Table of contents 目次

  1. About 199...991 199...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 199...991 199...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 199...991 199...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 199...991 199...991 について

1.1. Classification 分類

Plateau-and-depression of the form ABB...BBA ABB...BBA の形のプラトウアンドデプレッション (Plateau-and-depression)

1.2. Sequence 数列

19w1 = { 11, 191, 1991, 19991, 199991, 1999991, 19999991, 199999991, 1999999991, 19999999991, … }

1.3. General term 一般項

2×10n-9 (1≤n)

2. Prime numbers of the form 199...991 199...991 の形の素数

2.1. Last updated 最終更新日

December 12, 2014 2014 年 12 月 12 日

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

  1. 2×101-9 = 11 is prime. は素数です。
  2. 2×102-9 = 191 is prime. は素数です。 (Jean Claude Rosa / October 14, 2002 2002 年 10 月 14 日)
  3. 2×104-9 = 19991 is prime. は素数です。 (Jean Claude Rosa / October 14, 2002 2002 年 10 月 14 日)
  4. 2×108-9 = 199999991 is prime. は素数です。 (Jean Claude Rosa / October 14, 2002 2002 年 10 月 14 日)
  5. 2×1040-9 = 1(9)391<41> is prime. は素数です。 (Jean Claude Rosa / October 14, 2002 2002 年 10 月 14 日)
  6. 2×1086-9 = 1(9)851<87> is prime. は素数です。 (Jean Claude Rosa / October 14, 2002 2002 年 10 月 14 日)
  7. 2×10200-9 = 1(9)1991<201> is prime. は素数です。 (Jean Claude Rosa / October 14, 2002 2002 年 10 月 14 日)
  8. 2×10730-9 = 1(9)7291<731> is prime. は素数です。 (Patrick De Geest / November 24, 2002 2002 年 11 月 24 日)
  9. 2×101460-9 = 1(9)14591<1461> is prime. は素数です。 (Patrick De Geest / July 4, 2003 2003 年 7 月 4 日)
  10. 2×1023672-9 = 1(9)236711<23673> is PRP. はおそらく素数です。 (Patrick De Geest / November 25, 2004 2004 年 11 月 25 日)
  11. 2×1028630-9 = 1(9)286291<28631> is PRP. はおそらく素数です。 (Patrick De Geest / November 26, 2004 2004 年 11 月 26 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≤120000 / Completed 終了 / Ray Chandler / April 1, 2011 2011 年 4 月 1 日
  3. n≤150000 / Completed 終了 / Ray Chandler / April 9, 2011 2011 年 4 月 9 日
  4. n≤163000 / Completed 終了 / Ray Chandler / April 15, 2011 2011 年 4 月 15 日
  5. n≤200000 / Completed 終了 / Ray Chandler / May 4, 2011 2011 年 5 月 4 日

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

  1. 2×102k+1-9 = 11×(2×101-911+18×10×102-19×11×k-1Σm=0102m)
  2. 2×106k-9 = 7×(2×100-97+18×106-19×7×k-1Σm=0106m)
  3. 2×1015k+7-9 = 31×(2×107-931+18×107×1015-19×31×k-1Σm=01015m)
  4. 2×1016k+12-9 = 17×(2×1012-917+18×1012×1016-19×17×k-1Σm=01016m)
  5. 2×1018k+11-9 = 19×(2×1011-919+18×1011×1018-19×19×k-1Σm=01018m)
  6. 2×1022k+10-9 = 23×(2×1010-923+18×1010×1022-19×23×k-1Σm=01022m)
  7. 2×1028k+15-9 = 29×(2×1015-929+18×1015×1028-19×29×k-1Σm=01028m)
  8. 2×1032k+30-9 = 449×(2×1030-9449+18×1030×1032-19×449×k-1Σm=01032m)
  9. 2×1035k+24-9 = 71×(2×1024-971+18×1024×1035-19×71×k-1Σm=01035m)
  10. 2×1044k+7-9 = 89×(2×107-989+18×107×1044-19×89×k-1Σm=01044m)

Read more続きを読むHide more続きを隠す

2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 10.65%. 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 10.65% です。

3. Factor table of 199...991 199...991 の素因数分解表

3.1. Last updated 最終更新日

April 10, 2018 2018 年 4 月 10 日

3.2. Range of factorization 分解範囲

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

n=193, 198, 199, 201, 202, 203, 208, 210, 212, 214, 215, 221, 223, 226, 229, 231, 232, 233, 234, 236, 238, 239, 242, 245, 246, 248, 250, 251, 252, 254, 256, 258, 259, 260, 261, 262, 264, 266, 267, 268, 269, 272, 273, 275, 279, 281, 285, 287, 288, 289, 291, 292, 294, 295, 298, 299 (56/300)

