 8 月 18 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 6, 2006 2006 年 9 月 6 日)
  18. 9×101736+7 = 9(0)17357<1737> is prime. は素数です。 (discovered by: (発見: Jason Earls / August 18, 2004 2004 年 8 月 18 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / July 28, 2006 2006 年 7 月 28 日)
  19. 9×102914+7 = 9(0)29137<2915> is prime. は素数です。 (discovered by: (発見: Jason Earls / August 18, 2004 2004 年 8 月 18 日) (certified by: (証明: Serge Batalov / Primo 3.0.9 / October 15, 2010 2010 年 10 月 15 日)
  20. 9×107508+7 = 9(0)75077<7509> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 29, 2004 2004 年 12 月 29 日)
  21. 9×1015710+7 = 9(0)157097<15711> is PRP. はおそらく素数です。 (Sinkiti Sibata / PFGW / November 7, 2007 2007 年 11 月 7 日)
  22. 9×1016453+7 = 9(0)164527<16454> is PRP. はおそらく素数です。 (Sinkiti Sibata / PFGW / November 7, 2007 2007 年 11 月 7 日)
  23. 9×1017488+7 = 9(0)174877<17489> is PRP. はおそらく素数です。 (Sinkiti Sibata / PFGW / November 7, 2007 2007 年 11 月 7 日)
  24. 9×1018109+7 = 9(0)181087<18110> is PRP. はおそらく素数です。 (Sinkiti Sibata / PFGW / November 7, 2007 2007 年 11 月 7 日)
  25. 9×1021604+7 = 9(0)216037<21605> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  26. 9×1025891+7 = 9(0)258907<25892> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  27. 9×1026725+7 = 9(0)267247<26726> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  28. 9×1034838+7 = 9(0)348377<34839> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  29. 9×1067468+7 = 9(0)674677<67469> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 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 / October 26, 2015 2015 年 10 月 26 日

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

  1. 9×1013k+12+7 = 79×(9×1012+779+81×1012×1013-19×79×k-1Σm=01013m)
  2. 9×1016k+11+7 = 17×(9×1011+717+81×1011×1016-19×17×k-1Σm=01016m)
  3. 9×1018k+11+7 = 19×(9×1011+719+81×1011×1018-19×19×k-1Σm=01018m)
  4. 9×1021k+18+7 = 43×(9×1018+743+81×1018×1021-19×43×k-1Σm=01021m)
  5. 9×1022k+14+7 = 23×(9×1014+723+81×1014×1022-19×23×k-1Σm=01022m)
  6. 9×1026k+7+7 = 859×(9×107+7859+81×107×1026-19×859×k-1Σm=01026m)
  7. 9×1028k+8+7 = 29×(9×108+729+81×108×1028-19×29×k-1Σm=01028m)
  8. 9×1028k+8+7 = 281×(9×108+7281+81×108×1028-19×281×k-1Σm=01028m)
  9. 9×1032k+11+7 = 449×(9×1011+7449+81×1011×1032-19×449×k-1Σm=01032m)
  10. 9×1033k+11+7 = 67×(9×1011+767+81×1011×1033-19×67×k-1Σm=01033m)

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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 30.71%. 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 30.71% です。

3. Factor table of 900...007 900...007 の素因数分解表

3.1. Last updated 最終更新日

June 19, 2018 2018 年 6 月 19 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=188, 193, 197, 198, 201, 203, 207, 208, 209, 213, 219, 220, 222, 224, 229, 230, 232, 233, 234, 235, 236, 237, 238, 239, 240, 243, 244, 246, 247, 250 (30/250)

3.4. Factor table 素因数分解表

9×101+7 = 97 = definitely prime number 素数
9×102+7 = 907 = definitely prime number 素数
9×103+7 = 9007 = definitely prime number 素数
9×104+7 = 90007 = definitely prime number 素数
9×105+7 = 900007 = definitely prime number 素数
9×106+7 = 9000007 = 277 × 32491
9×107+7 = 90000007 = 859 × 104773
9×108+7 = 900000007 = 29 × 179 × 281 × 617
9×109+7 = 9000000007<10> = 59 × 152542373
9×1010+7 = 90000000007<11> = 1033 × 87124879
9×1011+7 = 900000000007<12> = 17 × 19 × 67 × 449 × 92623
9×1012+7 = 9000000000007<13> = 79 × 104759 × 1087487
9×1013+7 = 90000000000007<14> = 172171 × 522736117
9×1014+7 = 900000000000007<15> = 23 × 1429 × 2129 × 12861949
9×1015+7 = 9000000000000007<16> = definitely prime number 素数
9×1016+7 = 90000000000000007<17> = 71 × 1009 × 1733 × 724927261
9×1017+7 = 900000000000000007<18> = 339707 × 966893 × 2740057
9×1018+7 = 9000000000000000007<19> = 43 × 209302325581395349<18>
9×1019+7 = 90000000000000000007<20> = definitely prime number 素数
9×1020+7 = 900000000000000000007<21> = definitely prime number 素数
9×1021+7 = 9000000000000000000007<22> = 3970453 × 2266743870283819<16>
9×1022+7 = 90000000000000000000007<23> = 1051 × 1747 × 5811073 × 8435106247<10>
9×1023+7 = 900000000000000000000007<24> = 443 × 2031602708803611738149<22>
9×1024+7 = 9000000000000000000000007<25> = 21385879 × 149269957 × 2819311069<10>
9×1025+7 = 90000000000000000000000007<26> = 47 × 79 × 661 × 36670438289152925099<20>
9×1026+7 = 900000000000000000000000007<27> = 5119 × 175815588982223090447353<24>
9×1027+7 = 9000000000000000000000000007<28> = 17 × 197 × 391987 × 6855761451245195689<19>
9×1028+7 = 90000000000000000000000000007<29> = 666089 × 135117078948909229847663<24>
9×1029+7 = 900000000000000000000000000007<30> = 19 × 61 × 677767 × 1145720421127159419319<22>
9×1030+7 = 9000000000000000000000000000007<31> = 107 × 149 × 252079 × 145483843 × 15392920680517<14>
9×1031+7 = 90000000000000000000000000000007<32> = 2210389 × 2508313 × 16232748865096121251<20>
9×1032+7 = 900000000000000000000000000000007<33> = 4211 × 211008464101<12> × 1012878591105560537<19>
9×1033+7 = 9000000000000000000000000000000007<34> = 859 × 2027 × 105971 × 48776267559805457988469<23>
9×1034+7 = 90000000000000000000000000000000007<35> = 2671 × 33695245226506926244852115312617<32>
9×1035+7 = 900000000000000000000000000000000007<36> = 14041409 × 64096131663140073763252676423<29>
9×1036+7 = 9000000000000000000000000000000000007<37> = 23 × 29 × 281 × 48018695278695171986960256526541<32>
9×1037+7 = 90000000000000000000000000000000000007<38> = 28421969 × 3166564568415369111126678098903<31>
9×1038+7 = 900000000000000000000000000000000000007<39> = 79 × 4472687 × 106227954130559<15> × 23977731549094201<17>
9×1039+7 = 9000000000000000000000000000000000000007<40> = 43 × 1129 × 6985995157<10> × 321826330171<12> × 82457518096123<14>
9×1040+7 = 90000000000000000000000000000000000000007<41> = 13997 × 28123 × 10331017 × 34265195617<11> × 645876686057873<15>
9×1041+7 = 900000000000000000000000000000000000000007<42> = 29022857 × 16955113783<11> × 1828949182897990966981097<25>
9×1042+7 = 9000000000000000000000000000000000000000007<43> = 15443 × 195241 × 1039496963<10> × 63893549549<11> × 44942742880547<14>
9×1043+7 = 90000000000000000000000000000000000000000007<44> = 17 × 431 × 449 × 461 × 3067910548356271<16> × 19343112551741065939<20>
9×1044+7 = 900000000000000000000000000000000000000000007<45> = 67 × 356634327127602502687<21> × 37665571705017899674483<23>
9×1045+7 = 9000000000000000000000000000000000000000000007<46> = 10369 × 3979219 × 10819331 × 20160782567765016528409168127<29>
9×1046+7 = 90000000000000000000000000000000000000000000007<47> = definitely prime number 素数
9×1047+7 = 900000000000000000000000000000000000000000000007<48> = 19 × 349 × 25185075981569463503<20> × 5389149308924810689918799<25>
9×1048+7 = 9000000000000000000000000000000000000000000000007<49> = 153593087 × 3746756951916427<16> × 15639228263509408498386443<26>
9×1049+7 = 90000000000000000000000000000000000000000000000007<50> = 318116349006585356511371<24> × 282915355595687732229257717<27>
9×1050+7 = 900000000000000000000000000000000000000000000000007<51> = 2837 × 1738171 × 5813430457<10> × 31394834085695353139263185335513<32>
