Table of contents 目次

  1. About 699...991 699...991 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 699...991 699...991 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 699...991 699...991 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 699...991 699...991 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

69w1 = { 61, 691, 6991, 69991, 699991, 6999991, 69999991, 699999991, 6999999991, 69999999991, … }

1.3. General term 一般項

7×10n-9 (1≤n)

2. Prime numbers of the form 699...991 699...991 の形の素数

2.1. Last updated 最終更新日

October 15, 2015 2015 年 10 月 15 日

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

  1. 7×101-9 = 61 is prime. は素数です。
  2. 7×102-9 = 691 is prime. は素数です。
  3. 7×103-9 = 6991 is prime. は素数です。
  4. 7×104-9 = 69991 is prime. は素数です。
  5. 7×1014-9 = 6(9)131<15> is prime. は素数です。
  6. 7×1015-9 = 6(9)141<16> is prime. は素数です。
  7. 7×1023-9 = 6(9)221<24> is prime. は素数です。
  8. 7×1028-9 = 6(9)271<29> is prime. は素数です。
  9. 7×1054-9 = 6(9)531<55> is prime. は素数です。
  10. 7×10100-9 = 6(9)991<101> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 6, 2004 2004 年 12 月 6 日)
  11. 7×10272-9 = 6(9)2711<273> is prime. は素数です。 (Makoto Kamada / PPSIQS / January 5, 2004 2004 年 1 月 5 日)
  12. 7×10373-9 = 6(9)3721<374> is prime. は素数です。 (Makoto Kamada / PPSIQS / January 5, 2004 2004 年 1 月 5 日)
  13. 7×10403-9 = 6(9)4021<404> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 24, 2005 2005 年 1 月 24 日)
  14. 7×10568-9 = 6(9)5671<569> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006 2006 年 5 月 31 日)
  15. 7×10639-9 = 6(9)6381<640> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006 2006 年 5 月 31 日)
  16. 7×10842-9 = 6(9)8411<843> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006 2006 年 5 月 31 日)
  17. 7×10969-9 = 6(9)9681<970> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006 2006 年 5 月 31 日)
  18. 7×101255-9 = 6(9)12541<1256> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 9, 2006 2006 年 9 月 9 日)
  19. 7×101259-9 = 6(9)12581<1260> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 9, 2006 2006 年 9 月 9 日)
  20. 7×103047-9 = 6(9)30461<3048> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 18, 2004 2004 年 12 月 18 日) (certified by: (証明: Ray Chandler / Primo 4.0.1 - LX64 / January 29, 2013 2013 年 1 月 29 日)
  21. 7×104838-9 = 6(9)48371<4839> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 19, 2004 2004 年 12 月 19 日)
  22. 7×106389-9 = 6(9)63881<6390> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 24, 2004 2004 年 12 月 24 日)
  23. 7×1012755-9 = 6(9)127541<12756> is PRP. はおそらく素数です。 (Sinkiti Sibata / PFGW / December 28, 2007 2007 年 12 月 28 日)
  24. 7×1015142-9 = 6(9)151411<15143> is PRP. はおそらく素数です。 (Sinkiti Sibata / PFGW / December 28, 2007 2007 年 12 月 28 日)
  25. 7×1034943-9 = 6(9)349421<34944> 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. 7×1037652-9 = 6(9)376511<37653> 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. 7×1038108-9 = 6(9)381071<38109> 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. 7×1038686-9 = 6(9)386851<38687> 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. 7×1039384-9 = 6(9)393831<39385> 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)
  30. 7×1043393-9 = 6(9)433921<43394> 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)
  31. 7×1047280-9 = 6(9)472791<47281> 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)
  32. 7×1055030-9 = 6(9)550291<55031> 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)
  33. 7×10161192-9 = 6(9)1611911<161193> is PRP. はおそらく素数です。 (Bob Price / October 15, 2015 2015 年 10 月 15 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 15, 2015 2015 年 10 月 15 日

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

  1. 7×1013k+8-9 = 53×(7×108-953+63×108×1013-19×53×k-1Σm=01013m)
  2. 7×1015k+11-9 = 31×(7×1011-931+63×1011×1015-19×31×k-1Σm=01015m)
  3. 7×1016k+13-9 = 17×(7×1013-917+63×1013×1016-19×17×k-1Σm=01016m)
  4. 7×1018k+16-9 = 19×(7×1016-919+63×1016×1018-19×19×k-1Σm=01018m)
  5. 7×1022k+19-9 = 23×(7×1019-923+63×1019×1022-19×23×k-1Σm=01022m)
  6. 7×1026k+6-9 = 859×(7×106-9859+63×106×1026-19×859×k-1Σm=01026m)
  7. 7×1028k+6-9 = 29×(7×106-929+63×106×1028-19×29×k-1Σm=01028m)
  8. 7×1028k+6-9 = 281×(7×106-9281+63×106×1028-19×281×k-1Σm=01028m)
  9. 7×1032k+5-9 = 449×(7×105-9449+63×105×1032-19×449×k-1Σm=01032m)
  10. 7×1041k+40-9 = 83×(7×1040-983+63×1040×1041-19×83×k-1Σm=01041m)

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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 31.06%. 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 31.06% です。

3. Factor table of 699...991 699...991 の素因数分解表

3.1. Last updated 最終更新日

August 13, 2018 2018 年 8 月 13 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=195, 201, 202, 204, 208, 215, 217, 219, 220, 226, 228, 229, 230, 232, 233, 234, 236, 237, 238, 239, 243, 244, 245, 246, 247, 248 (26/250)