3.4. Factor table 素因数分解表

2×101-9 = 11 = definitely prime number 素数
2×102-9 = 191 = definitely prime number 素数
2×103-9 = 1991 = 11 × 181
2×104-9 = 19991 = definitely prime number 素数
2×105-9 = 199991 = 11 × 18181
2×106-9 = 1999991 = 7 × 47 × 6079
2×107-9 = 19999991 = 11 × 31 × 89 × 659
2×108-9 = 199999991 = definitely prime number 素数
2×109-9 = 1999999991<10> = 11 × 349 × 520969
2×1010-9 = 19999999991<11> = 23 × 3881 × 224057
2×1011-9 = 199999999991<12> = 11 × 19 × 1069 × 895171
2×1012-9 = 1999999999991<13> = 7 × 17 × 16806722689<11>
2×1013-9 = 19999999999991<14> = 11 × 246209 × 7384709
2×1014-9 = 199999999999991<15> = 97 × 2061855670103<13>
2×1015-9 = 1999999999999991<16> = 11 × 29 × 5879 × 26801 × 39791
2×1016-9 = 19999999999999991<17> = 73281367 × 272920673
2×1017-9 = 199999999999999991<18> = 112 × 6841 × 241615635431<12>
2×1018-9 = 1999999999999999991<19> = 7 × 593 × 481811611659841<15>
2×1019-9 = 19999999999999999991<20> = 11 × 540905219 × 3361368599<10>
2×1020-9 = 199999999999999999991<21> = 282893137 × 706980742343<12>
2×1021-9 = 1999999999999999999991<22> = 11 × 188791 × 1596319 × 603304189
2×1022-9 = 19999999999999999999991<23> = 31 × 645161290322580645161<21>
2×1023-9 = 199999999999999999999991<24> = 11 × 10559 × 44129 × 122039 × 319736189
2×1024-9 = 1999999999999999999999991<25> = 72 × 71 × 1118063929<10> × 514172601001<12>
2×1025-9 = 19999999999999999999999991<26> = 11 × 10567541 × 14556011 × 11820095731<11>
2×1026-9 = 199999999999999999999999991<27> = 249051812839<12> × 803045750681969<15>
2×1027-9 = 1999999999999999999999999991<28> = 11 × 311 × 2742739 × 8543341 × 24949663829<11>
2×1028-9 = 19999999999999999999999999991<29> = 17 × 170321092673<12> × 6907368722052551<16>
2×1029-9 = 199999999999999999999999999991<30> = 11 × 19 × 956937799043062200956937799<27>
2×1030-9 = 1999999999999999999999999999991<31> = 7 × 449 × 638865767 × 996038205406837511<18>
2×1031-9 = 19999999999999999999999999999991<32> = 11 × 151 × 179 × 35332266901<11> × 1903863596145389<16>
2×1032-9 = 199999999999999999999999999999991<33> = 23 × 3271 × 25463 × 40759 × 797063983 × 3213626057<10>
2×1033-9 = 1999999999999999999999999999999991<34> = 11 × 421 × 431872165838911682142085942561<30>
2×1034-9 = 19999999999999999999999999999999991<35> = 223 × 809 × 9679 × 26417 × 726350929 × 596919997679<12>
2×1035-9 = 199999999999999999999999999999999991<36> = 11 × 3769 × 59359 × 81268940353844096722975411<26>
2×1036-9 = 1999999999999999999999999999999999991<37> = 7 × 167 × 3949222367<10> × 99892213783<11> × 4336828601999<13>
2×1037-9 = 19999999999999999999999999999999999991<38> = 11 × 312 × 61 × 3329 × 246439 × 37806010866287404738031<23>
2×1038-9 = 199999999999999999999999999999999999991<39> = 22869686025577<14> × 8745200951876820488652383<25>
2×1039-9 = 1999999999999999999999999999999999999991<40> = 112 × 59 × 131 × 139 × 15385319440502704235288428698941<32>
2×1040-9 = 19999999999999999999999999999999999999991<41> = definitely prime number 素数
2×1041-9 = 199999999999999999999999999999999999999991<42> = 11 × 488085466331<12> × 37251300102199727218170656351<29>
2×1042-9 = 1999999999999999999999999999999999999999991<43> = 7 × 2287 × 6343 × 219943 × 98973449 × 904778413392343544599<21>
2×1043-9 = 19999999999999999999999999999999999999999991<44> = 11 × 29 × 4951 × 12663285147422799865009380328472953439<38>
2×1044-9 = 199999999999999999999999999999999999999999991<45> = 17 × 607 × 255713 × 75794828714918003030146126968744953<35>
2×1045-9 = 1999999999999999999999999999999999999999999991<46> = 11 × 941 × 5099 × 80091091 × 1395506425549<13> × 339036631874750701<18>
2×1046-9 = 19999999999999999999999999999999999999999999991<47> = 31798116143<11> × 628968078173485649942013924922218937<36>
2×1047-9 = 199999999999999999999999999999999999999999999991<48> = 11 × 19 × 599 × 881 × 636229411 × 33826015088399<14> × 84259019124818789<17>
2×1048-9 = 1999999999999999999999999999999999999999999999991<49> = 7 × 1062499290673<13> × 26862015890153<14> × 10010705959231474145977<23>
2×1049-9 = 19999999999999999999999999999999999999999999999991<50> = 11 × 475167911 × 3826398576358869868672974884833538731571<40>
2×1050-9 = 199999999999999999999999999999999999999999999999991<51> = 503 × 243233 × 2967343 × 2428201141143017<16> × 226875241853431164439<21>
2×1051-9 = 1(9)501<52> = 11 × 89 × 1181 × 8526781 × 103313435979709<15> × 1963611161204642162420521<25>
2×1052-9 = 1(9)511<53> = 31 × 47 × 23017 × 387232169 × 1540104881436003669179279644678106231<37>
2×1053-9 = 1(9)521<54> = 11 × 9161 × 1984697978585108811066675928590566730507784977821<49>
2×1054-9 = 1(9)531<55> = 7 × 23 × 359 × 3511 × 9855504069142983943772496450774277719796478519<46>
2×1055-9 = 1(9)541<56> = 11 × 24329 × 1643881 × 1852019620673087519<19> × 24546924838605519609223051<26>
2×1056-9 = 1(9)551<57> = 479 × 675931247 × 1380285167<10> × 333866376233417<15> × 1340449492002335043713<22>
2×1057-9 = 1(9)561<58> = 11 × 17939 × 6609521489<10> × 1533448029328542179619044592123105606284311<43>
2×1058-9 = 1(9)571<59> = 199 × 9728801 × 4172581807<10> × 2475783926244725981531905989967508192287<40>
2×1059-9 = 1(9)581<60> = 11 × 71 × 349291 × 425105039 × 14988753181<11> × 1664556822956551<16> × 69124369004420869<17>
2×1060-9 = 1(9)591<61> = 7 × 17 × 16806722689075630252100840336134453781512605042016806722689<59>
2×1061-9 = 1(9)601<62> = 112 × 23279 × 3598061 × 127820029 × 47427507781<11> × 325523665681511080222503357941<30>
2×1062-9 = 1(9)611<63> = 449 × 36583 × 46999087 × 9954309847472425961<19> × 26025780417222815046075447239<29>
2×1063-9 = 1(9)621<64> = 11 × 10186941682129<14> × 185213828976342192731<21> × 96365167462748220389917913519<29>
2×1064-9 = 1(9)631<65> = 263 × 862596250120486216020662040487<30> × 88159005288747673732550130223111<32>
2×1065-9 = 1(9)641<66> = 11 × 19 × 73576271 × 13006065488737016869976161187117816842836976598651788169<56>
2×1066-9 = 1(9)651<67> = 72 × 245664261756742446371429272873<30> × 166146781948400392963900622505781583<36>
2×1067-9 = 1(9)661<68> = 11 × 31 × 13198091 × 2975774110369<13> × 83064859216919519<17> × 17978241245941824709418187151<29>
2×1068-9 = 1(9)671<69> = 601 × 751 × 1223 × 1327 × 1762039 × 154953963782698536247047930651531943943676000440239<51>
2×1069-9 = 1(9)681<70> = 11 × 269 × 5431 × 15269 × 5067505969<10> × 50971410312541<14> × 31555401733735929967892935334937679<35>
2×1070-9 = 1(9)691<71> = 383 × 929428663 × 56184324012853329953900330736121910078530727607322415468479<59>
2×1071-9 = 1(9)701<72> = 11 × 29 × 109 × 136361 × 12951511 × 24584372577405139<17> × 132477788424192996402945207561495099409<39>