9×1051+7 = 9(0)507<52> = 71 × 79 × 269231 × 5959804381446739851550239052753353504282433<43>
9×1052+7 = 9(0)517<53> = definitely prime number 素数
9×1053+7 = 9(0)527<54> = definitely prime number 素数
9×1054+7 = 9(0)537<55> = 96667 × 32563592000353<14> × 2859117238343561366977616921778328357<37>
9×1055+7 = 9(0)547<56> = 587915503433<12> × 153083222800666585802401214018607490828393679<45>
9×1056+7 = 9(0)557<57> = 202726208959<12> × 4439485178662907331953211834637926294079494073<46>
9×1057+7 = 9(0)567<58> = 167 × 503 × 107141581647837525743741145938738824537803121391412007<54>
9×1058+7 = 9(0)577<59> = 23 × 7768757954124639374218829927<28> × 503689714799690874030324682567<30>
9×1059+7 = 9(0)587<60> = 17 × 859 × 5387 × 10687 × 40849 × 311551 × 20154581 × 110974219 × 102893998021<12> × 365511585221<12>
9×1060+7 = 9(0)597<61> = 43 × 1787 × 23569303783<11> × 4969386173806805680967405358356768068114258169<46>
9×1061+7 = 9(0)607<62> = 191 × 302443 × 25874539961<11> × 783797899245299137<18> × 76822577251443582964129027<26>
9×1062+7 = 9(0)617<63> = 15661 × 76064293 × 5391817055658913962413<22> × 140122229483223695588233907843<30>
9×1063+7 = 9(0)627<64> = 1187 × 6199 × 1223123059905985325513137496835169082493262970234756726939<58>
9×1064+7 = 9(0)637<65> = 29 × 79 × 281 × 139801264735441639962036189887397847992531505768355517722917<60>
9×1065+7 = 9(0)647<66> = 19 × 151 × 488639 × 15565855100049645789657947<26> × 41243057270786854086689174116591<32>
9×1066+7 = 9(0)657<67> = 4350067 × 11909368660141<14> × 3837713131702823<16> × 45267375514988686192573342044647<32>
9×1067+7 = 9(0)667<68> = 59 × 835772711 × 1825165752287357611552715921451933793411285962386083477843<58>
9×1068+7 = 9(0)677<69> = 3894571 × 231090921182333047722072597983192500534718714846898413201351317<63>
9×1069+7 = 9(0)687<70> = 77933 × 2032873 × 3532301 × 16082485291406512407293730220387529891576114100288823<53>
9×1070+7 = 9(0)697<71> = 3842977065455451556992473<25> × 23419343510792881490763675223526461774338881759<47>
9×1071+7 = 9(0)707<72> = 47 × 4931 × 229169007402534616701149<24> × 16945475709674125297636062030058685840841599<44>
9×1072+7 = 9(0)717<73> = 5902300651241<13> × 1524829135585915475643870986938958472948807264684243115356527<61>
9×1073+7 = 9(0)727<74> = 1181 × 665039 × 3327967 × 34432335884444838465407654764415807242941038070700028982019<59>
9×1074+7 = 9(0)737<75> = 347 × 23044619122306838333950723577130739<35> × 112549481881108171366522590225577624679<39> (Makoto Kamada / GGNFS-0.70.1 / 0.08 hours)
9×1075+7 = 9(0)747<76> = 17 × 229 × 277 × 449 × 6649596329432614981<19> × 2795353354079316563063129287317341384967621679123<49>
9×1076+7 = 9(0)757<77> = 5147 × 2964823 × 7789979 × 11653075961<11> × 64969975914081433636872249601472079479799280155713<50>
9×1077+7 = 9(0)767<78> = 67 × 79 × 170035896467031928962781031551105233327035707538258076705082184016625732099<75>
9×1078+7 = 9(0)777<79> = 163 × 11344059899<11> × 2140140836520737<16> × 1316920106472587579<19> × 1726969277561493714530753234176757<34>
9×1079+7 = 9(0)787<80> = 887 × 60204580433230036445475569<26> × 1685347089881237977241164817169150672317433377933569<52>
9×1080+7 = 9(0)797<81> = 23 × 3493444116795736567<19> × 11201105119866633846987553851635845511243003479047346047455927<62>
9×1081+7 = 9(0)807<82> = 43 × 12653 × 1074711494374362360131351<25> × 15391773081426389524940266255061439731360302352535583<53>
9×1082+7 = 9(0)817<83> = 113 × 63361 × 431993839 × 4806752850937592245584965049997<31> × 6053585733039901321452056359007073053<37>
9×1083+7 = 9(0)827<84> = 19 × 107 × 13477 × 87481 × 206669371 × 1816862436071974351664856163206415065435433852744791844318116377<64>
9×1084+7 = 9(0)837<85> = 37540872749803026780219257208280099711<38> × 239738699203449448401226911674682966084085583737<48> (Makoto Kamada / GGNFS-0.70.1 / 0.10 hours)
9×1085+7 = 9(0)847<86> = 859 × 460188116299589<15> × 227674266544468560029099294726620210900973819681465144164541450313857<69>
9×1086+7 = 9(0)857<87> = 71 × 109 × 16633 × 10229919692731<14> × 683462751827408425810699078598450505189470650104991204760672073431<66>
9×1087+7 = 9(0)867<88> = 183701486161669351<18> × 22555660007470486838578864250029<32> × 2172072414241268908665425047380640780933<40> (Makoto Kamada / msieve 0.83 / 3 minutes)
9×1088+7 = 9(0)877<89> = 889652508240511<15> × 1882044220804716949<19> × 57468419267717580741677<23> × 935326043004333592549650177498569<33>
9×1089+7 = 9(0)887<90> = 61 × 419 × 35212645252161665166868813333855002151883876520990649086427481513361242615125787393873<86>
9×1090+7 = 9(0)897<91> = 79 × 401 × 786963017 × 361007913654033055588366174089152146044528472763557134674252228694714741028849<78>
9×1091+7 = 9(0)907<92> = 17 × 226663 × 511757 × 1982093 × 23026351816405663175401007450085236204067413374946983623499053410694480617<74>
9×1092+7 = 9(0)917<93> = 29 × 281 × 2659418070948487361<19> × 41529009803866285174258566119030080668819790512972960627014868069214763<71>
9×1093+7 = 9(0)927<94> = 4519 × 22274809 × 52554354887<11> × 1652355971681<13> × 419928407977937<15> × 2451876550436662060992815668656141171343835903<46>
9×1094+7 = 9(0)937<95> = 16422263893289<14> × 133065403562241402623407235161<30> × 41185498539523277893642540909248923271719039100102983<53> (Makoto Kamada / GGNFS-0.71.4 / 0.35 hours)
9×1095+7 = 9(0)947<96> = 551927 × 3979115119387<13> × 119309829429943519351367381<27> × 3434773793680286789641493855776211035594901833206103<52>
9×1096+7 = 9(0)957<97> = 617 × 62969 × 123351872807<12> × 212913326286128764053610401451840837<36> × 8820271561229208530135721264201306393781901<43> (Makoto Kamada / GGNFS-0.71.4 / 0.33 hours)
9×1097+7 = 9(0)967<98> = 97 × 1005264169033<13> × 4686707131604272037<19> × 2282640880273846353261428003<28> × 86275039243430495169552987970112893537<38>
9×1098+7 = 9(0)977<99> = 8408017 × 349301040512037626427403<24> × 306442536887437639744097079990503423816378097131690321992383405203557<69>
9×1099+7 = 9(0)987<100> = 359 × 1506487 × 16164937 × 1029458055118304461905516790379596773016269339698973618665858253123227286441908397167<85>
9×10100+7 = 9(0)997<101> = 101925187499<12> × 883000583156965010078170962502062318624648714221150181491902089279864234630717399804937493<90>
9×10101+7 = 9(0)1007<102> = 19 × 1877 × 11633 × 17503027708594957<17> × 123942350331542861211340802912083776681110113908602010972497555223170095766269<78>
9×10102+7 = 9(0)1017<103> = 23 × 43 × 269913089511491976967<21> × 33714930716048616000868901517745205903073585405064620866765805414031203280047989<80>
9×10103+7 = 9(0)1027<104> = 79 × 1999 × 94765291 × 950835101 × 10350710598611195715112167757<29> × 611051692926898441324044625243224876026087201019011741<54>
9×10104+7 = 9(0)1037<105> = 3048173 × 23073218249<11> × 150373559191<12> × 4982691326905656873829657<25> × 17078875019843100655316058053111621111907753102153493<53>
9×10105+7 = 9(0)1047<106> = 1109 × 26804831 × 37523878698616077433418671<26> × 8068451011938861167044390430448780885272172524848974475160024137069723<70>
9×10106+7 = 9(0)1057<107> = 991 × 1661137 × 6622425586018027<16> × 2232398633384427063570953<25> × 3698065237118731975924001557313728741070405667045982772291<58>