3.4. Factor table 素因数分解表

7×101-9 = 61 = definitely prime number 素数
7×102-9 = 691 = definitely prime number 素数
7×103-9 = 6991 = definitely prime number 素数
7×104-9 = 69991 = definitely prime number 素数
7×105-9 = 699991 = 449 × 1559
7×106-9 = 6999991 = 29 × 281 × 859
7×107-9 = 69999991 = 307 × 228013
7×108-9 = 699999991 = 532 × 249199
7×109-9 = 6999999991<10> = 11149 × 627859
7×1010-9 = 69999999991<11> = 401 × 174563591
7×1011-9 = 699999999991<12> = 31 × 349 × 5209 × 12421
7×1012-9 = 6999999999991<13> = 719 × 1223 × 7960543
7×1013-9 = 69999999999991<14> = 17 × 33479 × 122991937
7×1014-9 = 699999999999991<15> = definitely prime number 素数
7×1015-9 = 6999999999999991<16> = definitely prime number 素数
7×1016-9 = 69999999999999991<17> = 19 × 3917 × 940569447617<12>
7×1017-9 = 699999999999999991<18> = 3539507 × 197767655213<12>
7×1018-9 = 6999999999999999991<19> = 283 × 24734982332155477<17>
7×1019-9 = 69999999999999999991<20> = 23 × 152391511 × 19971442247<11>
7×1020-9 = 699999999999999999991<21> = 59 × 40351 × 294030055752299<15>
7×1021-9 = 6999999999999999999991<22> = 53 × 117287257 × 1126085433971<13>
7×1022-9 = 69999999999999999999991<23> = 197 × 706550737 × 502907902619<12>
7×1023-9 = 699999999999999999999991<24> = definitely prime number 素数
7×1024-9 = 6999999999999999999999991<25> = 439 × 8677 × 213397 × 8611436681401<13>
7×1025-9 = 69999999999999999999999991<26> = 1153 × 60711188204683434518647<23>
7×1026-9 = 699999999999999999999999991<27> = 31 × 167 × 1549 × 115512181 × 755684776607<12>
7×1027-9 = 6999999999999999999999999991<28> = 1367 × 5120702267739575713240673<25>
7×1028-9 = 69999999999999999999999999991<29> = definitely prime number 素数
7×1029-9 = 699999999999999999999999999991<30> = 17 × 467 × 88172313893437460637359869<26>
7×1030-9 = 6999999999999999999999999999991<31> = 601079 × 4712747339<10> × 2471111420941411<16>
7×1031-9 = 69999999999999999999999999999991<32> = 22443647 × 3118922695585080267926153<25>
7×1032-9 = 699999999999999999999999999999991<33> = 859 × 16091 × 4075938721873<13> × 12424936995743<14>
7×1033-9 = 6999999999999999999999999999999991<34> = 1103 × 3049 × 11579 × 2252017 × 79821959478521971<17>
7×1034-9 = 69999999999999999999999999999999991<35> = 19 × 29 × 53 × 281 × 6211962037<10> × 1373205261208914401<19>
7×1035-9 = 699999999999999999999999999999999991<36> = 11968507 × 65115374179<11> × 898203041519418247<18>
7×1036-9 = 6999999999999999999999999999999999991<37> = 617 × 4937 × 263723 × 871664581 × 9996600626416433<16>
7×1037-9 = 69999999999999999999999999999999999991<38> = 449 × 42487 × 177400101813811<15> × 20684344746284987<17>
7×1038-9 = 699999999999999999999999999999999999991<39> = 3880999 × 180365931555251624646128483929009<33>
7×1039-9 = 6999999999999999999999999999999999999991<40> = 229 × 8087 × 22481 × 4782292477<10> × 35157934736975360641<20>
7×1040-9 = 69999999999999999999999999999999999999991<41> = 83 × 199 × 14081 × 992513 × 303247457866816806060790091<27>
7×1041-9 = 699999999999999999999999999999999999999991<42> = 23 × 31 × 13893431 × 41355185348647<14> × 1708712631800209951<19>
7×1042-9 = 6999999999999999999999999999999999999999991<43> = 164934551 × 970496719 × 43731293776396301260490639<26>
7×1043-9 = 69999999999999999999999999999999999999999991<44> = 11106808382555104469<20> × 6302440592199773403965339<25>
7×1044-9 = 699999999999999999999999999999999999999999991<45> = 472 × 149 × 39667 × 3344261 × 16031956850800023853001797573<29>
7×1045-9 = 6999999999999999999999999999999999999999999991<46> = 17 × 3919640159869712290637<22> × 105051660123831336940579<24>
7×1046-9 = 69999999999999999999999999999999999999999999991<47> = 99577 × 2536921 × 1925346921733<13> × 143920634053120072981531<24>
7×1047-9 = 699999999999999999999999999999999999999999999991<48> = 53 × 97 × 136160280101147636646566815794592491733125851<45>
7×1048-9 = 6999999999999999999999999999999999999999999999991<49> = 4007 × 22821090585503549107<20> × 76549490194924079952133259<26>
7×1049-9 = 69999999999999999999999999999999999999999999999991<50> = 653 × 1423603 × 9701213 × 7761933616444179059114953688709973<34>
7×1050-9 = 699999999999999999999999999999999999999999999999991<51> = 274009913 × 2611748383<10> × 978138674401529624850073127375729<33>
7×1051-9 = 6(9)501<52> = 271349425373391653599<21> × 25796995849051889688124365522409<32>
7×1052-9 = 6(9)511<53> = 19 × 1823 × 63693557 × 79931966784969871711<20> × 396955449301910954809<21>
7×1053-9 = 6(9)521<54> = 8501 × 8879069 × 58412089 × 1811930375309<13> × 87622643039546762581739<23>
7×1054-9 = 6(9)531<55> = definitely prime number 素数
7×1055-9 = 6(9)541<56> = 1021568011415096267<19> × 3643133669301479323<19> × 18808564405666102751<20>
7×1056-9 = 6(9)551<57> = 31 × 324539435794589<15> × 218358001979391821<18> × 318639606883459936365169<24>
7×1057-9 = 6(9)561<58> = 19703911 × 69411682303567<14> × 5118150267148581516851398425602423743<37>
7×1058-9 = 6(9)571<59> = 859 × 11813 × 5545640403607<13> × 940755542907563<15> × 1322257932751467570484453<25>
7×1059-9 = 6(9)581<60> = 1327 × 371263792633<12> × 1420837857915536825097690713749878956968536001<46>
7×1060-9 = 6(9)591<61> = 53 × 10875089 × 22844333 × 813988763803378208453<21> × 653119210982323517280427<24>
7×1061-9 = 6(9)601<62> = 17 × 61 × 21937 × 308621 × 9970491652745088652134058600929687482264953476559<49>
7×1062-9 = 6(9)611<63> = 29 × 281 × 3463 × 33581 × 660299 × 1118682814465094470993958292941212612296238147<46>
7×1063-9 = 6(9)621<64> = 23 × 4200564596937088482282701<25> × 72454028277264632343609034955413649317<38>
7×1064-9 = 6(9)631<65> = 317 × 196709 × 2584574197<10> × 4869382981085232119561<22> × 89197279656513356948920691<26>
7×1065-9 = 6(9)641<66> = 15373 × 690677096043165567058269235709<30> × 65927158605080334159640015235663<32>
7×1066-9 = 6(9)651<67> = 2473 × 8025672923669<13> × 352689448551458899208572288401083287390201152700643<51>
7×1067-9 = 6(9)661<68> = 1599715673923<13> × 43757775922979016048616514484275454823910920823697037117<56>
7×1068-9 = 6(9)671<69> = 35221 × 7941419 × 15793913 × 158455933266452057874214088948639587896535990709593<51>
7×1069-9 = 6(9)681<70> = 4492 × 258492685662236177<18> × 3760531227240978188599<22> × 35719707990493100588004017<26>
7×1070-9 = 6(9)691<71> = 19 × 81509 × 330606636232459<15> × 8779104591814097<16> × 15573172137340255745049809506903627<35>
7×1071-9 = 6(9)701<72> = 31 × 563 × 3911 × 179785556161493<15> × 961989804515978153<18> × 59294562391280460512472230846713<32>
7×1072-9 = 6(9)711<73> = 3413 × 52709415906457<14> × 1156397065361874670603<22> × 33648566508970817837441866894749017<35>
7×1073-9 = 6(9)721<74> = 53 × 1320754716981132075471698113207547169811320754716981132075471698113207547<73>
7×1074-9 = 6(9)731<75> = 701 × 3596653 × 277639646214539516840136162208818336263672385696593547123219691247<66>
7×1075-9 = 6(9)741<76> = 3630700847<10> × 883034280879212207<18> × 29419487474138246773<20> × 74215549448312697962377468123<29>
7×1076-9 = 6(9)751<77> = 109 × 1511 × 15679 × 505067 × 53671004560691696262195668121871284129630226221974025606021313<62>
7×1077-9 = 6(9)761<78> = 17 × 13229 × 17854464504271<14> × 174331261543101214451235408329980906103713980372625651017997<60>
7×1078-9 = 6(9)771<79> = 59 × 746041 × 159031565016681616012424818111623301295818726189424905283639725439727389<72>
7×1079-9 = 6(9)781<80> = 1307 × 6785081 × 7893460059806511896319863994618680062877548233011093918582511765650173<70>
7×1080-9 = 6(9)791<81> = 1453 × 3191745091<10> × 302786213659<12> × 5176932940723071893<19> × 96293193507834656986340282696713150391<38>
7×1081-9 = 6(9)801<82> = 83 × 179 × 1371703 × 343484250251585934609283702296470793379559591266855447903771218547392121<72>
7×1082-9 = 6(9)811<83> = 9658508443<10> × 163948327931<12> × 44205976091257372221263494665720945674176108520668304334166127<62>