2×1072-9 = 1(9)711<73> = 7 × 285714285714285714285714285714285714285714285714285714285714285714285713<72>
2×1073-9 = 1(9)721<74> = 11 × 2819 × 299777909 × 2151506233219133753265396066259903397930266654194380198978011<61>
2×1074-9 = 1(9)731<75> = 14903075017<11> × 24973833413251591441<20> × 537364407804581064874294092950427739989879503<45>
2×1075-9 = 1(9)741<76> = 11 × 14732791494611<14> × 1007927010484960949<19> × 12243996149395867256792018490682835328767179<44>
2×1076-9 = 1(9)751<77> = 17 × 23 × 1039 × 49230890414499481844878387392953582654972689163542556412446553714593759<71>
2×1077-9 = 1(9)761<78> = 11 × 18181818181818181818181818181818181818181818181818181818181818181818181818181<77>
2×1078-9 = 1(9)771<79> = 7 × 3433 × 11057 × 147426512069387119<18> × 51055819544426943468568569550721482086470953785642967<53>
2×1079-9 = 1(9)781<80> = 11 × 28020645479<11> × 4848071658217556101<19> × 13384129951234862675333966814839331774619359647639<50>
2×1080-9 = 1(9)791<81> = 3984365353<10> × 615763509445542041<18> × 84329318698071458777<20> × 966670132636951212017264586117071<33>
2×1081-9 = 1(9)801<82> = 11 × 698452841 × 2469886138112321<16> × 105395796334258832667738649489860221262251951222704585021<57>
2×1082-9 = 1(9)811<83> = 31 × 12007 × 177127 × 46394563186201<14> × 72427578264189535537<20> × 90277176974141879819834648189657364977<38>
2×1083-9 = 1(9)821<84> = 112 × 19 × 1060906434781<13> × 760689010157810281<18> × 6706874894835410693055991<25> × 16072616910932927008429559<26>
2×1084-9 = 1(9)831<85> = 7 × 761 × 9689 × 154112537 × 251437687119225263778989847231715716387376074335038155806265443469481<69>
2×1085-9 = 1(9)841<86> = 11 × 139 × 38611 × 52189 × 10564909523685143283128817379<29> × 614421922677651537806814146037367031790405619<45>
2×1086-9 = 1(9)851<87> = definitely prime number 素数
2×1087-9 = 1(9)861<88> = 11 × 1637599 × 185698729 × 1804658266189414213700049391<28> × 331303359429795821007123743278484646092092621<45>
2×1088-9 = 1(9)871<89> = 4702594789293358220779193<25> × 4252971156591046005277497048988465578309324788247970903656381487<64>
2×1089-9 = 1(9)881<90> = 11 × 461 × 518341 × 30686874688261752469374495132871<32> × 2479523124787057654376748439554576041515369667411<49> (Tetsuya Kobayashi / for P32 x P49 / February 8, 2003 2003 年 2 月 8 日)
2×1090-9 = 1(9)891<91> = 7 × 5743 × 1569161071<10> × 9177955008827624831100509280088159<34> × 3454456193422676960797304000075969739228719<43>
2×1091-9 = 1(9)901<92> = 11 × 3837889829531477287765030012452916487459<40> × 473745182623905220252084481452379767965484433955959<51> (Tetsuya Kobayashi / for P40 x P51 / February 8, 2003 2003 年 2 月 8 日)
2×1092-9 = 1(9)911<93> = 17 × 41719 × 129310897 × 5185728791082261297603911<25> × 420535109862140200194491107494918538812791186339965751<54> (Tetsuya Kobayashi / for P25 x P54 / February 8, 2003 2003 年 2 月 8 日)
2×1093-9 = 1(9)921<94> = 11 × 42519528089<11> × 15007925948617741706014894901261653159<38> × 284923451440497315611905436324802564574415531<45> (Tetsuya Kobayashi / for P38 x P45 / February 8, 2003 2003 年 2 月 8 日)
2×1094-9 = 1(9)931<95> = 71 × 257 × 449 × 311659154498655673<18> × 15582709370629701161<20> × 502654209187386329938742013378641361311535296507249<51>
2×1095-9 = 1(9)941<96> = 11 × 89 × 1614149 × 3208533603163552021<19> × 170003728747829609154624481<27> × 232027063348552646241296037648633500323621<42>
2×1096-9 = 1(9)951<97> = 7 × 2959968191<10> × 89702299849<11> × 1391901576011417<16> × 3754812050209796153<19> × 205894432967825576185719968107845579508807<42>
2×1097-9 = 1(9)961<98> = 11 × 31 × 59 × 61 × 191 × 126271 × 55768451 × 305452591 × 2251385779481<13> × 17618724677425071671784264623789242536856340618575092529<56>
2×1098-9 = 1(9)971<99> = 23 × 47 × 5481927244780791569<19> × 33749786850391023485940722220440056940053553577732261544990618650004208918719<77>
2×1099-9 = 1(9)981<100> = 11 × 29 × 919 × 668639342089243085299<21> × 14762311076206596302501<23> × 691158290945453415809586448213697497358573444151169<51>
2×10100-9 = 1(9)991<101> = 4739143 × 4573967723977<13> × 922650213479204150032549075155424866683684367063300609483609933949012880196577481<81>
2×10101-9 = 1(9)1001<102> = 11 × 193 × 1559 × 3929 × 814869736566609349<18> × 531080279074329811549193426242635276219790073861711605689766610870433181<72>
2×10102-9 = 1(9)1011<103> = 7 × 85009 × 284156489537<12> × 12720431958892201187993<23> × 929838683912369476841837029095350554286473305287063843960454377<63>
2×10103-9 = 1(9)1021<104> = 11 × 73721 × 944279221 × 25093621345034999<17> × 1040836034603295951020514841066319747972655779422221919544149299889819759<73>
2×10104-9 = 1(9)1031<105> = 58246367832510471330922533301678866841362759833<47> × 3433690501957258584231539706004296854340296493847755296527<58> (Makoto Kamada / SNFS for P47 x P58 / 8:06:04:89)
2×10105-9 = 1(9)1041<106> = 113 × 2971 × 20599921 × 5659518290751751<16> × 1070317885998757833926482645825851901<37> × 4053138858740958727027836989962856809621<40>
2×10106-9 = 1(9)1051<107> = 113 × 151 × 2713 × 63113047 × 411665601962159<15> × 1432111535005091142017<22> × 11611390766636117670384446064721333547715431796204997729<56>
2×10107-9 = 1(9)1061<108> = 11 × 52981 × 355525815660275383459613214754961<33> × 965263796763183037481762891813628879233328943534391097601992763507841<69> (Robert Backstrom / GMP-ECM 5.0c for P33 x P69 / June 6, 2003 2003 年 6 月 6 日)
2×10108-9 = 1(9)1071<109> = 72 × 17 × 1813106638159485199<19> × 1324224584269856521943230565035264850203152761706792328409849922321578856016283869002073<88>
2×10109-9 = 1(9)1081<110> = 11 × 7854434914481<13> × 231484739255995064985784945791920228634829602740847811282765188237297057609311031012732073407701<96>
2×10110-9 = 1(9)1091<111> = 97 × 1841341838064183395175874922541951809<37> × 1119757139864229255891290602518972434056764124343105959652676734802902167<73> (Tetsuya Kobayashi / NFSX 1.8 for P37 x P73 / March 27, 2003 2003 年 3 月 27 日)
2×10111-9 = 1(9)1101<112> = 11 × 8344960682147582539<19> × 1156089100292742055124651<25> × 18846109453076619520247177339329395464997784606309477022326870383629<68>
2×10112-9 = 1(9)1111<113> = 31 × 997496911 × 174038483110194129004712807<27> × 3716305883993959982617433460653691519920563429334657011003571487209773092193<76>
2×10113-9 = 1(9)1121<114> = 11 × 149 × 122025625381330079316656497864551555826723611958511287370347773032336790726052471018913971934106162294081757169<111>