9×10107+7 = 9(0)1067<108> = 17 × 449 × 3793 × 1428226259<10> × 18185642971779607238865540378270917<35> × 1196847260703678301945986408871021597746664671533002159801<58> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2972516740 for P35 / October 28, 2007 2007 年 10 月 28 日)
9×10108+7 = 9(0)1077<109> = 37871 × 3406331833<10> × 88079868587<11> × 144064331776620889004606685503461<33> × 5498138252554114429604456503865744400402842973430807<52> (Jo Yeong Uk / Msieve v. 1.28 for P33 x P52 / 19.2 minutes on Core 2 Quad Q6600 / November 5, 2007 2007 年 11 月 5 日)
9×10109+7 = 9(0)1087<110> = 8861 × 95737 × 145753 × 3084865037<10> × 2005489201489<13> × 1143490754045839181779<22> × 102890032020257046174039252298599233433946828738369861<54>
9×10110+7 = 9(0)1097<111> = 67 × 43399073 × 748646649156295913<18> × 413437978525873637862364508106443655329950933187075273278213406991514247944266185029<84>
9×10111+7 = 9(0)1107<112> = 131 × 859 × 682916690512923260407060455419117<33> × 51118310350528656363520883890560151<35> × 2291046123805509364111583138403788910949<40> (Robert Backstrom / GMP-ECM 6.0.1 B1=598500, sigma=2450905158 for P33, Msieve v. 1.29 for P35 x P40 / November 5, 2007 2007 年 11 月 5 日)
9×10112+7 = 9(0)1117<113> = 1706363 × 6132851 × 14021233 × 366287276724937330096345104351579811913585089<45> × 1674559682769946750885495255184227109771029382647<49> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.89 hours on Core 2 Quad Q6600 / November 5, 2007 2007 年 11 月 5 日)
9×10113+7 = 9(0)1127<114> = 691 × 1091 × 10177 × 79435844459<11> × 264144729178810890855853<24> × 350555964194053249420381543<27> × 15947922287921696095546131546866260790470951<44>
9×10114+7 = 9(0)1137<115> = 653 × 4287299 × 249763385813<12> × 115630510169949718409527011290812428381853<42> × 111312603505914666012718121697883345483669372301240129<54> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.90 hours on Core 2 Quad Q6600 / November 5, 2007 2007 年 11 月 5 日)
9×10115+7 = 9(0)1147<116> = 41389800449<11> × 49442606979709<14> × 1208116837272685326229307<25> × 177678281399335906395434141059<30> × 204882343520358898834628465918312493379<39> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3723551422 for P30 / October 28, 2007 2007 年 10 月 28 日)
9×10116+7 = 9(0)1157<117> = 79 × 787157062331151619<18> × 20335399885619279726241161324393<32> × 711707110636624387503508211626233636313618046171221768038049418699<66> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1562534670 for P32 / October 28, 2007 2007 年 10 月 28 日)
9×10117+7 = 9(0)1167<118> = 47 × 443867 × 17471857037357853190634584935442902072067<41> × 24691798610564857752888526692177153472802870226100236461016311059115929<71> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 2.78 hours on Pentium 4 2.4GHz, Windows XP / November 6, 2007 2007 年 11 月 6 日)
9×10118+7 = 9(0)1177<119> = 1809173 × 7836379505685731093<19> × 414101468025620512984167535433<30> × 15329930341257740147908572071334777181473774872861935942459866311<65> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2104043857 for P30 / October 28, 2007 2007 年 10 月 28 日)
9×10119+7 = 9(0)1187<120> = 19 × 321486829 × 62046400978007<14> × 142955807387387<15> × 16611441673500251778148440867388517884982624520227796655298609723769769937757103573<83>
9×10120+7 = 9(0)1197<121> = 29 × 281 × 386471 × 142583653 × 266099299493114096677875328801409<33> × 75319566589929176165358361692126958829966221213822132241587381268023129<71> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 2.09 hours on Pentium 4 2.46GHz, Windows XP / November 5, 2007 2007 年 11 月 5 日)
9×10121+7 = 9(0)1207<122> = 71 × 10733 × 14298301 × 13437563210843<14> × 46754707307478264058557236237372093839004268587<47> × 13147183761460396406902731745730328931732164333889<50> (Sinkiti Sibata / Msieve v. 1.28 / 39.6 hours on Pentium3 750MHz, Windows Me / November 7, 2007 2007 年 11 月 7 日)
9×10122+7 = 9(0)1217<123> = 373 × 821 × 4957 × 401381 × 7420538329<10> × 746169961869543652361<21> × 31868011160704704569275664659756981<35> × 8371179526300102535493648044260881054098483<43> (Makoto Kamada / Msieve 1.29 for P35 x P43 / 11 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / November 4, 2007 2007 年 11 月 4 日)
9×10123+7 = 9(0)1227<124> = 17 × 43 × 433 × 11100899 × 24530511751<11> × 51734818150807670030951<23> × 2018317795905495505469921474422236136664624693042659533700301140110152747825591<79>
9×10124+7 = 9(0)1237<125> = 23 × 457 × 599 × 5073457 × 16615407572899<14> × 260586084936521<15> × 79737552713919697515769<23> × 8160984346776014555404163965119493999131072122016855502987109<61>
9×10125+7 = 9(0)1247<126> = 59 × 197 × 780276504913993749776514163<27> × 168433376589385637858874337945123<33> × 589179444496025582370853279278377242678265721322770523869579241<63> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2361933230 for P33 / October 29, 2007 2007 年 10 月 29 日)
9×10126+7 = 9(0)1257<127> = 18386461 × 1742218293047<13> × 13822662893206118250744627949841<32> × 20325913755563927082639117313372686004914219990075373791674260136282142256981<77> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 3.97 hours on Pentium 4 2.4GHz, Windows XP / November 5, 2007 2007 年 11 月 5 日)
9×10127+7 = 9(0)1267<128> = 344206321 × 33157853781215682395478284485540807<35> × 7885645618034098004254139912968642957732499669205257892740457352566043261860258601681<85> (Robert Backstrom / GMP-ECM 6.0.1 B1=907500, sigma=3852484092 for P35 / November 5, 2007 2007 年 11 月 5 日)
9×10128+7 = 9(0)1277<129> = 611549 × 1471672752306029443266197802629061612397371265425992030074450289347215022835455539948556861347169237460939352365877468526643<124>
9×10129+7 = 9(0)1287<130> = 792 × 20153348113<11> × 449928652266029<15> × 657777356433487<15> × 4516316879352371386169<22> × 53534548543679115437812940898891666518314603059535163946831691717<65>
9×10130+7 = 9(0)1297<131> = 1117 × 64871 × 471277 × 7026630811159<13> × 23839607767091720240800997<26> × 2711253821099303589206868267614807<34> × 5802913273845990223168853880312421469788456133<46> (Makoto Kamada / Msieve 1.29 for P34 x P46 / 17 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / November 5, 2007 2007 年 11 月 5 日)
9×10131+7 = 9(0)1307<132> = 38921 × 632971 × 968437 × 83275116371<11> × 274255609394142444443<21> × 2288057282169860293574275141471863042313<40> × 721881101657780564083407600404226856588479089<45> (Jo Yeong Uk / Msieve v. 1.28 for P40 x P45 / 20.86 minutes on Core 2 Quad Q6600 / November 5, 2007 2007 年 11 月 5 日)
9×10132+7 = 9(0)1317<133> = 491 × 85117573 × 139221663158686554389864242499707408798312738177711<51> × 1546802865177850881667388439251649501422697254868710734255734319160698559<73> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 3.77 hours on Core 2 Quad Q6600 / November 5, 2007 2007 年 11 月 5 日)
9×10133+7 = 9(0)1327<134> = 5881 × 26930082287<11> × 176964956297383872307<21> × 25264976655443100325796147326226279933324489<44> × 127100563245798676374051740186784449244832505678728530547<57> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 8.81 hours on Pentium 4 2.4GHz, Windows XP / November 6, 2007 2007 年 11 月 6 日)