7×1083-9 = 6(9)821<84> = 397259 × 48533531291684874475043310367<29> × 36306334392159591871690594681309433317007261491547<50>
7×1084-9 = 6(9)831<85> = 131 × 859 × 338323 × 169439817263<12> × 13861039041779<14> × 78287206438859709874601961365769572312018827087649<50>
7×1085-9 = 6(9)841<86> = 23 × 661 × 212241131 × 277674421 × 1528560215850266240097607<25> × 51111751820488007598569996009292231446221<41>
7×1086-9 = 6(9)851<87> = 31 × 53 × 113 × 63337 × 836471 × 344081953433<12> × 193512277560173350885335989<27> × 1068816712100875280175997470842951<34>
7×1087-9 = 6(9)861<88> = 1969829173632841194304683706673<31> × 3553607639534705326098147460687934955266194754946936787367<58> (Makoto Kamada / GGNFS-0.70.3 / 0.15 hours)
7×1088-9 = 6(9)871<89> = 19 × 2297 × 8951 × 1394539 × 22901293 × 1580561501<10> × 2772096625367<13> × 1014661128929015261<19> × 1262061250545387607303577363<28>
7×1089-9 = 6(9)881<90> = 227 × 726963781 × 35881789864109353145705630645174237189<38> × 118218463500944725646795691167087710752037<42> (Makoto Kamada / GGNFS-0.70.3 / 0.15 hours)
7×1090-9 = 6(9)891<91> = 29 × 47 × 281 × 2971 × 877463 × 13366844637367335133286680395331<32> × 524487931580487799595358413662132611448042819<45> (Makoto Kamada / msieve 0.83 / 12 minutes)
7×1091-9 = 6(9)901<92> = 134989152107<12> × 958924509667<12> × 1308009413743<13> × 1189939718671632467612763103<28> × 347439283577433885449113398791<30>
7×1092-9 = 6(9)911<93> = 146891 × 78152033 × 20015164653398291985105716405836813079<38> × 3046515594062724677900236292359230283243043<43> (Makoto Kamada / GGNFS-0.71.1 / 0.30 hours)
7×1093-9 = 6(9)921<94> = 17 × 433 × 950957750305664991169678032875967939138703980437440565140605895938051895122945252003803831<90>
7×1094-9 = 6(9)931<95> = 1445771 × 22736479 × 1823438587<10> × 1167842241019817980875273241397181543662001925323893922497031801015436577<73>
7×1095-9 = 6(9)941<96> = 2341 × 2394729004403299<16> × 124864865015264218394575582585749559062968304996835254249302244444965492025049<78>
7×1096-9 = 6(9)951<97> = 5233 × 50599 × 5532071 × 8135801 × 55205063631751955989<20> × 10639920769929440223306158395925323510860795221295373267<56>
7×1097-9 = 6(9)961<98> = 1409391757<10> × 5280519208379718820423<22> × 9405668890330999362112448627619847261928122301969342209263792400981<67>
7×1098-9 = 6(9)971<99> = 1427 × 3167 × 986451758445266456542306483<27> × 157018257035127172514336620959131444330898107873147312728312942753<66>
7×1099-9 = 6(9)981<100> = 53 × 132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547<99>
7×10100-9 = 6(9)991<101> = definitely prime number 素数
7×10101-9 = 6(9)1001<102> = 31 × 449 × 8089 × 2272300714180442793943<22> × 2736083611544163204365565828392337141806610405552934479293496480591005207<73>
7×10102-9 = 6(9)1011<103> = 1254600491120498807<19> × 11337584783797312963091987<26> × 492121159988223191961267092426246766263374349339380761945499<60>
7×10103-9 = 6(9)1021<104> = 3362705057<10> × 20816574398722236792353924247243310937810862548091740060091746547725847726644674326547694010263<95>
7×10104-9 = 6(9)1031<105> = 457 × 614683 × 10304587 × 784703085174773<15> × 308173071816774340459673322686612595157917025374502729419945628032212200811<75>
7×10105-9 = 6(9)1041<106> = 28051 × 2143763 × 116405344597190031191901805135847981119232304049116843498687768944335162152597547134452739242207<96>
7×10106-9 = 6(9)1051<107> = 19 × 122323 × 3141040178363<13> × 3992705548929701<16> × 2401571606554999444278126303319542175254100775281143857688583997874014761<73>
7×10107-9 = 6(9)1061<108> = 23 × 443130646503105367<18> × 68681285866520115699706148638335760380632596349081223347818631243836775083347605879124551<89>
7×10108-9 = 6(9)1071<109> = 404321 × 378807857 × 2663967441313171836581746263544242756268412123<46> × 17156308633252668896929507566790813539577265672261<50> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P46 x P50 / 4.81 hours on Cygwin on AMD 64 3200+ / December 27, 2007 2007 年 12 月 27 日)
7×10109-9 = 6(9)1081<110> = 17 × 5250587928510849009183117637<28> × 784225902867864207360231754958821339359705294994107011669171493784173460189631579<81>
7×10110-9 = 6(9)1091<111> = 859 × 1009 × 24243911 × 33312791674628217482346439393324067765371289521980792112336000123496601843965398888874627190008051<98>
7×10111-9 = 6(9)1101<112> = 1069 × 277437895352022854995069<24> × 23602312355297082015927167678140560343508592065308502398856544057659641295240594264431<86>
7×10112-9 = 6(9)1111<113> = 53 × 40708325839<11> × 32444338836351822183116581229336641053098571635341899476915791474615044956229189053551757907065706773<101>
7×10113-9 = 6(9)1121<114> = 491 × 2423 × 4003873 × 184432465107840005841929350652158018855881137453<48> × 796792925041443202307060294296189274485989498333919823<54> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 2.40 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / December 27, 2007 2007 年 12 月 27 日)
7×10114-9 = 6(9)1131<115> = 121257213803424719<18> × 57728524187831009080731290680637814679125480153081993912147907087167318137639275275802041880800089<98>
7×10115-9 = 6(9)1141<116> = 97250820285663120463<20> × 719788273192791955965746282238644653846287927798006385921017997045176263876158935002054839607257<96>
7×10116-9 = 6(9)1151<117> = 31 × 4485581 × 669776469149<12> × 92090922434349821621<20> × 178568102619862404424812210551227279<36> × 457053511390114417546219792302625404555491<42> (Makoto Kamada / Msieve 1.32 for P36 x P42 / 6.6 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 25, 2007 2007 年 12 月 25 日)
7×10117-9 = 6(9)1161<118> = 965127703405741647531200158987421082342396773977<48> × 7252926193392239386243000349720048960099140101219877063658000208088783<70> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 1.05 hours on Core 2 Quad Q6600 / December 26, 2007 2007 年 12 月 26 日)
7×10118-9 = 6(9)1171<119> = 29 × 281 × 479 × 564899 × 1984136958064167375045366373528421<34> × 15999844291278446970836451631567805232288393575182670206207520554418064299<74> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.24 hours on Core 2 Duo E6300 1.86GHz , Windows Vista / December 26, 2007 2007 年 12 月 26 日)
7×10119-9 = 6(9)1181<120> = 38149 × 2419159905731<13> × 14581036054489<14> × 520189907386696827300001381733679773554344541535309841482892667130817655268641804704841601<90>
7×10120-9 = 6(9)1191<121> = 197 × 419 × 1323129079639263647678527821934298050401138159281717<52> × 64093734415499366088944419295581630353010019359658087508532919861<65> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 1.47 hours on Cygwin on AMD 64 3200+ / December 26, 2007 2007 年 12 月 26 日)
7×10121-9 = 6(9)1201<122> = 61 × 181 × 35329121 × 17964677206821421693<20> × 334211158690645380842918043611<30> × 29889347464454773363724797797419966103587991932040263599541497<62> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3212389331 for P30 / December 18, 2007 2007 年 12 月 18 日)
7×10122-9 = 6(9)1211<123> = 83 × 13523 × 244861 × 1071691642724939<16> × 82895830946665960950649287503567133316049651<44> × 28669805558837951631417683899953649248910278323675131<53> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 3.38 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 26, 2007 2007 年 12 月 26 日)
7×10123-9 = 6(9)1221<124> = 1050041917<10> × 302916609883091<15> × 239018721205781689<18> × 34818487614485931662968674032860210843<38> × 2644396018118121895004088022885829241424618139<46> (Makoto Kamada / Msieve 1.32 for P38 x P46 / 36 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 25, 2007 2007 年 12 月 25 日)
7×10124-9 = 6(9)1231<125> = 19 × 617 × 16007 × 1017799 × 78637659172668992987<20> × 5049086622571583865989<22> × 31658163005376569439686030385629<32> × 29158031481352998719705506784590386527<38> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2819111382 for P32 / December 18, 2007 2007 年 12 月 18 日)