2×10114-9 = 1(9)1131<115> = 7 × 350431 × 546241 × 17149772513<11> × 7132522710977830981296719<25> × 963586917546074670988104859727<30> × 12663469868819886488801157501096575887<38> (Tetsuya Kobayashi / GMP-ECM 5.0.1 B1=250000 for P25 / May 11, 2003 2003 年 5 月 11 日) (Tetsuya Kobayashi / GMP-ECM 5.0.1 B1=250000 for P30 x P38 / May 22, 2003 2003 年 5 月 22 日)
2×10115-9 = 1(9)1141<116> = 11 × 3969947675674974075325996365289549567648871<43> × 457986343075085812910403468446788759785902892257732718573067650529098611<72> (Robert Backstrom / NFSX v1.8 for P43 x P72 / June 3, 2003 2003 年 6 月 3 日)
2×10116-9 = 1(9)1151<117> = 1300077873236814617625875427828886902290588172083356016807<58> × 153836938630497839571709555448490510158389234978218219454513<60> (Robert Backstrom / NFSX v1.8 for P58 x P60 / June 3, 2003 2003 年 6 月 3 日)
2×10117-9 = 1(9)1161<118> = 11 × 147275489 × 24469994737259<14> × 41414714242405865473394362405266901<35> × 1218199149732943613769732728577161927926373873717269492670131<61> (Robert Backstrom / NFSX v1.8 for P35 x P61 / June 19, 2003 2003 年 6 月 19 日)
2×10118-9 = 1(9)1171<119> = 6271 × 777648281 × 29458936251591842088888931959868494080794462012513<50> × 139217207425244098873436846882057928906682882694072426257<57> (Robert Backstrom / NFSX v1.8 for P50 x P57 / June 20, 2003 2003 年 6 月 20 日)
2×10119-9 = 1(9)1181<120> = 11 × 19 × 3525343069<10> × 12830777786521666579063883794076551<35> × 21155794470796657835817597776291486582930993643991210891207607504380429621<74> (Robert Backstrom / NFSX v1.8 for P35 x P74 / June 23, 2003 2003 年 6 月 23 日)
2×10120-9 = 1(9)1191<121> = 7 × 232 × 937 × 561097 × 1034233 × 30956857 × 32086584760886232435260255164910602361731689772346415867148089697425319897877860320867391188833<95>
2×10121-9 = 1(9)1201<122> = 11 × 1051 × 79280891 × 20144637692819865339657824839<29> × 10489573112550245363753764243159<32> × 103263965092626010157759995764072167016601312937741<51>
2×10122-9 = 1(9)1211<123> = 4831 × 8719 × 26111 × 318310799 × 571283134592509917770648860992931202988496863968094089615704423026047275318150366184605109917824279671<102>
2×10123-9 = 1(9)1221<124> = 11 × 509 × 6741559648522798608961389652036416202320903697879152911<55> × 52985757401382608119750656846599231077949363231208239596430954119<65> (Robert Backstrom / NFSX v1.8 for P55 x P65 / July 5, 2003 2003 年 7 月 5 日)
2×10124-9 = 1(9)1231<125> = 17 × 401 × 4244688115289<13> × 29168872800930361<17> × 23695794222845543472144587669128208477570378616737857497538855252112745603749750074308922087<92>
2×10125-9 = 1(9)1241<126> = 11 × 349 × 1430997457979<13> × 36406004737431600073777554780869053446902351175118673830744727930164953673092068664391474400522986744339900811<110>
2×10126-9 = 1(9)1251<127> = 7 × 449 × 2744573888374974060345943730911359860900897570077723540177<58> × 231851915065514293604722643132995107535289072169906760240165370881<66> (Robert Backstrom / NFSX v1.8 for P58 x P66 / July 21, 2003 2003 年 7 月 21 日)
2×10127-9 = 1(9)1261<128> = 112 × 29 × 31 × 599399 × 2848739 × 794801472802789<15> × 17045983166123225959<20> × 7947591560253927552849580220915157175710611102965496042279964350835133911739<76>
2×10128-9 = 1(9)1271<129> = 24342640238672508623881009393<29> × 8216035649340341089902476985988296609514057949756161264597798825789716110953918210637129768156579687<100> (Tetsuya Kobayashi / GMP-ECM 5.0.1 B1=250000 for P29 x P100 / May 11, 2003 2003 年 5 月 11 日)
2×10129-9 = 1(9)1281<130> = 11 × 71 × 237859 × 3620929774119161145065008275818860531<37> × 3194496410275118558619826433857192151411<40> × 930758190542741141297577277292754927901684969<45> (Robert Backstrom / GMP-ECM 5.0c, PPSIQS Ver 1.1 for P37 x P40 x P45 / July 11, 2003 2003 年 7 月 11 日)
2×10130-9 = 1(9)1291<131> = 193 × 4639 × 2618352182233<13> × 423055140719303<15> × 205956770194082476817<21> × 97914543563056064554749600829609152424912014602205835291688154827201383381751<77>
2×10131-9 = 1(9)1301<132> = 11 × 139 × 121141655523918011<18> × 660681793720134019<18> × 255234654554421703109524862149<30> × 6403199397620080243415089796785880325998809233259881532578467219<64> (Tetsuya Kobayashi / GMP-ECM 5.0.1 B1=250000 for P30 x P64 / May 11, 2003 2003 年 5 月 11 日)
2×10132-9 = 1(9)1311<133> = 7 × 27743 × 49955005113339505177<20> × 11247549729990561991216522489<29> × 18329119554344267438037680207487927672825047706285748799968475794628047934135647<80> (Tetsuya Kobayashi / GMP-ECM 5.0.1 B1=250000 for P29 x P80 / May 3, 2003 2003 年 5 月 3 日)
2×10133-9 = 1(9)1321<134> = 11 × 3089 × 588598840460284293239942317313634892139262485652903263780570352276406015480149504105476912210482945348597663262603372671355837429<129>
2×10134-9 = 1(9)1331<135> = 158800147201<12> × 58162433076076080770392918305091655606634983253482373981793<59> × 21653920060883623476839767076368426645852142119974389294590361687<65> (Robert Backstrom / NFSX v1.8 for P59 x P65 / August 30, 2003 2003 年 8 月 30 日)
2×10135-9 = 1(9)1341<136> = 11 × 439 × 153786680434528085060726068335061<33> × 345063667656267171646118159465539<33> × 7804675190477549930518786297471879204229396433729266237711035950301<67> (Robert Backstrom / GMP-ECM 5.0c for P33(1537...) x P33(3450...) x P67 / July 19, 2003 2003 年 7 月 19 日)
2×10136-9 = 1(9)1351<137> = 115525247 × 2717026063<10> × 4535926271009657<16> × 22533562178525023361<20> × 1248987189170342404235704172777<31> × 499120563718165570649877011896877136304172960831516039<54>
2×10137-9 = 1(9)1361<138> = 11 × 19 × 419 × 3491 × 236701 × 174401772469481941<18> × 44122787807001685051<20> × 43143117777902240545629269<26> × 8325194323122042227380045898351461187089905845919036118568489<61>
2×10138-9 = 1(9)1371<139> = 7 × 1361 × 28067396514726202523860938206489746457258001501485978553895083833<65> × 7479485083314129370275849920397548796557371512278764262868303993853001<70> (Greg Childers / GGNFS for P65 x P70 / December 21, 2004 2004 年 12 月 21 日)
2×10139-9 = 1(9)1381<140> = 11 × 892 × 13747381 × 7146571832041<13> × 17963539613629<14> × 130061167717437332083824666512298983881870883441403315869480225811084928632218463637178809414366259629<102>
2×10140-9 = 1(9)1391<141> = 17 × 59113 × 11920269538992421121435956097648950019099811559<47> × 16695983163826097420159437859577435460952586279369215627290094387500562238589852030582969<89> (Greg Childers / GGNFS for P47 x P89 / December 21, 2004 2004 年 12 月 21 日)
2×10141-9 = 1(9)1401<142> = 11 × 631 × 13166084339<11> × 166073887821810483025497421<27> × 7182404357407176819191288294411<31> × 18347635945878811125425180600708486525299918329547912228632200452871839<71> (Tetsuya Kobayashi / GMP-ECM 5.0.1 B1=250000 for P27 / May 3, 2003 2003 年 5 月 3 日) (Robert Backstrom / GMP-ECM 5.0c for P31 x P71 / July 26, 2003 2003 年 7 月 26 日)