9×10134+7 = 9(0)1337<135> = 22488960520231<14> × 40019635375781942287308278458911705523150226777318042871215798287894773297218465985743236760206350004672974237980499729697<122>
9×10135+7 = 9(0)1347<136> = 1002121 × 14760091 × 588447254183867044277609191468715934421424931568990421<54> × 1034012456449314522976535796820781617144073180839915839118262268905897<70> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 4.84 hours on Cygwin on AMD 64 3200+ / November 5, 2007 2007 年 11 月 5 日)
9×10136+7 = 9(0)1357<137> = 107 × 12437053595063143<17> × 22550053545005988063274052033<29> × 2999118656732694548692186091248794631299515848412730884971053308986847079572429229153734179<91>
9×10137+7 = 9(0)1367<138> = 19 × 859 × 20563 × 2399769503<10> × 188265085079<12> × 1778158252400731<16> × 179047631315557466711<21> × 18643651008000491201796705329263656278184486474567604340088694226607133577<74>
9×10138+7 = 9(0)1377<139> = 29537 × 33587 × 12815293 × 141456967 × 50022985511<11> × 100042013036097848736050797990265280606211593075465633151068911696717595658249012161231613754711251346033<105>
9×10139+7 = 9(0)1387<140> = 17 × 449 × 4391 × 2685244340675994748020102216511072172416078133210973710473315190430218808925262877216038916709180549056684105737403451666780391737169<133>
9×10140+7 = 9(0)1397<141> = 151 × 160910339138441<15> × 119266962910373522768317901849023<33> × 1073502048919627741496999269090973341811523617<46> × 289306754986378993892936910082750693641415226647<48> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 6.15 hours on Core 2 Quad Q6600 / November 5, 2007 2007 年 11 月 5 日)
9×10141+7 = 9(0)1407<142> = 16931 × 57373 × 611247706213202431484119<24> × 5792751735469845586935304109<28> × 2616677390398689523178966211329234708530941624641108281963018891061172203453819059<82>
9×10142+7 = 9(0)1417<143> = 79 × 571 × 25439 × 42557 × 265021 × 22878221 × 96583740842819843<17> × 3147035976036150520987219177046911060214015951519515885189364143642655871909765749720792056505580427<100>
9×10143+7 = 9(0)1427<144> = 67 × 14449 × 16764671435106466291549252481783<32> × 55454254267525152340965490394347806129765919513362592966669387843539324159605808600050322487693263291392363<107> (Robert Backstrom / GMP-ECM 6.0.1 B1=499500, sigma=3166951252 for P32 / November 5, 2007 2007 年 11 月 5 日)
9×10144+7 = 9(0)1437<145> = 43 × 277 × 755604063470741331542271849550835362270170430694316178322558979094954243976156493997145495760221643858618084123919066409201578372932583326337<141>
9×10145+7 = 9(0)1447<146> = 19577 × 32427523 × 13022329653449<14> × 782973965017999975662824355872611<33> × 13904218568670339449430188271837855895874959750974946433657093832640870849598606047965103<89> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1309427083 for P33 / October 30, 2007 2007 年 10 月 30 日)
9×10146+7 = 9(0)1457<147> = 23 × 4271 × 437543 × 5421833 × 8849681 × 23988971368700909013664451648647553<35> × 18191938657561789126660465345836496511300044062263632583171015546703249344891910371448337<89> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=443481190 for P35 / November 5, 2007 2007 年 11 月 5 日)
9×10147+7 = 9(0)1467<148> = 25951 × 1738969 × 197021917 × 92978880982634662097<20> × 102931531869565976194616134711<30> × 2005256885602141410291462050850625780121<40> × 52744753108364828721861464937342277420987<41> (JMB / GMP-ECM 6.1.3 B1=3000000, sigma=519784128 for P30, Msieve 1.29 for P40 x P41 / November 5, 2007 2007 年 11 月 5 日)
9×10148+7 = 9(0)1477<149> = 29 × 281 × 11044299914099889557000859001104429991409988955700085900110442999140998895570008590011044299914099889557000859001104429991409988955700085900110443<146>
9×10149+7 = 9(0)1487<150> = 61 × 181 × 81536713 × 49357794583378872791<20> × 20254669152677377266280922095175893962356955823963752764712100727117933189387492639975894464403380479340287196615945769<119>
9×10150+7 = 9(0)1497<151> = 19732343 × 326052556279<12> × 589499724724831441087810448027951375963<39> × 2372972128635709558872684003447910854760650370032899324921933688620430554494554451055042317237<94> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 12.90 hours on Core 2 Quad Q6600 / November 6, 2007 2007 年 11 月 6 日)
9×10151+7 = 9(0)1507<152> = 269 × 21613 × 67791928153<11> × 44970969250703<14> × 383031576676808952277813<24> × 6810025963958582438251862479127272552967<40> × 1946621858651143417424307752923064400610721325684111628979<58> (JMB / Msieve 1.29 for P40 x P58 / November 5, 2007 2007 年 11 月 5 日)
9×10152+7 = 9(0)1517<153> = 4761397 × 170458908643<12> × 49688519499466733076979<23> × 703840987201156095759020645169329337871<39> × 31707193373284828223436939712373236806907701314756561688871528206762760813<74> (JMB / GGNFS-0.77.1-20060513-athlon-xp / November 6, 2007 2007 年 11 月 6 日)
9×10153+7 = 9(0)1527<154> = 907 × 1567 × 51635332541907318461<20> × 4772486568530653705948719675085861919871051034726502704647793<61> × 25696533054533355691086868666739471157508323084478430890473067987511<68> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 26.78 hours on Cywin on AMD 64 3200+ / November 8, 2007 2007 年 11 月 8 日)
9×10154+7 = 9(0)1537<155> = 342774283579171568600971909894532466448184589420657720323497289127488139607<75> × 262563454469922156375323276959104849917481523961677799993943153957816466910677201<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.29 / November 7, 2007 2007 年 11 月 7 日)
9×10155+7 = 9(0)1547<156> = 17 × 19 × 79 × 6709727 × 9693407 × 32223117980178911<17> × 1318096742024160957917<22> × 220228970282779081724330072917<30> × 57975206121455256625031982521359268473033279314724398614041353953025341<71> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=940415250 for P30 / October 31, 2007 2007 年 10 月 31 日)
9×10156+7 = 9(0)1557<157> = 71 × 191 × 5441 × 121975348483909438941722360497844282231386124743023352275336959949570511922812481563934307275771259954255720586244425235284687278449567550632407622207<150>
9×10157+7 = 9(0)1567<158> = 47237 × 1991089 × 39596002810909<14> × 24166746248250206178005679631799168880616857854837584695075779328676802149270930138770761112345345957557654944976003160326033945850311<134>
9×10158+7 = 9(0)1577<159> = 1163 × 68163803 × 11352956716236722360810968213197343812611542493049514504411287321342814254780662355974070521932150466266167594334140486142052432189550528913944862063<149>
9×10159+7 = 9(0)1587<160> = 163 × 2131 × 103549 × 34492044571<11> × 112885640420266756353793<24> × 64264022555252895661814765721900491510523326149930205284378092418318098645083931683721727368179898766585834308829777<116>
9×10160+7 = 9(0)1597<161> = 193 × 233 × 43499 × 1514405906081012721338467999<28> × 9539345889759064940903674568760087065552798466254478738629<58> × 3184850972645850020285709503660847208668237617514389096861847478007<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 30.91 hours on Core 2 Quad Q6600 / November 7, 2007 2007 年 11 月 7 日)
9×10161+7 = 9(0)1607<162> = 32742491009<11> × 15305913553837<14> × 2871374186022696036738055549847702632759229312163023359543043<61> × 625434371370412843235342091358846490870084281799111208724718685614180061274753<78> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.30 / December 6, 2007 2007 年 12 月 6 日)