7×10125-9 = 6(9)1241<126> = 17 × 53 × 2647 × 13963 × 1044761 × 1390280563617935629<19> × 14471753817307893884145108822799115764049852030062297362838935317717597952001945213709183099<92>
7×10126-9 = 6(9)1251<127> = 311 × 51157 × 47616383 × 20706073799<11> × 8197545011882838090704072765843473<34> × 54437053775701211157352173944971804135504984853025897634831653286613<68> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2887025868 for P34 / December 18, 2007 2007 年 12 月 18 日)
7×10127-9 = 6(9)1261<128> = 349 × 4483 × 38567 × 94421 × 12286252053820531235898840216597784288999138262437218845755634025411245687087146881539233939777769719541943430939<113>
7×10128-9 = 6(9)1271<129> = 193 × 101574349 × 16472182583<11> × 15690820524959<14> × 24520580133893<14> × 61342395908275873142783<23> × 91847725389181320183447907285466322171928818317546658846241<59>
7×10129-9 = 6(9)1281<130> = 23 × 77641 × 3919936967413563989891042552035763264926699978664343077363315997878754109633917086613247258984075536065380068688495488992537<124>
7×10130-9 = 6(9)1291<131> = 2331790871595725223809887<25> × 121486076386989425190994558849<30> × 247105229357886499742603117907178725533261641742249826966467842473182053082857<78> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=685742332 for P30 / December 18, 2007 2007 年 12 月 18 日)
7×10131-9 = 6(9)1301<132> = 31 × 1008086585501132741209<22> × 22399509611632412435317217769878768797093691276214282863054555407464845083783104689389885887218774118364718929<110>
7×10132-9 = 6(9)1311<133> = 1292567 × 190646486287<12> × 10653299394346279999189253853948866948741<41> × 2666441366915221621544897168193843156735547511317187784920639757035112567619<76> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 5.77 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 26, 2007 2007 年 12 月 26 日)
7×10133-9 = 6(9)1321<134> = 449 × 1493 × 90917 × 94389114492319<14> × 85173022756831337810382828011673697322037311<44> × 142864005459473961587757841830261127716190760624346731496837517471<66> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 8.35 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 27, 2007 2007 年 12 月 27 日)
7×10134-9 = 6(9)1331<135> = 72089441 × 335074768187<12> × 146241799665334969702251263<27> × 20135344504565562376342185050464403393369<41> × 9841336209634974359251395167641210798116774569059<49> (Makoto Kamada / Msieve 1.32 for P41 x P49 / 1.8 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / December 25, 2007 2007 年 12 月 25 日)
7×10135-9 = 6(9)1341<136> = 3673 × 255019 × 84498497 × 15088353311<11> × 2619090469168430611738435623980583053<37> × 2238016293251830424874207565385593578321653128229251831899397482529153343<73> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 6.83 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 27, 2007 2007 年 12 月 27 日)
7×10136-9 = 6(9)1351<137> = 47 × 59 × 859 × 170372520579279611<18> × 1528448959415478502358003<25> × 112850767580475999098519341290326761537684048177582015080167140213439675324675866106367361<90>
7×10137-9 = 6(9)1361<138> = 9041 × 162129560783<12> × 63195768153342995547599618615921084920365446753767<50> × 7556685842419476053247753995520570438772601000514461987314342496480958991<73> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 4.07 hours on Core 2 Quad Q6600 / December 27, 2007 2007 年 12 月 27 日)
7×10138-9 = 6(9)1371<139> = 53 × 51600811 × 13878683279<11> × 8646687306199<13> × 21328859054736563069383953455246447382924778411368997650321239762099378748992519605318312540959154329654937<107>
7×10139-9 = 6(9)1381<140> = 199 × 1093 × 50363 × 4507795008012558253237675801<28> × 1417584811269264650854104633179695072457419963018010240790042119247735303708763948459036916172114421151<103>
7×10140-9 = 6(9)1391<141> = 26003 × 49967046113187701<17> × 3072384756632832193294930209979933326902287322161<49> × 175353850256855514724412620180648233024414774451978568104314670271200777<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 6.12 hours on Core 2 Quad Q6600 / December 28, 2007 2007 年 12 月 28 日)
7×10141-9 = 6(9)1401<142> = 17 × 1138237 × 303685163 × 3342992330567<13> × 356334165905534944800189881105649323262735993212622399006901200741518827628836005277207887512297309538298790092799<114>
7×10142-9 = 6(9)1411<143> = 19 × 223 × 5431 × 18701 × 785700341891186083<18> × 2160116886846590585524781<25> × 15174573929900875998654000472424296906583891<44> × 6316030855475744522615578081679974514949366821<46> (Makoto Kamada / Msieve 1.32 for P44 x P46 / 1.8 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / December 25, 2007 2007 年 12 月 25 日)
7×10143-9 = 6(9)1421<144> = 97 × 317 × 571 × 11669963674208858774803484401760836297661604636382205067928038771673<68> × 3416342715437805134104596866257027736379971208960481691857755728114273<70> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.32 / December 27, 2007 2007 年 12 月 27 日)
7×10144-9 = 6(9)1431<145> = 1487 × 3084617 × 6753139867<10> × 2066420873807475272508154570496764559275489805725499291<55> × 109360704402145490620976185805347880615820804660378980898198273592328057<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 10.14 hours on Core 2 Quad Q6600 / December 28, 2007 2007 年 12 月 28 日)
7×10145-9 = 6(9)1441<146> = 94261 × 1021695068102849396044532089064863<34> × 726849841772289840962937682508573633040889067399121266108989206433699098743911136797514039693842951036128037<108> (Robert Backstrom / GMP-ECM 6.0.1 B1=672000, sigma=2836317521 for P34 / December 27, 2007 2007 年 12 月 27 日)
7×10146-9 = 6(9)1451<147> = 29 × 31 × 281 × 2770971304612875516093405484148064872396771422577082483898677454981612626128675990325351616465903198096738566774470645517558061745157727645189<142>
7×10147-9 = 6(9)1461<148> = 44253346650419<14> × 640263926981563<15> × 2384930862846177191492797<25> × 345533806013666402094028972113839143<36> × 299796493353162488095487968396822078060268288441471385866693<60> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs for P36 x P60 / 11.00 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / December 27, 2007 2007 年 12 月 27 日)
7×10148-9 = 6(9)1471<149> = 7354479179<10> × 18371504286793171<17> × 2814258676699625279171724231993155814622006129842908123<55> × 184093046599172102452699913165893938014185229449403497478166109476613<69> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 15.54 hours on Core 2 Quad Q6600 / December 29, 2007 2007 年 12 月 29 日)
7×10149-9 = 6(9)1481<150> = 1117 × 626678603401969561324977618621307072515666965085049239033124440465532676812891674127126230975828111011638316920322291853178155774395702775290957923<147>
7×10150-9 = 6(9)1491<151> = 647 × 1543 × 2005183 × 646461489522371<15> × 2174918059576277<16> × 2487071445148018907055123375719728218895276013300639734344051218625383384649231714454210002245367387382902311<109>
7×10151-9 = 6(9)1501<152> = 23 × 53 × 263 × 218342654485226000243296100712108971699672797936349997036778260557647139555267204621378241218726313720964325929437892431931677464230794424152440603<147>
7×10152-9 = 6(9)1511<153> = 642738965504016239<18> × 12499425996572633795685838286539<32> × 87131128901653143200613872829832683606052695848751370614553206443217691319643034696885938619060585421771<104> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=1541462935 for P32 / December 26, 2007 2007 年 12 月 26 日)
7×10153-9 = 6(9)1521<154> = 137945979054044323691<21> × 772167558584103691869638283989203<33> × 65716956589780721844302884925214520835046088468765165698360498247128407329527151604691722545317100967<101> (Robert Backstrom / GMP-ECM 6.1.3 B1=1170000, sigma=4085508329 for P33 / December 29, 2007 2007 年 12 月 29 日)
7×10154-9 = 6(9)1531<155> = 24187568437147<14> × 357505542381274647193<21> × 87307807817705591131142443529365687<35> × 92719261960991305708767306625668063796197431975684064005420378748486361040936361668683<86> (Robert Backstrom / GMP-ECM 6.0.1 B1=2160000, sigma=4055603832 for P35 / December 31, 2007 2007 年 12 月 31 日)