2×10142-9 = 1(9)1411<143> = 23 × 31 × 4821403844377<13> × 1925837354763431152978123661821696597769<40> × 3020976519048945912969246806072424580400392622424521165416090871659382240657443469991839<88> (Robert Backstrom / GMP-ECM 5.0c for P40 x P88 / July 27, 2003 2003 年 7 月 27 日)
2×10143-9 = 1(9)1421<144> = 11 × 414389 × 636499 × 808651 × 2829709 × 68895319511<11> × 148810761068999180150604202077241<33> × 2938355958031759584343133195531046718361797091700151490971832113763607251419<76> (Robert Backstrom / GMP-ECM 5.0c for P33 x P76 / July 29, 2003 2003 年 7 月 29 日)
2×10144-9 = 1(9)1431<145> = 7 × 47 × 1697 × 4751 × 15421121 × 324513125593<12> × 573979583578236121980436103332418434430645159014685375809<57> × 262495926279377751706900324634363777228196866952780943282841<60> (Greg Childers / GGNFS for P57 x P60 / December 21, 2004 2004 年 12 月 21 日)
2×10145-9 = 1(9)1441<146> = 11 × 128631961 × 3058504163210787541565734541<28> × 4621461548680485432770137084655508103711899990253073462930407206738395008931268027893096129138805531956481281<109>
2×10146-9 = 1(9)1451<147> = 1471 × 958054117111388133836953<24> × 248481397786006983813082785705803914377145937759<48> × 571127931149896369612391508288727305834841885540092677990337631749027823<72> (Greg Childers / GGNFS for P48 x P72 / December 21, 2004 2004 年 12 月 21 日)
2×10147-9 = 1(9)1461<148> = 11 × 68180906411<11> × 1623435592189<13> × 49499916383731193531<20> × 80860585291091922488687339449<29> × 752237361418547331317351905668601661<36> × 545560892455767788091635557127182197821<39> (Tetsuya Kobayashi / GMP-ECM 5.0.1 B1=250000 / May 22, 2003 2003 年 5 月 22 日)
2×10148-9 = 1(9)1471<149> = 57431787553239244660626976882036073<35> × 252248599228180796094726301293542573587723903<45> × 1380539695291779642420640847677458347322068680428219755758017617145889<70> (Greg Childers / GGNFS for P35 x P45 x P70 / December 21, 2004 2004 年 12 月 21 日)
2×10149-9 = 1(9)1481<150> = 112 × 1346265092881<13> × 387992200624859100187751<24> × 2531711749931587522393223600637769<34> × 1249904372706401956986958189545297767572898964186908737074327655472199107457889<79> (Robert Backstrom / GMP-ECM 5.0c for P34 x P79 / August 13, 2003 2003 年 8 月 13 日)
2×10150-9 = 1(9)1491<151> = 72 × 313 × 5857 × 19249 × 48073 × 2145366910370960233318195778943906318667242154816224697409<58> × 11215105892080335130809942373623305706116017816514634296425819268673685145143<77> (Greg Childers / GGNFS for P58 x P77 / December 21, 2004 2004 年 12 月 21 日)
2×10151-9 = 1(9)1501<152> = 11 × 28977484241<11> × 18375169252060969<17> × 22548083877070097907679<23> × 18013004842843604596374731<26> × 4655013022923270932988561001253591<34> × 1806045038483440273580255784582611178647471<43> (Makoto Kamada / msieve 0.86 for P34 x P43 / 12 minutes)
2×10152-9 = 1(9)1511<153> = 1116296695923497978473<22> × 5199593364457887425999<22> × 34457278693517194077316857526581508846708883813704415804700412601291268625407614569807538834906796005729342833<110>
2×10153-9 = 1(9)1521<154> = 11 × 14143455769740740001759009960126743688349<41> × 453912657024767148614711372141519336680287959<45> × 28321058492200039254937740121739341593546053812714710601460743639391<68> (suberi / GGNFS-0.77.1-20060513-pentium4 for P41 x P45 x P68 / 37.97 hours on Pentium 4 2.26GHz, Windows XP and Cygwin / June 20, 2006 2006 年 6 月 20 日)
2×10154-9 = 1(9)1531<155> = 682199509510458346711<21> × 29316936938802347979391917249290618328209010966349894409649251807510494055398191134873193977207410428908272133807507630300782707712481<134>
2×10155-9 = 1(9)1541<156> = 11 × 19 × 29 × 59 × 521564171 × 45948806279<11> × 631230959468165622425170279<27> × 36971189687843049014584624398373318741185394002800764771942255530825232021645069972337431397407461591019<104>
2×10156-9 = 1(9)1551<157> = 7 × 172 × 4463 × 10284359 × 2849130261940733497<19> × 16898555617138742719<20> × 631855909108883008824359866689035739181056737<45> × 708027384596563532504630820087246335731726729305545444147311<60> (Anton Korobeynikov / GGNFS-0.73.3 gnfs for P45 x P60 / 21.71 hours / March 9, 2005 2005 年 3 月 9 日)
2×10157-9 = 1(9)1561<158> = 11 × 31 × 61 × 199 × 389 × 719310401 × 17267392614467203203092890110854489739887276370136967572293760711488767643188574186970711036416614936152764854616791944513844744416108175581<140>
2×10158-9 = 1(9)1571<159> = 449 × 647 × 263423 × 24629981367007296663635744349139127212651564923379917379247<59> × 106111291216604957235287331858373630426835509120007905601583219050565604016518888425492737<90> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P59 x P90 / 37.18 hours on Cygwin on AMD XP 2700+ / April 26, 2007 2007 年 4 月 26 日)
2×10159-9 = 1(9)1581<160> = 11 × 24691 × 52861 × 266261 × 4151011 × 40930808775623536636245772098276860041853369431<47> × 3079296349757713797324715535825813229817563878384139018839754824005144136790174117702778331<91> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P47 x P91 / 23.56 hours on Core 2 Quad Q6600 / July 28, 2007 2007 年 7 月 28 日)
2×10160-9 = 1(9)1591<161> = 158642813009799873789292199<27> × 514829968216555250825419476063055331353216130401<48> × 244875747315362559771904473968778705005860870814895857896156971504755878896463497536209<87> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs for P27 x P48 x P87 / 39.32 hours on Cygwin on AMD XP 2700+ / October 6, 2007 2007 年 10 月 6 日)
2×10161-9 = 1(9)1601<162> = 11 × 8009 × 46649 × 5470052140709707519<19> × 21260817950106947166511<23> × 38623719592924262442438059227864671483234091<44> × 10834057799333342211229610150242910516634871944815694724812226195039<68> (Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs for P44 x P68 / 38.14 hours on Pentium 4 3.0 Ghz Windows Xp Pro Sp2 - 512 Mb / January 22, 2006 2006 年 1 月 22 日)
2×10162-9 = 1(9)1611<163> = 7 × 2166233 × 2135889447020276760751<22> × 61751572044055904905787426693315371750047528441837089424630652723251573766088926827349503905369000230889497829598793774110690098420311<134>
2×10163-9 = 1(9)1621<164> = 11 × 1818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181<163>
2×10164-9 = 1(9)1631<165> = 23 × 71 × 627656571791<12> × 197829276153372503<18> × 400404802647198353513<21> × 2463382719864551929861374144340515770390327134582352152793573794219905024407065447563530700577846252346990643223<112>
2×10165-9 = 1(9)1641<166> = 11 × 457527644458064916785243595451<30> × 10380464989853334806493414428274868458216509448469<50> × 38282753110901991590906115105218234489358257188870210443245138602465182775068426383299<86> (Makoto Kamada / GMP-ECM 6.0.1 B1=11000000, sigma=3982948600 for P30 / April 9, 2005 2005 年 4 月 9 日) (matsui / GGNFS-0.77.1-20060513-prescott snfs for P50 x P86 / March 14, 2008 2008 年 3 月 14 日)