9×10162+7 = 9(0)1617<163> = 5675476123<10> × 19653188594940718862107501<26> × 688903506523745903246622831283151599<36> × 117124780898551182812517761055884645674869174813318998257172923202640159324081908982573296791<93> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=1722669635 for P36 / November 6, 2007 2007 年 11 月 6 日)
9×10163+7 = 9(0)1627<164> = 47 × 349 × 859 × 58211 × 818470811192938112676337938572201<33> × 873583190755642325776044428797599382814221<42> × 153466481365034760327052932409167822889494591377902353931701362171082781011161<78> (Robert Backstrom / GMP-ECM B1=706500, sigma=1325755017 for P33, GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.29 / November 11, 2007 2007 年 11 月 11 日)
9×10164+7 = 9(0)1637<165> = 883 × 24573393591862132649<20> × 2564993881968404917452325855647781<34> × 16170756423913671663934778083625100661998605305949217253030068605305369307115708420697061171260255444165225841<110> (JMB / GMP-ECM B1=3000000, sigma=652730646 for P34 / November 11, 2007 2007 年 11 月 11 日)
9×10165+7 = 9(0)1647<166> = 43 × 23131 × 1418088383<10> × 35942958881<11> × 316632999964816314980011979278660259022505001<45> × 74603769316589492099122294657235536113237612649<47> × 7515287056062349794626336991939024137322161656577<49> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.33 / February 1, 2008 2008 年 2 月 1 日)
9×10166+7 = 9(0)1657<167> = 1052881 × 85479745574286172891333398551213290010931909684000376110880526859160721866953625338476048100402609601654887874318180307176214595951489294611641771482247281506647<161>
9×10167+7 = 9(0)1667<168> = 313 × 8956176269<10> × 135292943581<12> × 1749166838037127<16> × 1318100722407302189<19> × 1029249252893857176249574167415492597911554157335312647739585988530140635652764140082211495840740260382282481717<112>
9×10168+7 = 9(0)1677<169> = 23 × 79 × 206052919 × 518574098737<12> × 9433668111111252131<19> × 4913799101147233797409286892484343931875925190278627935886573064039079910184675560176867149080967383889157094205766334909396547<127>
9×10169+7 = 9(0)1687<170> = 2111 × 1429958609<10> × 56769904881370799699375018291651<32> × 525185398197314224568248713026766256427182001005757531713576174925963787257959304880282840700874560113146274753741218461103843<126> (JMB / GMP-ECM B1=3000000, sigma=2265572958 for P32 / November 11, 2007 2007 年 11 月 11 日)
9×10170+7 = 9(0)1697<171> = 11593 × 647317419452212964571902174202614495944617659<45> × 439565483361516384512985467534108059954554466647701<51> × 272838590381901265341010790500512053115606212399648275844615354818716361<72> (Tyler Cadigan / GGNFS, Msieve / 93.71 hours on core 2 quad Q6600 2.40 GHz, 2 gb RAM / January 30, 2008 2008 年 1 月 30 日)
9×10171+7 = 9(0)1707<172> = 17 × 449 × 4703 × 26111 × 363220799 × 663447595827760319<18> × 39844779653149576319973767926010150085500680448921436278309559997793747243727949456197744427433891665203116701295972268169376875992823<134>
9×10172+7 = 9(0)1717<173> = 144013 × 382692063491194607055392279269<30> × 59637355769764003773393044656644535007043331503234583411<56> × 27382492480539936276791175824084954351631345763429132395991529184934063839601220221<83> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=4119772042 for P30 / November 1, 2007 2007 年 11 月 1 日) (Sinkiti Sibata / Msieve 1.40 snfs / April 30, 2010 2010 年 4 月 30 日)
9×10173+7 = 9(0)1727<174> = 19 × 647 × 224401 × 4204449134966651726234511502249<31> × 77598037366254001837116882823105292830227805356149887771917581121716866409828186604482406682111147355193961123945624774784312354859251<134> (JMB / GMP-ECM B1=3000000, sigma=2897406131 for P31 / November 11, 2007 2007 年 11 月 11 日)
9×10174+7 = 9(0)1737<175> = 213169063 × 64080489533<11> × 436773716425002099851<21> × 1508467703459663143953333757246377455642578806715172554853192697956754383600532209235858297749557104731204975902715126108436614742315583<136>
9×10175+7 = 9(0)1747<176> = 5209 × 17277788443079285851411019389518141677865233250143981570358994048761758494912651180648876943751199846419658283739681320790938759838740641197926665386830485697830677673257823<173>
9×10176+7 = 9(0)1757<177> = 29 × 67 × 281 × 2213 × 24019 × 4682059 × 207316764377111<15> × 31948888131092494186674004607385867654777386268194086358069247188332213605356771316117800266887295653993111594831673732811817613194906936489043<143>
9×10177+7 = 9(0)1767<178> = 153438528657199<15> × 32667044190772508911<20> × 231363885166211856645528826109773<33> × 7760731807961019750154843183467424612751080704744319434512584619725381829268383039969389480897051376995338032131<112> (JMB / GMP-ECM B1=3000000, sigma=2512640220 for P33 / November 12, 2007 2007 年 11 月 12 日)
9×10178+7 = 9(0)1777<179> = 149 × 34477381911603229695013790339605181<35> × 33122271528685322696431320399610814886866058262192470354090077<62> × 528934443107416369616401547326191577278980257832232752196080088752266739605666739<81> (JMB / GMP-ECM B1=3000000, sigma=1063157681 for P35 / November 15, 2007 2007 年 11 月 15 日) (Ben Meekins / MSieve V1.52 (SVN 945) snfs / October 16, 2013 2013 年 10 月 16 日)
9×10179+7 = 9(0)1787<180> = 367699 × 313009111137872717<18> × 1707358559977705545311234918697001<34> × 4580030236511827524816894288626065240922568714998170751384355667293248449614016116415020750898340461128531874477462326513929<124> (JMB / GMP-ECM B1=3000000, sigma=1191697203 for P34 / November 13, 2007 2007 年 11 月 13 日)
9×10180+7 = 9(0)1797<181> = 174763 × 1485819953<10> × 14249168538389101<17> × 2432412960142440603930360250671094773103444995191883961268622814522744268875467906180373051125872598032936560663403268537599273252415961140489508943513<151>
9×10181+7 = 9(0)1807<182> = 79 × 257 × 244637 × 8512657957698933206364996840866746830424447731789547<52> × 2128604465477319399779522456754361848962080507428346805103942531536208640072972366805607636173490224009642228179113256471<121> (matsui / GGNFS-0.77.1-20060722-nocona / May 7, 2009 2009 年 5 月 7 日)
9×10182+7 = 9(0)1817<183> = 681997 × 5371290194501118001753<22> × 15159963126712966411921<23> × 6744944339966240521048365048076011509<37> × 19234654468418325743668292529120757280653<41> × 124916706233941797813783021695951936693773474351449547931<57> (JMB / GMP-ECM B1=3000000, sigma=3205671956 for P37, Msieve 1.29 for P41 x P57 / November 12, 2007 2007 年 11 月 12 日)
9×10183+7 = 9(0)1827<184> = 59 × 5879009045374855927<19> × 81464545498575947436007410472506863<35> × 318506082558980426195556346049653444619519149682263511747011957601975589600934055977483795167502851069663481908650764978825371373<129> (JMB / GMP-ECM B1=3000000, sigma=2615577722 for P35 / November 11, 2007 2007 年 11 月 11 日)
9×10184+7 = 9(0)1837<185> = 617 × 3725507 × 159746791 × 1198459567<10> × 80746431532206891622049<23> × 666062407088402900138543<24> × 11636058351571852705216457129789359016330456971195199<53> × 326792650541123463809952364790176505238645003791330917413293<60> (JMB / GGNFS-0.77.1-20060513-athlon-xp / November 6, 2007 2007 年 11 月 6 日)