7×10155-9 = 6(9)1541<156> = 29173 × 913656634473352296477347<24> × 26262371220714013517427050722097014494839154559277063715376971066002533205465023622994672768241965919381715041311499951132881161<128>
7×10156-9 = 6(9)1551<157> = 2260571 × 21161214882893<14> × 625086523594801<15> × 15854608314307477257889614412447463<35> × 14765346313638338741527800132362791570551309344130945927519948485674768514606278097831519<89> (JMB / GGNFS-0.77.1-20060513-pentium4 / December 30, 2007 2007 年 12 月 30 日)
7×10157-9 = 6(9)1561<158> = 17 × 373 × 102922158772755053<18> × 107258421178208200504024871002063695036492420154577297736764790262498570755829236524648783705280347573978939616905224425867392921490839767<138>
7×10158-9 = 6(9)1571<159> = 665507 × 4787893769<10> × 4551229532797823713440523924237357<34> × 48269429654485286004700435874371392955763120608188765913835335149678303496468383067863156974558912669025897961<110> (Robert Backstrom / GMP-ECM 6.1.3 B1=460000, sigma=4264591698 for P34 / December 28, 2007 2007 年 12 月 28 日)
7×10159-9 = 6(9)1581<160> = 283 × 44059 × 7694021 × 1415428272491<13> × 51550838674885184106526083938030244199127645047555938962734860470005338508317664645956597445523156116174008521020464366063573648048073<134>
7×10160-9 = 6(9)1591<161> = 19 × 307 × 25703 × 1959110710717852532165249<25> × 238321524535432050122944439811318913537818088929116644173613986973299481543129337516595261289373180324672198930123072423800404841<129>
7×10161-9 = 6(9)1601<162> = 31 × 238529 × 16165785424707406853881795571381<32> × 1154734515303355813588848626575829<34> × 5071263789375496111006719685471610072718773087775179235920085143775708329815366365895324241<91> (Makoto Kamada / GMP-ECM 6.1.3 B1=11000, sigma=2881549954 for P32 / December 16, 2007 2007 年 12 月 16 日) (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=223357812 for P34 / January 16, 2008 2008 年 1 月 16 日)
7×10162-9 = 6(9)1611<163> = 859 × 118247 × 2662639391<10> × 68628329971<11> × 436977788659416077831566216483<30> × 863057237779628902143622988929371538585971609219344275040457451654589439284920068001169478963439353329509<105> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=2029589823 for P30 / December 27, 2007 2007 年 12 月 27 日)
7×10163-9 = 6(9)1621<164> = 83 × 2447 × 590732534224585594774305619<27> × 129176060038429313134294565540217914223913<42> × 120256406964389982245302914445931857545867029<45> × 37558205196955967532214995487858032886370144357<47> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=3000000, sigma=1287683819 for P42, Msieve v. 1.32 for P45 x P47 / 1.65 hours on Core 2 Quad Q6600 / March 11, 2008 2008 年 3 月 11 日)
7×10164-9 = 6(9)1631<165> = 53 × 226030643 × 402888866351<12> × 367237046175187<15> × 394932703653576027487914095246244689798585859601052218782363423434472225311946961020913370378737680933273414547659452762250757517<129>
7×10165-9 = 6(9)1641<166> = 449 × 96293 × 193732283 × 119720935477183205712026361015748167111027951799849560997421<60> × 6980473515066820668028752248342210383473908035017528053560574089914810233581451339796380341<91> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.32 / December 31, 2007 2007 年 12 月 31 日)
7×10166-9 = 6(9)1651<167> = 971 × 420691 × 5160037 × 65820677509334269<17> × 372447795625959253<18> × 904713053389830803<18> × 22012899639353369009<20> × 68021609961278375487961175623259531769426640092790359816708588953678310022702217<80>
7×10167-9 = 6(9)1661<168> = 1315096889<10> × 2924704534089087990741564307<28> × 32171713835165356860545627602731658117138163<44> × 5656972847387801199256068528668241589373474506207018297434013731023661520263653791197559<88> (Markus Tervooren / GGNFS-0.77.1-20060722-nocona snfs / 76.94 hours on Q6700, Linux2.6.22 / November 22, 2008 2008 年 11 月 22 日)
7×10168-9 = 6(9)1671<169> = 9843923 × 117894475991<12> × 1261779092388631<16> × 27635543446430167<17> × 1537937361615581169410967292004327295366166873569433<52> × 112472511207691888590129843674497489028548891319841138462050561658307<69> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P52 x P69 / 45.59 hours on Core 2 Quad Q6600 / January 4, 2008 2008 年 1 月 4 日)
7×10169-9 = 6(9)1681<170> = 208699 × 241417849 × 260261239348850539688922265966919165310599<42> × 5338248691337501107137922770641624082752782783076792345043666099791736776212975427477023032244417290856029907636859<115> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.36 / 76.95 hours on Cygwin on AMD 64 3400+ / July 22, 2008 2008 年 7 月 22 日)
7×10170-9 = 6(9)1691<171> = 1888933069<10> × 960609759386506771<18> × 9799579277074828605525641<25> × 175154766503563259185085659<27> × 224752786451467689464784674977968389374665367051015041143571563533474550986697022411575290811<93>
7×10171-9 = 6(9)1701<172> = 1951 × 32173 × 42839 × 191392620057115592363<21> × 121675574481606991533348359183<30> × 37422933325867189106477419970456951426047763<44> × 2987056712446451498387325795625445621950302093418101807281997373189<67> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=3791932801 for P30, pol51+Msieve 1.36 gnfs for P44 x P67 / 12.00 hours on Opteron-2.6GHz; Linux x86_64 / August 8, 2008 2008 年 8 月 8 日)
7×10172-9 = 6(9)1711<173> = 10598698069<11> × 223245829680143568677436140783698003000608237638667397220569703726322445019<75> × 29584359061808698085356769885290337868193171920464425723391688951441403237695049377138881<89> (Serge Batalov / Msieve-1.38 snfs / 34.00 hours on Opteron-2.6GHz; Linux x86_64 / October 15, 2008 2008 年 10 月 15 日)
7×10173-9 = 6(9)1721<174> = 17 × 23 × 16421 × 951988489 × 967778104050840161<18> × 5822198849636541604216008139984546047314947195596463077900521<61> × 20324841068780494305293498995060419802226786782151713853158153045709315773873709<80> (Wataru Sakai / 117.44 hours / October 27, 2009 2009 年 10 月 27 日)
7×10174-9 = 6(9)1731<175> = 29 × 281 × 1823796208039336577<19> × 470996211442646025750939478655942186726221011346236552366354576411053857775974580419407982600498562396402232108375191437035834695707512298293812377552667<153>
7×10175-9 = 6(9)1741<176> = 1301 × 700849 × 2998263129687771495713319147093796698599357538666071288999<58> × 25605103830539641054955333281714615256570243024259263526043334000070733816061239428491153704128112278858660541<110> (matsui / GGNFS-0.77.1-20060513-pentium-m snfs / 120.77 hours / July 6, 2008 2008 年 7 月 6 日)
7×10176-9 = 6(9)1751<177> = 31 × 284227 × 1471607402359269526317161020368119<34> × 53985739075515634697915501772688348506596820268762244897523775610785131164014476184599853349601190834688415144297768454969091079778009397<137> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=1000000, sigma=3920796782 for P34 / November 4, 2008 2008 年 11 月 4 日)
7×10177-9 = 6(9)1761<178> = 53 × 10806931 × 1532362774773961413316989871<28> × 16355013078228492064453493967087754617300913502022018300051109<62> × 487648960536517434429738499186995203200651167075800879123844409853127228376999883<81> (Warut Roonguthai / Msieve 1.48 snfs / April 2, 2012 2012 年 4 月 2 日)
7×10178-9 = 6(9)1771<179> = 19 × 2539 × 12897341641762311482225721924377786620072960817038184469508152023<65> × 112507515436489482196909605851330785043044214218396095102143177575566128872215934971677861051720757848691700337<111> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.36 snfs / 57.99 hours, 5.9 hours / September 22, 2008 2008 年 9 月 22 日)
7×10179-9 = 6(9)1781<180> = 26849 × 2710397 × 1257951721263604352139589829106892400427551425645294710182642789568763<70> × 7646682242190591161556198373637317987171335314757235302755083444223092418917335695838897522440941369<100> (Robert Backstrom / Msieve 1.44 snfs / February 8, 2012 2012 年 2 月 8 日)