2×10166-9 = 1(9)1651<167> = 4342608369450320053307697679764984011450663<43> × 4605526977909722451833107953713650779997398871974627226660275324682668177795505331963035514480056136584527504258436835169457<124> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 for P43 x P124 / 69.64 hours on Core 2 Duo E6300@2.33GHz / February 15, 2007 2007 年 2 月 15 日)
2×10167-9 = 1(9)1661<168> = 11 × 25693999 × 213778048882883699682952867750597400299228114685941<51> × 253294029617274149322595661355934135791715095080163601<54> × 13068253350533572176578369071664035808002504957074122959<56> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.29 for P51 x P54 x P56 / November 16, 2007 2007 年 11 月 16 日)
2×10168-9 = 1(9)1671<169> = 7 × 1087 × 8537489959<10> × 367694783292840547667053261930530350154041<42> × 17966034076031944574391153471623679589453353622292711<53> × 4660500063909969005743702902671272798968399002082218677735511<61> (Makoto Kamada / GMP-ECM 5.0.3 B1=400000, sigma=4275561283 for P42 / January 24, 2005 2005 年 1 月 24 日) (Sinkiti Sibata / GGNFS-0.77.1 gnfs for P53 x P61 / 58.38 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / March 30, 2006 2006 年 3 月 30 日)
2×10169-9 = 1(9)1681<170> = 11 × 131 × 1218179 × 4915970726941<13> × 166065331635001<15> × 13956182537834658156643457652618573113257477876537309557957964583738064010532136928903626428256160603561645591634168121739550131758409<134>
2×10170-9 = 1(9)1691<171> = 2927 × 175911118129<12> × 20461530396754200059131643273<29> × 18983481832409700627689118817669173998276546104832673602564601813378340117732096379364534168100333930658183775574866300916838849<128>
2×10171-9 = 1(9)1701<172> = 112 × 541 × 77524813986331865479<20> × 5034377696798900669436721889289682064351<40> × 334794278410722364007416315208828631701999789<45> × 233820618672097095012926459422107581471500507709899340258393951<63> (Dmitry Domanov / for P45 / June 10, 2009 2009 年 6 月 10 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P40 x P63 / 3.55 hours on Core 2 Quad Q6700 / June 11, 2009 2009 年 6 月 11 日)
2×10172-9 = 1(9)1711<173> = 17 × 31 × 20023 × 6637427143417951<16> × 66028934282635233891831912901618375839864457254966050086431689<62> × 4324701912262433203651625569596822613898499886371331781703808091038595706400686381022889<88> (Wataru Sakai / Msieve for P62 x P88 / 69.35 hours / October 8, 2009 2009 年 10 月 8 日)
2×10173-9 = 1(9)1721<174> = 11 × 19 × 421 × 3041 × 747455244706401429831056166705899969581935089050640612310253767820047787878360583539654961728067791679245248396176872561971504995417183717274993893384082654288618459<165>
2×10174-9 = 1(9)1731<175> = 7 × 67807 × 195697 × 7483601 × 90799214287<11> × 174469979351152785406123306399771303<36> × 181618394791561707872745497404891429823321019239014722523833973110879902107321452734442912936754551424231080727<111> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=3677067375 for P36 x P111 / December 6, 2009 2009 年 12 月 6 日)
2×10175-9 = 1(9)1741<176> = 11 × 2104936691786471<16> × 2999235301404108672880852229001943743610905187225557697685545402923389<70> × 287996846831064477423205097882532373558238456659108938210015914290084744018871680277303599<90> (Serge Batalov / Msieve-1.38 snfs for P70 x P90 / 35.00 hours on Opteron-2.6GHz; Linux x86_64 / October 7, 2008 2008 年 10 月 7 日)
2×10176-9 = 1(9)1751<177> = 977 × 30422398200031601<17> × 671851302766021349481441049<27> × 21877620172248112352137872588858671<35> × 457792574155442948477112056665511633163701347669187524881302075112906813001557315246521154535777<96> (Andreas Tete / Syd`s Database / June 20, 2009 2009 年 6 月 20 日) (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=4212978986 for P35 / January 12, 2010 2010 年 1 月 12 日)
2×10177-9 = 1(9)1761<178> = 11 × 139 × 1308044473512099411379986919555264879005886200130804447351209941137998691955526487900588620013080444735120994113799869195552648790058862001308044473512099411379986919555264879<175>
2×10178-9 = 1(9)1771<179> = 911 × 18481 × 289228011298481<15> × 221280173552000716911237096439263441890326348361377<51> × 18561082318616494135355771282942297359949369034556643650271161463829648378462904777206533132526875781163673<107> (Robert Backstrom / Msieve 1.44 snfs for P51 x P107 / January 16, 2012 2012 年 1 月 16 日)
2×10179-9 = 1(9)1781<180> = 11 × 109 × 1531 × 197084090167072070444501<24> × 30192185167289557139962813541<29> × 11175180923359872868625684424731<32> × 38745744185364135989275373176013064492968519<44> × 42287395639301185430766513250585783292869637311<47> (anonymous / GMP-ECM B1=250e3 for P32 / January 26, 2007 2007 年 1 月 26 日) (Shaopu Lin / Msieve v. 1.16 for P44 x P47 / January 27, 2007 2007 年 1 月 27 日)
2×10180-9 = 1(9)1791<181> = 7 × 82939584913<11> × 871243568591655604819543<24> × 3953943989419104295200149896389163303020815255328731181790802826878235261637229213699474019776459427102972654594165197833246715355092773554133607<145>
2×10181-9 = 1(9)1801<182> = 11 × 151 × 10799 × 16385760357836479<17> × 68047194271676624979683442959271990905014592809411007915004486534294561269469642532600595836182252888373831755597344750327974753436728402956615993566243862611<158>
2×10182-9 = 1(9)1811<183> = 311 × 691199 × 2752961 × 463656400827184289<18> × 720124831099404032414004397163732542365451969<45> × 1012190834704104933514976220750778239330826955459392216982460060901542283935837926598805692017448206884319<106> (Dmitry Domanov / Msieve 1.50 snfs for P45 x P106 / May 16, 2013 2013 年 5 月 16 日)
2×10183-9 = 1(9)1821<184> = 11 × 29 × 89 × 181 × 199744837434442791340990120371036864210437097079699444679911<60> × 1948476479308863608330608439312461206938858412379710908007928999570893351886680145473233888864975347874868634937712811<118> (Wataru Sakai / Msieve for P60 x P118 / 168.64 hours / April 20, 2009 2009 年 4 月 20 日)
2×10184-9 = 1(9)1831<185> = 44460607 × 1515650074457<13> × 296794373051824221415342858566714125768918553733260051315696066534502162022380447724011729666621686211314993312220371601699994516844707551502654447480403622971178609<165>
2×10185-9 = 1(9)1841<186> = 11 × 431 × 712822190229871<15> × 41923145739683839081792694069691701563673251<44> × 1411643285044701092494671131705837219943076551220724985129379796388243775339249001499306233048351268769249907355874986691031<124> (Dmitry Domanov / Msieve 1.50 snfs for P44 x P124 / August 19, 2013 2013 年 8 月 19 日)