9×10185+7 = 9(0)1847<186> = 3260111 × 16002389063807038301896669024272082879641164981792275113754829766261058133472766404528443<89> × 17251437819596683036560616627382651350704560527929204910892350271133158669382239777179811659<92> (Wataru Sakai / 307.81 hours / November 22, 2008 2008 年 11 月 22 日)
9×10186+7 = 9(0)1857<187> = 43 × 179 × 111427 × 320027 × 1764798836793745988561<22> × 19608191619841530716063<23> × 947569805333121029756005712219395622576412023617093538308914427789335659162926973504107798605592421304934812396034086549251128873<129>
9×10187+7 = 9(0)1867<188> = 172 × 132978624379<12> × 9732595564367067043<19> × 46713538271396399288601288628180779266286619539229457831275785464552417<71> × 5150998105922014663665893801435813375125865465877686848176569656698182698626488585687<85> (LegionMammal978 / Msieve 1.53 snfs for P71 x P85 / July 11, 2017 2017 年 7 月 11 日)
9×10188+7 = 9(0)1877<189> = 2213551 × 38989493 × 652917848061364990158139<24> × [15971542021600508622319355227196166051435400544466499230869687565476299432098383275387383260213256675227142385710526846682243190058269989430888225372191<152>] Free to factor
9×10189+7 = 9(0)1887<190> = 107 × 859 × 23081 × 4242393482643187227298858552498369962828803519184935073323617520052390467277171569000673005288676603562385039356257742247315453824765739639599142405436906680324634529715525319843319<181>
9×10190+7 = 9(0)1897<191> = 23 × 1303 × 5562423025121<13> × 96763374188051<14> × 760252392184689963142116340169836650365375240659571<51> × 7339009404615560184285320145763109680478367901420261041555093795841090296070211976181788959666021826568726783<109> (Kenji Ibusuki / Msieve v. 1.49 (SVN unknown) + GGNFS-0.77.1-VC8 with factMsieve.pl (decomposed + modified) snfs (without procrels.exe, matbuild.exe for "finalFF" calculation) / June 19, 2018 2018 年 6 月 19 日)
9×10191+7 = 9(0)1907<192> = 192 × 71 × 223 × 5348430907<10> × 7081217033400011183081<22> × 4467601201156530952852184773<28> × 16211565179348756515840607697259<32> × 21676057655573837315308075461982724731<38> × 2648244977702149059480307274983753320329588866774945947601<58> (JMB / GMP-ECM B1=3000000, sigma=1309460285 for P32, Msieve 1.29 for P38 x P58 / November 12, 2007 2007 年 11 月 12 日)
9×10192+7 = 9(0)1917<193> = definitely prime number 素数
9×10193+7 = 9(0)1927<194> = 97 × 24329 × 85239169 × 137663371 × [3250041523050880615321685222455062995653569802851624081711673811890186036476064823622620134217460920482180458538096673578394266544203039644075465610181899098442782954818861<172>] Free to factor
9×10194+7 = 9(0)1937<195> = 79 × 109 × 113 × 337 × 5693 × 2054783547710041169679272379174477499196820044377403<52> × 234624474162576730798241102819884412484721379969640372301129617478773041857423131220526843063369689752555865655691486796574658227363<132> (Robert Backstrom / Msieve 1.44 snfs / March 9, 2012 2012 年 3 月 9 日)
9×10195+7 = 9(0)1947<196> = 704607636554329<15> × 1952466020713770378354966701066170212630281<43> × 6542017163585783656838731897757279460480160029220905776573875329096270773257438906850546347725951695175877360281842150195043284289886402343<139> (Serge Batalov / GMP-ECM B1=11000000, sigma=2477634717 for P43 / October 15, 2010 2010 年 10 月 15 日)
9×10196+7 = 9(0)1957<197> = 379 × 84347 × 2793581839990665879086071955488871732154051874807346381894557450536389<70> × 1007795141038902862381302247759455291325233747340278362348189347943401583915173253582538601189245685674010445568232328851<121> (matsui / Msieve 1.42 snfs / 502.44 hours / August 9, 2009 2009 年 8 月 9 日)
9×10197+7 = 9(0)1967<198> = 700849 × 1175267 × 242544833 × 2410098021328339<16> × [1869195712625022073731132253769949703982655845596961100773778877211629077824700799990050608001076241719191682836135742724731028463699707680418614443004462229479567<163>] Free to factor
9×10198+7 = 9(0)1977<199> = 330787 × 3308150472229<13> × 6266116393177<13> × [1312533398188009920711798088775670146008446823514273093798712655062787096910136356963525988612621392849933099266698116732636069400664766788358692197934757327534094740017<169>] Free to factor
9×10199+7 = 9(0)1987<200> = 2861 × 31457532331352673890248164977280671094023068857042991960852848654316672492135616917161831527437958755679832226494232785739252009786787836420831876966095770709542118140510311080041943376441803565187<197>
9×10200+7 = 9(0)1997<201> = 16363 × 1185871 × 11041256557141927631<20> × 1129520353150946514870638937980393951891<40> × 3719029026601584878459985815308542356310526920113885973087730339593263375620616238307141131837874615521876099561714963205165591240279<133> (JMB / GMP-ECM B1=3000000, sigma=750054211 for P40 / November 20, 2007 2007 年 11 月 20 日)
9×10201+7 = 9(0)2007<202> = 113209853 × 975169344437825360828431784019707115618539<42> × [81522641392670968047609948270870860243643825113968223841098342767065974056624548244466163052588893650224400795148247308905575225436258433727926846609721<152>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2806140711 for P42 / February 10, 2014 2014 年 2 月 10 日) Free to factor
9×10202+7 = 9(0)2017<203> = 2633 × 6269 × 19541 × 65851 × 666762539458067341<18> × 1046788095214178400011255561371<31> × 6070916427670932706370047451211098324515520917438378723819783036441147821605873843610082395929448472170594599972150567126187075518719174691<139> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3791936002 for P31 / November 15, 2013 2013 年 11 月 15 日)
9×10203+7 = 9(0)2027<204> = 17 × 449 × 19373 × 62603 × 130367 × 1498097 × 11569867 × 8743129349<10> × [4920988463509342788100565123847882715659841420279587394928340517374276717433494116994080610490449423796801815890059438994121534891576561721466688427747170468981473<163>] Free to factor
9×10204+7 = 9(0)2037<205> = 29 × 281 × 2229299 × 11158361 × 609611269 × 172855363249<12> × 86349716792179<14> × 2576190412701613<16> × 148665270048642533<18> × 225574212907931149427355731<27> × 56480140060889239692322375883517576697358823248256395967606990188325962013657236178829132456837<95>
9×10205+7 = 9(0)2047<206> = 7079641853<10> × 230629900375803225690323162555585023<36> × 187141777794326606939453562934790715326041<42> × 887214475636592077781116707928179558902689<42> × 331983301899164769371000489579942672961936407076314259566041257275484436717397<78> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=1435173889 for P36 / January 1, 2014 2014 年 1 月 1 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1671514279 for P42 / February 11, 2014 2014 年 2 月 11 日) (Dmitry Domanov / Msieve 1.50 gnfs for P42 x P78 / February 12, 2014 2014 年 2 月 12 日)
9×10206+7 = 9(0)2057<207> = 2853899603<10> × 1465928911293419615395660202639<31> × 215125012332627908011456044073475133852934355437500239816900643160059791394476523796673107298648459125521915774038798985239679140610581552354708595775124505247339131571<168> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2079260946 for P31 / November 15, 2013 2013 年 11 月 15 日)
9×10207+7 = 9(0)2067<208> = 43 × 79 × 6607 × [400998414764155678456124023284819505489646020431582118304423649656774317958504594929446333914320629154037258723152432106624230935165284194928180961138842626790909045138564779444856903492914513954945333<201>] Free to factor