7×10180-9 = 6(9)1791<181> = 9521 × 198160716463<12> × 4548271447823<13> × 19621014190235027443<20> × 1660094651293268747131111<25> × 25043627343713814794844118895772844081224864870667546823460200467693966774671428762293723587780092269937579323<110>
7×10181-9 = 6(9)1801<182> = 61 × 24261697 × 231437543 × 609870487 × 16310561610643<14> × 16717951075581074590093<23> × 156932322691243375623534129601937<33> × 7830892015959968705004048065722168586730354618782817830772496580628340016890487858634181<88> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=267773023 for P33 / December 23, 2007 2007 年 12 月 23 日)
7×10182-9 = 6(9)1811<183> = 47 × 2909 × 8412983 × 197529555280333365899<21> × 551024823684035448740408536106657207<36> × 120505114541548280042487841757872247892709036654778083<54> × 46397835349507535301741903585430930023363737967949935765765821<62> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=3000000, sigma=820661537 for P36 / December 1, 2008 2008 年 12 月 1 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P54 x P62 / 22.15 hours on Core 2 Quad Q6700 / December 2, 2008 2008 年 12 月 2 日)
7×10183-9 = 6(9)1821<184> = 1657888650017788234967<22> × 2177844410694236710673789480452302228723381261719<49> × 1938723309657920789206475056921505553905736789461719815906725083680072375291377040179661939044445917137710636720967<115> (Pipao / GMP-ECM B1=110000000, sigma=715931293 for P49 / November 5, 2010 2010 年 11 月 5 日)
7×10184-9 = 6(9)1831<185> = 109 × 1140031069<10> × 563319590426342425498333003056656651923856994752022174369177797502301824459384596655531542834894795020472175080872146706718675489814594862291906939876211680925012893484717071<174>
7×10185-9 = 6(9)1841<186> = 7681 × 175417656210821<15> × 7962085544181486905582787097431331669084443869126091386612582637426287<70> × 65249942241341562867665751014964663626829018890285536781847520007074741504860160218117892922974693<98> (Dmitry Domanov / Msieve 1.40 snfs / May 13, 2012 2012 年 5 月 13 日)
7×10186-9 = 6(9)1851<187> = 1882873212211<13> × 5833979226117373<16> × 47533639674475314086029<23> × 22494947546032604356359491<26> × 2515472027805282686708792675704535850836383<43> × 236922626264959098658721156310440198919184175106191358028227502394681<69> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P43 x P69 / 19.07 hours on Cygwin on AMD 64 3200+ / December 28, 2007 2007 年 12 月 28 日)
7×10187-9 = 6(9)1861<188> = 461 × 923371 × 473554153625182489683337<24> × 4690476648547345168326374837406127<34> × 132247220045280786396912011749138627359993288829687<51> × 559819090026885770857005522645932550743849730325918357433966783937734297<72> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=1000000, sigma=603318502 for P34 / November 4, 2008 2008 年 11 月 4 日) (Dmitry Domanov / Sieving done by gnfs-lasieve4I12e, postprocessing and linear algebra by msieve. for P51 x P72 / 1.24 hours / May 12, 2009 2009 年 5 月 12 日)
7×10188-9 = 6(9)1871<189> = 233 × 859 × 977 × 1979 × 356749 × 45284116079<11> × 279525333020076779648841331<27> × 5935197639708550652804657116360631605744747044741335669<55> × 67490645040119700812655693745827992826945287817226716777168488006215732427500739<80> (Robert Backstrom / Msieve 1.44 gnfs for P55 x P80 / May 14, 2012 2012 年 5 月 14 日)
7×10189-9 = 6(9)1881<190> = 17 × 52219901 × 44999932897<11> × 3678442597154743878960862634350531636580393790963394244328757558451823823335050187799<85> × 47636212633950322265615824829692335586306517833298148385227391512296278609903311523141<86> (He Jiahao / Msieve 1.53 snfs for P85 x P86 / November 7, 2017 2017 年 11 月 7 日)
7×10190-9 = 6(9)1891<191> = 53 × 569 × 104107 × 1483907 × 345080665654807232107<21> × 507646619486579613433558690339<30> × 85771136186162851881469759878437505454102969685026092495262931468124073457171969193192101906318528829048354310172383828309619<125> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=154776249 for P30 / December 24, 2007 2007 年 12 月 24 日)
7×10191-9 = 6(9)1901<192> = 31 × 28283 × 242813 × 3288053973442086278914586610528205166004572595510931246385392329675392901903833923762196663895214651308538958580233733841833637907417703130500069018157625244006374397315619087839559<181>
7×10192-9 = 6(9)1911<193> = 149 × 167 × 15872476757358930071814952703<29> × 164558127467128678980877276515560772170879<42> × 107703858906058344934309942486907780929278544045522190161642686884258571375885827755865003911230798792755471060365538221<120> (Grubix / GMP-ECM B1=110000000, sigma=1218408363 for P42 / November 12, 2010 2010 年 11 月 12 日)
7×10193-9 = 6(9)1921<194> = 148773167 × 490799597 × 624265043 × 279332624936131460064588188231867<33> × 37884492928419836911819165511031793770820752008293983909175079<62> × 145116594055854621090516235617703602703646727344434298837285228367717596891<75> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3695353944 for P33 / December 24, 2007 2007 年 12 月 24 日) (Robert Backstrom / Msieve 1.44 gnfs for P62 x P75 / May 5, 2012 2012 年 5 月 5 日)
7×10194-9 = 6(9)1931<195> = 59 × 503 × 19009 × 4546319117<10> × 3201890183553739545421<22> × 3663534177803835316717<22> × 5453825411908180414535101<25> × 52063286361231377503035962252713421659616793211<47> × 81944416344344076297954674797070896167668217005498046483209993<62> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P47 x P62, Msieve 1.32 / December 27, 2007 2007 年 12 月 27 日)
7×10195-9 = 6(9)1941<196> = 23 × 11873647 × 446469337 × 2166345721<10> × [26501268828979351686493807189887728475618581590367686628199290125264705758664427403096679774204229195517235053113223283322785171453699281428219526186683109221083305442943<170>] Free to factor
7×10196-9 = 6(9)1951<197> = 19 × 1709 × 2131 × 1011623540023100568054076076200167406353755994176574640092164107131453151981219180075941423008345561814598857810545195575083486761699256432130082763378609315627859597809407263610206073351291<190>
7×10197-9 = 6(9)1961<198> = 449 × 3992849491<10> × 761458444133<12> × 2906695017509<13> × 23613190777085118197489<23> × 7470822358757516694376023502485149120828010135091508808544969902792011604366736031668150066428550848493390279780581479167855086175934922853<139>
7×10198-9 = 6(9)1971<199> = 113 × 557 × 14669 × 1011899197<10> × 264988857469403991211956741757711<33> × 28274766614610714157255420998775798591008627434112116606543963199796112209476723290238538742147137438714006318672046665431077283855690553184035469237<149> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3404709547 for P33 / October 21, 2008 2008 年 10 月 21 日)
7×10199-9 = 6(9)1981<200> = 7085518471<10> × 14063637477180853<17> × 702471554040682805242329783699393716629784654585987492565860173442612180815087577069399847948920121838876411940815482915009967832162942015243043315915479061483642925345160557<174>
7×10200-9 = 6(9)1991<201> = 15764641 × 11284635217137977617526487653933<32> × 3934834132347528894029161821328170864341780603433105197044385991837432909415350859571119308115656096581344079723625343143220426630178141030835445756037523722590547<163> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=13078247 for P32 / September 10, 2008 2008 年 9 月 10 日)
7×10201-9 = 6(9)2001<202> = 293467 × 73169704094815449574606193<26> × [325992395164676216164840041590839865892320717591158424645647735476658609574183523089452986097973476641718296930931138612258288161671209027994385437961634744266698409961061<171>] Free to factor
7×10202-9 = 6(9)2011<203> = 29 × 227 × 281 × 23567 × [1605696878895639762815053491855164664924763460963756290311473037214360471008590480343620561612659663189135999173199701349069639378513664145112547263868557923617695012945300391300592221763817351<193>] Free to factor
7×10203-9 = 6(9)2021<204> = 53 × 257 × 69379 × 3176479 × 371868033113<12> × 590224501463<12> × 28662426364783<14> × 37067729917307556653795924113534948731168731207077501146782296613627613309720875391160224285116538543690096128126194982143807365420156084339372206061703<152>