2×10186-9 = 1(9)1851<187> = 7 × 23 × 2423 × 19559 × 56543 × 4863112952611000814088932508306690169<37> × 35054895007074389149555082237116177199951<41> × 27193316925340364197216164300107244882363333786168809594227912799048158910622017930873881006399<95> (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=3952842734 for P37, B1=11000000, sigma=2024333617 for P41 x P95 / January 12, 2010 2010 年 1 月 12 日)
2×10187-9 = 1(9)1861<188> = 11 × 31 × 232591 × 1114999 × 33386162835946576289<20> × 6773945928077052881314007320331858765099546017999350259081226295105722658975983441320119057927058199782700840076712366137904062328166651794261630018618451<154>
2×10188-9 = 1(9)1871<189> = 17 × 156083835959<12> × 116098705756986833<18> × 1528557664610115047105616481<28> × 11850267833117636089279825943451630668842365234326345903782094263<65> × 35841466648932980827554785774378751162588213168557293505385813501703<68> (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=1508648790 for P28 / February 8, 2005 2005 年 2 月 8 日) (Warut Roonguthai / Msieve 1.49 gnfs for P65 x P68 / April 11, 2012 2012 年 4 月 11 日)
2×10189-9 = 1(9)1881<190> = 11 × 27109 × 123004222519<12> × 22228635033329<14> × 10235905476260465357569393480049424439910731<44> × 239642990562554755138199160662108731331039477467670418812099221776208598926253211177900837301269273760076660147119589<117> (Dmitry Domanov / Msieve 1.50 snfs for P44 x P117 / March 17, 2014 2014 年 3 月 17 日)
2×10190-9 = 1(9)1891<191> = 47 × 449 × 11622972521<11> × 6341277798583167100964294139041<31> × 50680062607953557679144633161928029907736514165318468273<56> × 253719977252865278207737749414682282553737607421048350784017208805958954385289780911162049<90> (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=511965629 for P31 / January 14, 2010 2010 年 1 月 14 日) (Dmitry Domanov / Msieve 1.50 snfs for P56 x P90 / March 18, 2014 2014 年 3 月 18 日)
2×10191-9 = 1(9)1901<192> = 11 × 19 × 23864081784098238712567049<26> × 778219755946725917399850386711<30> × 51527222038994152650195531815232912991979495275318766226747424885244754562768982626118823605600262353516678700395732460832634976485641<134> (Makoto Kamada / GMP-ECM 5.0.3 B1=78530, sigma=1599640853 for P30) (Makoto Kamada / GMP-ECM 5.0.3 B1=400000, sigma=1965997098 for P26 x P134)
2×10192-9 = 1(9)1911<193> = 72 × 191 × 234467264994790103711<21> × 911419530857067556001147013020418456227492530421410228637842914234618285403694896154707127343878769970497762657753800466250709908952565473342882531764640722687061618759<168>
2×10193-9 = 1(9)1921<194> = 112 × 229 × 751 × 1389008490432229693915637396036821<34> × [691933417297017957104478334368940847492681960800916503025598061193956200601528866970042838166170253705478669766997332550958436576230148828520831637814969<153>] (matsui / GMP-ECM 6.2.1 for P34 / November 9, 2008 2008 年 11 月 9 日) Free to factor
2×10194-9 = 1(9)1931<195> = 851881 × 36229185784529250353<20> × 350679958567627000639<21> × 18479130959171056066202249179555223942942853525648955297838539947174590476462413142824103269527475771008766372922452370390958506797084358259337854833<149>
2×10195-9 = 1(9)1941<196> = 11 × 36288541519<11> × 17540295340251835573132392429819529<35> × 285647807601379394175092595084308055809638896382277354713937104292787490457559199067284142596434264947742727411425516972204367371903135968410131002131<150> (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=421498009 for P35 x P150 / January 13, 2010 2010 年 1 月 13 日)
2×10196-9 = 1(9)1951<197> = 577 × 13780783 × 14719751 × 67067526692869132643082144969723620388698279<44> × 2547812911112682758933613358750294371677324092689435735442275039900285465315508819061260922760235158117004216926138635734958975066027369<136> (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=1159700811 for P44 x P136 / January 14, 2010 2010 年 1 月 14 日)
2×10197-9 = 1(9)1961<198> = 11 × 24422549 × 3069053877636163811209<22> × 17082856976752619130670684090199212230671<41> × 26854367296513604675835702481280880891377811659523611436119<59> × 528769478333804444847416808783697943132910903891502042324659821937809<69> (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=239735945 for P41 / January 14, 2010 2010 年 1 月 14 日) (Sinkiti Sibata / Msieve 1.40 gnfs for P59 x P69 / April 19, 2010 2010 年 4 月 19 日)
2×10198-9 = 1(9)1971<199> = 7 × 64713901797511<14> × 9916372246526737433949447954712733233<37> × [445227056823413204335080095187015621695823394884255936475263332923408208646560723205386467339105880811035168419307597227960941801394154491792686551<147>] (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=1210903332 for P37 / January 14, 2010 2010 年 1 月 14 日) Free to factor
2×10199-9 = 1(9)1981<200> = 11 × 71 × 3779 × 315521 × 10482811 × [2048783389441440771229557973075720287058355428296910864030509219645134206492641019751555022949028607089243046628799041351027126055177108318048575972923088961577398713918207923863939<181>] Free to factor
2×10200-9 = 1(9)1991<201> = definitely prime number 素数
2×10201-9 = 1(9)2001<202> = 11 × 409 × 1871 × 2909 × 336790674841<12> × 3244163086531077487208990901611<31> × [74753883128523052738026538623151664673439692879259426514500080703022293349719032216354989421268182305258845712048182921998676887903895940922731928581<149>] (KTakahashi / GMP-ECM 6.4.3 B1=1000000, sigma=1390441919 for P31 / March 8, 2013 2013 年 3 月 8 日) Free to factor
2×10202-9 = 1(9)2011<203> = 31 × 167 × 842124260800708318921<21> × 8853397177260157664437596726791<31> × [518162171105803343108707481464468898874041058304411802625669976277169975883687870300619572976320444545967433416802804532387852578264108148819711953<147>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=535802893 for P31 / February 23, 2013 2013 年 2 月 23 日) Free to factor
2×10203-9 = 1(9)2021<204> = 11 × 722843382432991169967599<24> × [25153191719927888759381237410542184198120110871897863652893389553937649345697372656463050722353869955219281261536903331910565902471001832043322338474698080800748021330112214686219<179>] Free to factor
2×10204-9 = 1(9)2031<205> = 7 × 17 × 24645485910312924023<20> × 681939189604001404630800255124681083472683840899955527985269477931500894094674373396166898997199933393768116894772237768084229999370300682815053284146693281284779778039021517415103943<183>
2×10205-9 = 1(9)2041<206> = 11 × 34501 × 94476979 × 5129181807998863178815609<25> × 1967930595393639631055085991<28> × 55261384139925358283253046803391421804284767102785745090191326678403783118567263175824707830166524685414893241111851498217690069213098086581<140>
2×10206-9 = 1(9)2051<207> = 97 × 433 × 465228289 × 147177469343078583361<21> × 69544520814211330639114623745811104039583633692644140738976886114415762118051185394808012889519232095238902785971883093588182421471066018741279429586904668508088438904539079<173>