9×10208+7 = 9(0)2077<209> = 32411 × [2776835025145783838820153651538058066705748048502051772546357718058683780198080898460399247169170960476381475425010027459813026441640183888186109654129770756841812964734195180648545246984048625466662552837<205>] Free to factor
9×10209+7 = 9(0)2087<210> = 19 × 47 × 61 × 67 × 92378222449799089167980477535034067524901<41> × [2669419395113278323064546171479758505436976809394284680684446960270388338615785604994028596017907880239198640099298445892015776427830615440495987529122030441364577<163>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=447963037 for P41 / February 17, 2014 2014 年 2 月 17 日) Free to factor
9×10210+7 = 9(0)2097<211> = 91002181 × 4230183605695381771309244266091<31> × 23379299295391411310910177695916563169116982235305330414076031641622321077048948803573934684604351776057145514235908087699423405614637126424936393312923315494577789413064017<173> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=4181351214 for P31 / November 15, 2013 2013 年 11 月 15 日)
9×10211+7 = 9(0)2107<212> = 1849919 × 103297459 × 1439613933293158333<19> × 10387620285229626354161<23> × 31494741699308044431473954933678160045771821098017448541410616596756809135434974736819854512455046409882468390640315293333520081543726326089098853230313641359<158>
9×10212+7 = 9(0)2117<213> = 23 × 91331 × 909743 × 43669099051<11> × 4193649349289<13> × 26813110696857204820349<23> × 95910066167432628230539462187889352867551183692435772583840124893534755578995396814251054567973192853298777468046644764674419429344292265221481298252027443<155>
9×10213+7 = 9(0)2127<214> = 277 × 1021 × 17080813 × 225876944410597<15> × 1021280438509871<16> × 25934776776403426724293<23> × [311407471480630378964806412625893991855960301737936439981726265625792288322067578192182328945886963889338973805314356601509275453302208678750840865237<150>] Free to factor
9×10214+7 = 9(0)2137<215> = 55372845497<11> × 1625345405174744653776628364914529904278507589299082034133449871244206686357352180123596078160201975433619461118371790796900899239333884290233949650839270106726189650488136264398122881245002456009507536831<205>
9×10215+7 = 9(0)2147<216> = 151 × 859 × 11631752965487702622599573677100981143925700681605640980215276100583567184504984022474857<89> × 596523047939634859668561823414241476242912088522201937610305799141463311897676615327168122696635227693059712350587054841739<123> (Serge Batalov / for P89 x P123 / December 15, 2014 2014 年 12 月 15 日)
9×10216+7 = 9(0)2157<217> = 6073 × 126967 × 4472608801283656128575694311520901<34> × 2609681195086928616964491698119697421088504889375207415047961568425208333847666144261769816690360026640393777405921630917296722278361019075378008423520349906547827659957170277<175> (Serge Batalov / GMP-ECM B1=1000000, sigma=1744400224 for P34 / January 6, 2014 2014 年 1 月 6 日)
9×10217+7 = 9(0)2167<218> = 1583036347<10> × 94074332951<11> × 2980612679711<13> × 647511390980608922679961085207<30> × 313132047542949975973077258452008515066956358346514309584792361922393778435096428631599905154131387480926829764971823729867055582345999729430180385505611403<156> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2972051337 for P30 / November 15, 2013 2013 年 11 月 15 日)
9×10218+7 = 9(0)2177<219> = 3229 × 3971661672112744021511209841808879578599<40> × 70178198997797752961661024313000665073893917769202679646389886626704726031897972719844134468402760474039333493147062846735592093309865678526651337585358515233410816489488388117<176> (Serge Batalov / GMP-ECM B1=11000000, sigma=3756021527 for P40 / December 4, 2013 2013 年 12 月 4 日)
9×10219+7 = 9(0)2187<220> = 17 × 557 × 22193 × 296587 × 96814413733<11> × 50835725135217802574145287<26> × [29340075419911642187226742169112904167932910848067244536106592500799997635347845445740545886791386917459686505621729479017711191303385923577809265983371393524003513412323<170>] Free to factor
9×10220+7 = 9(0)2197<221> = 79 × 21926321 × 551291077 × 34748400858949439<17> × 76292089645819424532515506787<29> × [35551207302900375123574816010353118522193497949778862001213898764052006998281426526893430698438838077366271468870039823014290320490607337556417888745395609993<158>] Free to factor
9×10221+7 = 9(0)2207<222> = 3049 × 125303 × 382940942789<12> × 13810389526433051<17> × 29054091091571010128245728388267632663751<41> × 15331286233198408635524700861793732313546026469400941914282974884117686807246129580478407958464455398068666975334745446305499789972292625514987929<146> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=576486280 for P41 / January 2, 2014 2014 年 1 月 2 日)
9×10222+7 = 9(0)2217<223> = 953 × 142297045000649576294478005435172025232087<42> × [66367235454456337834835922831807205249536648302761581676830243633870462789874597846935722687528967244532919038608916215810422137934341563165162373919994557674478774898765238037337<179>] (Serge Batalov / GMP-ECM B1=43000000, sigma=423615864 for P42 / January 5, 2014 2014 年 1 月 5 日) Free to factor
9×10223+7 = 9(0)2227<224> = 167 × 197 × 598613 × 35619959 × 128298108250331950522851179603507171383734303219468287085251607968229996779131388856202314663025790197175056793899838534311406858074879620222967974388603589525097766786271233483178805538009295226783062241679<207>
9×10224+7 = 9(0)2237<225> = 1583 × 66109 × 47726156978014618368949447<26> × [180195749022292999324815804528429383883654429866658070727057670274416965469463145344534327729666398945872503872692665041665892968684347304704692661730347017397407072476025452858623386298289723<192>] Free to factor
9×10225+7 = 9(0)2247<226> = 683 × 941 × 52210292661521<14> × 49615468464346702991200046624124311670379<41> × 5405787359630890455512038443034203930511060956117668282842743909243452898604370016971079167665687041319422053085921189882412484192556138322171757282595682210487525291<166> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4079313249 for P41 / February 17, 2014 2014 年 2 月 17 日)
9×10226+7 = 9(0)2257<227> = 71 × 8731 × 10067 × 1729504059838726995527958369425692432019<40> × 8338703235213527662441421817318225520115654679015460090444086173355604083695045060421479394215467089665953248251651411258923533870651039179963494071841138938045767257089713215259<178> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1354890808 for P40 / February 14, 2014 2014 年 2 月 14 日)
9×10227+7 = 9(0)2267<228> = 19 × 78787 × 46387427 × 485710871 × 26684325939695587948573806437530420227415030765108081191531162598021656468866737888456906444934030104267150563310891416300000685729773206422349885311673088127177045751668734186510794769997001220834014450707<206>
9×10228+7 = 9(0)2277<229> = 43 × 389 × 631 × 6198220984897<13> × 488677661009273<15> × 13036562657783898890903<23> × 106083295228792347581684102225158748873<39> × 203561411097997595093659814198011667661729548859217377446245308830729852953874260426847525295582274055520855762477144913079813948209249<135> (Serge Batalov / GMP-ECM B1=3000000, sigma=3411684468 for P39 / January 9, 2014 2014 年 1 月 9 日)
9×10229+7 = 9(0)2287<230> = 383 × 5639 × 2004817 × 1770709141<10> × 140799596475221<15> × [83371624758328362861240784479230585164590937058795619199472894311864629675808417535552513062698390501129908238649645727920127352071375520501103870972440195597861198840316678298491383463548647303<194>] Free to factor