7×10204-9 = 6(9)2031<205> = 83 × 70249 × 48304432805902352254277294970553080841<38> × [24853800861479463800671588109305432383960604575404456721434845284823347979705323170549903368554863325470657170318538591079273583716935548560087873886550822543453<161>] (Wataru Sakai / GMP-ECM 6.4.2 B1=3000000, sigma=511449929 for P38 / April 11, 2012 2012 年 4 月 11 日) Free to factor
7×10205-9 = 6(9)2041<206> = 17 × 6043511381<10> × 57052536779333<14> × 361049740018879647609362842810658413<36> × 1952513626146037296567604737036445649<37> × 3603955538038514578257936804040418599602942413<46> × 4700502416164435260236574042336835880822079821813200907141443271<64> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1557939850 for P36 / April 9, 2012 2012 年 4 月 9 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=460151510 for P37 / April 13, 2012 2012 年 4 月 13 日) (Warut Roonguthai / Msieve 1.48 gnfs for P46 x P64 / April 15, 2012 2012 年 4 月 15 日)
7×10206-9 = 6(9)2051<207> = 31 × 2707 × 592276642926138123615982107802672014513103526993394041821956036274258673568861513233040422084827<96> × 14083917885491531212085391871325978765324985847874073744051414575336044347969150442226196207274686199116649<107> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs / August 12, 2012 2012 年 8 月 12 日)
7×10207-9 = 6(9)2061<208> = 13389664319<11> × 148607967719515819<18> × 14697881284544770392351911<26> × 239348946577865672106460528268259823563753014624164580095971068321309672397759441228797005529418891894786106831537119234265642586370798544548074425737947821<156>
7×10208-9 = 6(9)2071<209> = 6689 × 126461347 × [82752103240024515229109500758315343838310696745425049581962643318157307616099212995418388807541924702766586343539059593851800149308793064247574640082968801302226805299982787751791956739802700769277<197>] Free to factor
7×10209-9 = 6(9)2081<210> = 1882211 × 2579582680332429719119079<25> × 144171786641849605369900153710785159143261428333176734356594463777308727137111742179074459412837439269089180052509682536262334971706084090032448894878509533508878338351388696410139<180>
7×10210-9 = 6(9)2091<211> = 401 × 51047 × 2030719 × 1426692073<10> × 2962605847<10> × 1032108713813<13> × 20012543165399633<17> × 1928864681493275553118835838240703040828850871683728684368053078862504801618786245154892430300812578662322518520540491980561386467629718904213210450813<151>
7×10211-9 = 6(9)2101<212> = 139654125536833359470539767777495855976117<42> × 501238325261917941587887013470493749402120334825925708560215940938915470428557696100312962051174450354977953824590071285788378534730113432445251068074902706576853429932923<171> (Serge Batalov / GMP-ECM B1=2000000, sigma=98502713 for P42 / April 10, 2012 2012 年 4 月 10 日)
7×10212-9 = 6(9)2111<213> = 617 × 35839 × 263443 × 613337 × 6161213 × 2264791569059381983<19> × 721206381419646846727738708427<30> × 19467811893493453065741202158422142810686981027755018008026601661568202259398357343165250464113885685870830273948484806548768782646500893619<140> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1860997204 for P30 / April 9, 2012 2012 年 4 月 9 日)
7×10213-9 = 6(9)2121<214> = 4787 × 771498992168517952697042399993102610596570961768860968409655526142194457020881629048494769<90> × 1895392900030684783665579794111218864118106543746116272832983123968073976237137443601385254204358838951772548163821579197<121> (Bob Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs for P90 x P121 / September 12, 2017 2017 年 9 月 12 日)
7×10214-9 = 6(9)2131<215> = 19 × 131 × 859 × 24379 × 1481231 × 7702099 × 238344935240719<15> × 3680252687114921314782673<25> × 5522060789491596727197741397<28> × 2237821493449558590631168069020599<34> × 10859804642487211216068243286558156591030466198493407588854477856704893418122130074069406031<92> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=2798277235 for P34 / April 6, 2012 2012 年 4 月 6 日)
7×10215-9 = 6(9)2141<216> = 52453 × 967628131271525206507<21> × 8393934158702252681141<22> × [1643060910173575198967355226948363052328384018001232208370662626363212460104939785676288781771247874911051458857039419183025447627487381198824250466829140912498243279581<169>] Free to factor
7×10216-9 = 6(9)2151<217> = 53 × 162257 × 919696849 × 33891323559913<14> × 565369280318760291268891<24> × 227954867848321575193998924030404849<36> × 202630316285360715213030585524118580086527966342358763050630639817465527803518361244966841282127887378409254419673004466926268137<129> (Serge Batalov / GMP-ECM B1=2000000, sigma=3776467598 for P36 / April 10, 2012 2012 年 4 月 10 日)
7×10217-9 = 6(9)2161<218> = 23 × 1268326140149391599834684033<28> × [2399602250972360151901966221000602879953610275871121931216634762972141971180083052646222566229727177916461629412998462694714823522611280154164875199066136158285512369413384151654094901977249<190>] Free to factor
7×10218-9 = 6(9)2171<219> = 197 × 3553299492385786802030456852791878172588832487309644670050761421319796954314720812182741116751269035532994923857868020304568527918781725888324873096446700507614213197969543147208121827411167512690355329949238578680203<217>
7×10219-9 = 6(9)2181<220> = 50123 × 34200911 × 70826219636965808987<20> × 6145583130131402681630181873643<31> × [9381367503947885524303351816083340087912613218329956970415790184787073158797506765178860279704169936331233073640594999074958464310781485005341955432900739667<157>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=903785568 for P31 / April 9, 2012 2012 年 4 月 9 日) Free to factor
7×10220-9 = 6(9)2191<221> = 72894507887<11> × [960291824845199259833230733392906264946577428562426807621147936977497905308000203524304231510093711869769248477319101707045728230941174472243542893019050857866449238383072205347584748144223382923405454226329593<210>] Free to factor
7×10221-9 = 6(9)2201<222> = 172 × 31 × 1261157 × 2664811 × 165631762529<12> × 140365156086191133128234661509456795707207739627393557900831458635400464334238968853368797861276845879679221950093877564237345109444718022326389358646208043957105801191783025622509866715518556703<195>
7×10222-9 = 6(9)2211<223> = 317 × 587 × 33851 × 140197 × 16559869 × 185222241247643<15> × 83705382131559374857626736396943<32> × 298929440520726130389031357251224413<36> × 103280504023187053380573323540918475719481910744761144663905763763181024989548445190214312039300911824147855181879489819<120> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=889358622 for P32 / April 7, 2012 2012 年 4 月 7 日) (Wataru Sakai / GMP-ECM 6.4.2 B1=3000000, sigma=559976036 for P36 / April 11, 2012 2012 年 4 月 11 日)
7×10223-9 = 6(9)2221<224> = 2237 × 495067 × 37525582546445337067<20> × 1684382166765208341673782353942114917020158635761131506901081337138397957069818974311700202521607942437963044297396713109612393515447200230850072409889266329855940777210464830439714934577227310187<196>
7×10224-9 = 6(9)2231<225> = 11311129 × 996712537 × 1122591571<10> × 55309583310904078031785094899582770611643614220756657498153328101881343896504635780141600885493042576398913746101945282339175157196033687794348313735726308435568380084450570685182152666111659914666077<200>
7×10225-9 = 6(9)2241<226> = 24550433 × 2516993913527<13> × 113280907209691477290811659474340203211209126673962134013488217284485382162943372646038658622357264234512217722610413735688833375109929901286692458638158943657272275613987316276294976651113704521824256240801<207>
7×10226-9 = 6(9)2251<227> = 3275213 × 8113862173<10> × 6832459686272374330075744543<28> × [385526101567642625713037847807126717319064626439197589530735410847803818144036130095357037023765080533377288646658398760080031694595919583528840259664783582332038100121755929196153713<183>] Free to factor