9×10230+7 = 9(0)2297<231> = 19163 × 20307217870307<14> × 7720289831500849<16> × 18192493067601118167323<23> × 787227101711564633255831<24> × [20917160157468957496494522108167658451339629067117797629838810819508944993035812673815749323213800422330600959276059552809701909279286963161930212699171<152>] Free to factor
9×10231+7 = 9(0)2307<232> = 11138322538151603<17> × 808021133269637192484479586427628680800804819457685162874725558270837620916222941950169431637940997076861021226440321870216609082317234600204702770558713950385604041751057009160782349059337135307470776734296568619869<216>
9×10232+7 = 9(0)2317<233> = 29 × 281 × 53365051931<11> × 1006498897160763381559<22> × [205621229608357523909743643220878065702916826267128633074220005009045442048771292659077495779624433794184453953830232458706383498080435373213373736651073800490459644016666210629645241757193396537367<198>] Free to factor
9×10233+7 = 9(0)2327<234> = 79 × 14887 × 283511 × 341634960068447<15> × 104347438181595838877<21> × 1879488883793073702284881<25> × [40286028619355567311455791515812931976755124702680939576125046343555815416733145129618031764342418648568911694666108372627802154378373007684425464784574048209262771<164>] Free to factor
9×10234+7 = 9(0)2337<235> = 23 × 2765346817<10> × 2600284471159<13> × [54418204049690637101766191308539002298932695577473501195394179854875366554879665227816600722933649155688750495673409820134178649497243968576935090586968734316883851648629750909715869346444698674817554193901653303<212>] Free to factor
9×10235+7 = 9(0)2347<236> = 17 × 449 × 121017289325033390837784637974462677<36> × [97431598126774846399561095578732390001046435939879812064355602217093016309668767183721769108359788364157604472729123618425613353696513342190402848052977559231155074735271081974389128124207840098427<197>] (Serge Batalov / GMP-ECM B1=11000000, sigma=2935732093 for P36 / December 4, 2013 2013 年 12 月 4 日) Free to factor
9×10236+7 = 9(0)2357<237> = 569 × 13740421 × [115114545606674093934744940021483947877321219788428446667591349408912242229055068915727981913372452186661542302592069691496032496157816375321385118241137885058540368289999884730689282010266450076125114709390370532603904967110643<228>] Free to factor
9×10237+7 = 9(0)2367<238> = 92761 × 41629351 × 44044597 × 1352346113<10> × 49101381817<11> × [796898914601478556213307509231633690812995266830063622941568132521356211053109293754462540748576381352252119681962647531423716241862265299003414965965435067936469080308698682429523655970705544569901<198>] Free to factor
9×10238+7 = 9(0)2377<239> = 20501021 × 3700528283<10> × 229790322743<12> × [5162636600096189684648081917109535481162288088592818829769710346793262382628995866727778559350971011681558058077072798250811075510352950415850211450381354079610049464627161029742014544669134484389585104113514943<211>] Free to factor
9×10239+7 = 9(0)2387<240> = 50110334921347<14> × 102667963126567<15> × 501437254522840920587<21> × [348870028814809257917936163237714340645121648573670520758524830722173462141718530711468942878437219638439504296783300040256976369290415421014394505330605755285651060452441934552900016635625089<192>] Free to factor
9×10240+7 = 9(0)2397<241> = 163 × 1287762137<10> × 866490120724229<15> × [49482956263514112636776846733122868225657550454004138582329393503223542989405387512517628565055759242775786489362222098601706703246615335291811186287092146111983954933633792014678495933974934702643465005012114797393<215>] Free to factor
9×10241+7 = 9(0)2407<242> = 59 × 131 × 859 × 90709 × 1026847 × 43720619 × 5167458944978128969<19> × 2100381677437420183077936704698222439<37> × 306696176955271931612834122610454663208287170779064436265947259127798358959265256935980071732838710223669547973206787211368718919972449863154177584323142021470211<162> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2853497892 for P37 / January 14, 2014 2014 年 1 月 14 日)
9×10242+7 = 9(0)2417<243> = 67 × 107 × 263 × 67187 × 191977997 × 44152161254849<14> × 344614344027703<15> × 2432238492165920016498768462482753392102518844685422405269422926358841534239468099019452617760932247926832916742679786883410292358077215192358926016527135425662116615847798732879475752964844279057<196>
9×10243+7 = 9(0)2427<244> = 1667 × [5398920215956808638272345530893821235752849430113977204559088182363527294541091781643671265746850629874025194961007798440311937612477504499100179964007198560287942411517696460707858428314337132573485302939412117576484703059388122375524895021<241>] Free to factor
9×10244+7 = 9(0)2437<245> = 443 × [203160270880361173814898419864559819413092550790067720090293453724604966139954853273137697516930022573363431151241534988713318284424379232505643340857787810383747178329571106094808126410835214446952595936794582392776523702031602708803611738149<243>] Free to factor
9×10245+7 = 9(0)2447<246> = 19 × 661 × 1808003 × 39635861505360453638216479848640467558306378217406227684336988583588168981722961234653390068091986553477437144051788987868689170803987110844672645347091870513635580667753829404809719142647229963083831963154403438405313257839474863692291<236>
9×10246+7 = 9(0)2457<247> = 79 × 9949 × 86843 × 1284917 × 5171779 × 116052250908577727<18> × 25710891438213305650349864941<29> × [6649904879405012280723922865445247352794300005019688264542081375351204850630994990232164256709939906826565335238183926635017242799984668554153991963145497962772705514103758613219<178>] (Serge Batalov / GMP-ECM B1=1000000, sigma=1058861003 for P29 / January 6, 2014 2014 年 1 月 6 日) Free to factor
9×10247+7 = 9(0)2467<248> = 347 × 69682517 × 4203477389069618717<19> × [885483533796438276438650000352369402478004193284101164005732966911857312078446259967228403219290783475768006003931275679385185770646061954042026062847737509829419288171180850521116030612612148874475292544332047662680229<219>] Free to factor
9×10248+7 = 9(0)2477<249> = 24746123950844617839472004012789559625701316316587281572191163087<65> × 36369332093694690044740674414909180490917176967109285151663713777042043964425205666014145034748139276988982961701612665737048964393131019147983177915594782015550945118299054581284089161<185> (NFS@Home + Dmitry Domanov / ggnfs-lasieve4I14e on the NFS@Home grid + msieve for P65 x P185 / November 28, 2016 2016 年 11 月 28 日)
9×10249+7 = 9(0)2487<250> = 43 × 3747391 × 55852812151546328855785078825663346938933569862959478046285759134635890832153716769135994169164999155102098847525006436571160364451514555432125667486873487602813623888515850714692273997785982114576669847194711523110965891041353527616761188139<242>
9×10250+7 = 9(0)2497<251> = 65568997342340377559862604777849853<35> × [1372599912274144254386492543073270359372612409833617679605114425811817439882930737575479085064390490783610912425097249149886778359661760384832248658889439324126593823839327259174953572621772585558453665783464278497619<217>] (Serge Batalov / GMP-ECM B1=11000000, sigma=240409859 for P35 / December 3, 2013 2013 年 12 月 3 日) Free to factor
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