7×10227-9 = 6(9)2261<228> = 1534411 × 298494443006004641806601127159132965602758203214669455643936366229<66> × 1528340375438381774010373496637848407832095373163139240021668916473689296847026211300363175784588797942213622286413593981699236871266668668419418446668736689<157> (Bob Backstrom / Msieve 1.53 snfs for P66 x P157 / August 12, 2018 2018 年 8 月 12 日)
7×10228-9 = 6(9)2271<229> = 47 × 1457879 × 99688506457<11> × [1024787011699124635063165772477709592678237006039551169028724966515948411902637917424609344072873081879858583416334837648079386986710860891718106129117103411978998086851638731417183046395044555209407067386850951<211>] Free to factor
7×10229-9 = 6(9)2281<230> = 53 × 449 × 8210561 × 749471422122959786719933777<27> × [478022038801598601161324458326081507170824682651708210320295238096362921970260658304771744869778644063101950567292436195511337135226610152894667424238682275704789748815090206737862062629489099<192>] Free to factor
7×10230-9 = 6(9)2291<231> = 29 × 281 × 77731 × 7234771 × 133491466081<12> × 11647462275997477143229<23> × [98240341381592586865180163947619175992820360778528365317352233019478192807308064688581438408233226173794890027813733562265623485113445007407249726632514265798861935454343354776820591<182>] Free to factor
7×10231-9 = 6(9)2301<232> = 5953 × 1175877708718293297497060305728204266756257349235679489333109356626910801276667226608432722996808331933478918192507979170166302704518730052074584243238703174869813539391903242062825466151520241894842936334621199395262892659163447<229>
7×10232-9 = 6(9)2311<233> = 19 × 691 × 1987 × 625831 × 1393338617349053<16> × 62157637104520553076881821699<29> × 120564030757881086955962479211<30> × [410622292271483379810643091100667793132394370325483570800212471721109240910412439089658383759749875109159298906176909449765665669086581838774195871<147>] (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=3226678475 for P30 / April 8, 2012 2012 年 4 月 8 日) Free to factor
7×10233-9 = 6(9)2321<234> = 10607 × 35217000684324359<17> × [1873928884375628629293843065310239401172555486837756916428509125256046746109657548346913918074820821134172510267188859225005229808127904928470882993587833640311513890518859811796016507162989380631986609905785822207<214>] Free to factor
7×10234-9 = 6(9)2331<235> = 877 × 603037817 × [13235912842124442981230650260740579799508716727006949290945932800927285750827930557232183327015205665426887670291887096985346828394883711485735076895899811740859764669255629719871234748123918574072655207782925695558311879499<224>] Free to factor
7×10235-9 = 6(9)2341<236> = 49020443 × 873829549 × 4694040077729421599<19> × 127067835279917045179<21> × 1827577457767759582475882242136071<34> × 316188143641271607137124213659163904245529<42> × 4741221921515178223597897064678032431599875207961169208833078366212395819341801159416213090256929131726267<106> (Serge Batalov / GMP-ECM B1=2000000, sigma=1111106710 for P42 / April 10, 2012 2012 年 4 月 10 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3009347335 for P34 / April 12, 2012 2012 年 4 月 12 日)
7×10236-9 = 6(9)2351<237> = 31 × 6002265527<10> × [3762020367095686231983845604090447071146589467197465614768082315236961573746549224456076003680042654216007425331811931072302367532580223117584374952348318635981145311064584157856154533405593086205794681625601852948590016832543<226>] Free to factor
7×10237-9 = 6(9)2361<238> = 17 × 3461 × 6359 × 342941177 × [54555565306518059364821657044923099481078186769722182697080744535993993771452719980551306100788235215096688150190449192184585417153271853246499113545802021729891857549555062840162534267098706093176677836995665682849258501<221>] Free to factor
7×10238-9 = 6(9)2371<239> = 199 × 3269143 × 11891187412751194272046478217589522793<38> × [9048692327163425362005443839788677649612422026947506678164073426406397578545081309077303518330959578510625574524433636174789600429693817014236282588606445648489496653502712630836379093320790591<193>] (Wataru Sakai / GMP-ECM 6.4.2 B1=3000000, sigma=1467907849 for P38 / April 12, 2012 2012 年 4 月 12 日) Free to factor
7×10239-9 = 6(9)2381<240> = 23 × 97 × 523 × 13163 × [45576597454634578291426661929493291651557370803313246407501095271234580491122539594989539858033374550683333737794166187829872746638972881492122801431304837659917005957517394995811315040097152002292510144223712029591287723319421289<230>] Free to factor
7×10240-9 = 6(9)2391<241> = 859 × 1381 × 371774883805499011<18> × 2942827038281946740644609<25> × 5393446975479018897383674988229035536937168974863782678835049681022465256608725704610523056560385930743968751584538209675380780971271600956559579938740363797688138628387000831168582206592120571<193>
7×10241-9 = 6(9)2401<242> = 61 × 3889 × 963812717387014254187583<24> × 306152358458823736028299289885858309911497362606473604797309883109316802799245307307211663831005058085203418334441087389291350540440717353951228835854875530235402831361247034684366034036199957052380627256761763213<213>
7×10242-9 = 6(9)2411<243> = 53 × 17767102531<11> × 21210880631<11> × 59432896690247<14> × 589684841846356182898409269160342192756508199940855952348073092535491954621849810601767276441574255196286754977473341779431053176370927853160489448720214883878257845627406331642953372824951003370580733182441<207>
7×10243-9 = 6(9)2421<244> = 349 × 439 × 1129 × 15711760696469393<17> × [2575664517059589864575416765804690647334109223273960277626292029323352266981029361524908151899462975624003981613541982508773156341504795180638509120356897408026254077534903430214517222659734227320894818869773842308857373<220>] Free to factor
7×10244-9 = 6(9)2431<245> = 230374225591619453<18> × 219940864001388301081<21> × [1381523335048062046516787950379089724819201574035164247148832929784051696134453433037710692492384762674399091327101857614100916957798430968633106867032814652324057183446675761126022091379549689267556766260987<208>] Free to factor
7×10245-9 = 6(9)2441<246> = 83 × 941 × 14242117 × 407014879 × [1546128156779539563876591245771215747407539600555924059841448089358537751216948580192286899422486246108767817304352323790543719286587307935052085757580157773146525248142487216796408390939536031625696777295716023313660098366579<226>] Free to factor
7×10246-9 = 6(9)2451<247> = [6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<247>] Free to factor
7×10247-9 = 6(9)2461<248> = 83104605854927725917557188201<29> × 217068505770770066227857390473659<33> × [3880396723527917586771515933380418318467025074962412952755736361786009813399332218219544042145947073252637449138610244046133058796110369068051827052138965659728912611200810842443432805549<187>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3193638921 for P29 / April 9, 2012 2012 年 4 月 9 日) (Serge Batalov / GMP-ECM B1=2000000, sigma=1747604101 for P33 / April 10, 2012 2012 年 4 月 10 日) Free to factor
7×10248-9 = 6(9)2471<249> = 10631 × 1312170719<10> × 625519224257<12> × 88704096371036838820034799341<29> × [904376444152668275655197037801911554785095354035952153464186605822696580197534003809616295703150797439832320273263829518351114842219610005633827911879149040959266389388590881613710367004171046187<195>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=340158212 for P29 / April 9, 2012 2012 年 4 月 9 日) Free to factor
7×10249-9 = 6(9)2481<250> = 8491741 × 125218811 × 457802137489<12> × 421531543259259599<18> × 34113307588147328504841295635519566575956543356316664954420729459958332597861246505669726432183850664029520260157081245136737780484969330283469116944457955899266506704494972920069201275519511846404276029831<206>
7×10250-9 = 6(9)2491<251> = 19 × 332583180443<12> × 37889575864681<14> × 292364348761888995784382462090016211359660070395577265848195258136752932697350415961106454833802329247839298361839480994491285398594658902159897210160749553145328689857568984054214734888715411167196337002939943425462274274783<225>
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