2×10207-9 = 1(9)2061<208> = 11 × 1021 × 1369685269339<13> × 130014198604056310143845095227159734338493304774941115108526522097011796011284172845153211580520499511155696441464023979623681060170435577832732220483219873191481178879480236203972568325170699<192>
2×10208-9 = 1(9)2071<209> = 23 × 6687186001<10> × 18231883519<11> × [7132260861284067169925067002824222917786046135804139549985653861482439477703680593251066996611869716422463463497964819419141162023846144325781079756328619311601775446901439394834675940143<187>] Free to factor
2×10209-9 = 1(9)2081<210> = 11 × 19 × 179 × 171276701 × 469891059509471<15> × 60404812644435461<17> × 12478316345262174390829<23> × 2789898755629575621871650919<28> × 216993443857412166372641692846793299<36> × 925668330244820911500900823773834709<36> × 157259616795220572837814985602302479659600711<45> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1805118727 for P36(2169...), YAFU 1.24 for P36(9256...) x P45 / March 8, 2013 2013 年 3 月 8 日)
2×10210-9 = 1(9)2091<211> = 7 × 18199 × 23497 × 64104769383436746781681921120199107750529<41> × [10422734417531307779217869037397368559804232688580459913495957140237256459575459472859747873198303588212321165872182090969168693601036130693477028505108356255199<161>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1753095681 for P41 / March 17, 2014 2014 年 3 月 17 日) Free to factor
2×10211-9 = 1(9)2101<212> = 11 × 29 × 11959 × 80021 × 74470126831<11> × 879748183726289797435873811980335358714662880086795292522335050470163523101540404702532739197073116509683701312012510143771002276792864576967165644884288234853964301077697827687651314026221<189>
2×10212-9 = 1(9)2111<213> = 5113 × 7457 × 194131859195809<15> × [27020491595037199550639372128410079953642827089942902673049366178349288606470056422087960166317205094817056567344313530055064328058950027773154352400593475083092135095510725356629913987720239<191>] Free to factor
2×10213-9 = 1(9)2121<214> = 11 × 59 × 3081664098613251155624036979969183359013867488443759630200308166409861325115562403697996918335901386748844375963020030816640986132511556240369799691833590138674884437596302003081664098613251155624036979969183359<211>
2×10214-9 = 1(9)2131<215> = 5125496007375122969<19> × [3902061375371635744920865864792928737667071213800851198818345099058439885889193889581197050208460575228726385407318161279638381935268808594369079313768657528879549590218322867251541957514982941839<196>] Free to factor
2×10215-9 = 1(9)2141<216> = 112 × 132331 × 6633768749<10> × 222892719412951137019<21> × [8447473148715487227144656642593223865424644227596516734273370067284917322427547890594132066584621218015586080776947920949080604993124559844621749955002168596552650942547575747411<178>] Free to factor
2×10216-9 = 1(9)2151<217> = 7 × 12647 × 12992591 × 356203343 × 24711961721<11> × 7264013725469096067635050807<28> × 27193605947855852260880374839621817397353472785976502386521819866758254996876452238008137280920743505957311244773891474368059859978052104136259204242591852889<158>
2×10217-9 = 1(9)2161<218> = 11 × 31 × 61 × 2153662504628927316931561199<28> × 446445176012319679347174589667086154695852094080642810416926557631890251905242963602285848248890223102426073374074831333327615876583339776454496081389831708865236742455245742034017943609<186>
2×10218-9 = 1(9)2171<219> = 1132 × 233 × 324871 × 491417777 × 2941179668256203714255075871930181789195289<43> × 143164000073411497891367589140881189535229032454305904846210538096602274803014713539144458013862829859495619336298413007451369201428716402106759934995288641<156> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2211067922 for P43 x P156 / April 15, 2013 2013 年 4 月 15 日)
2×10219-9 = 1(9)2181<220> = 11 × 291997726947001<15> × 128412277334858385842197759<27> × 587105946232194567013096946501<30> × 1763429319191019510804130988496115764979584303123464612245453609<64> × 4683567196849420048234151596946304785263459662863981992298080079468044222529092673951<85> (KTakahashi / GMP-ECM 6.4.3 B1=1000000, sigma=3072749348 for P30 / March 8, 2013 2013 年 3 月 8 日) (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P64 x P85 / August 27, 2017 2017 年 8 月 27 日)
2×10220-9 = 1(9)2191<221> = 17 × 3943 × 6833679863<10> × 10715495283825654261551387374647168956076522551<47> × 4074622867141723736181513733049401409020197941468298865885323797945429434531594617264588577454341215783748463408083904488316281880637729667811987019601324306897<160> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P47 x P160 / April 10, 2018 2018 年 4 月 10 日)
2×10221-9 = 1(9)2201<222> = 11 × 3581 × 15325319 × 111061651 × 2461869315302994982735271<25> × [1211697873474053486912253350906506594491970886174866563510668136689300476528181302401249832635596656746677522944673029010388082668789445109063018610681756974572814360959587536099<178>] Free to factor
2×10222-9 = 1(9)2211<223> = 7 × 449 × 2311 × 1419511 × 193975512006623474551862809092551851862331462584850976811311741194622370397939279346203578226448889106253729758919600529367699545968580423948990633779397767241540602552423317920953071054409132152408985273191697<210>
2×10223-9 = 1(9)2221<224> = 11 × 139 × 980528892933915049481<21> × [13340193062523635509280857796662056793491295302269776689609303284754911703117306698221494867602355498339123455501873979142601489994034349709133842260816934562227435972776285974006503336110114979205559<200>] Free to factor
2×10224-9 = 1(9)2231<225> = 524251588504841<15> × 381496221252085298722788047534705720900041659301758888857081994743527355212671108717900354369067675957074078337660209849354394324585390125288446553564383964158832142917783631276751027795863795030618630864209151<210>
2×10225-9 = 1(9)2241<226> = 11 × 22369 × 16740431 × 485538984677961519946676600599158296743856560546811910841953654232517795131669098150456703369067708871631225591470051752650995164092822786884321906982306722673074793995987112392070034646127552021292294529951859979<213>
2×10226-9 = 1(9)2251<227> = 991 × 38182943 × 11524975961<11> × 62137860767<11> × 1492618885134473<16> × 2029281705655495885794218915499002209<37> × [243668474216918565441581292401634723676881426854512216745195345882245694850477820204842583369125157633920227570388774422756903273128882716316073<144>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3222769883 for P37 / March 8, 2013 2013 年 3 月 8 日) Free to factor
2×10227-9 = 1(9)2261<228> = 11 × 19 × 89 × 213949 × 49355733259555835867328986447110774070521<41> × 1018229871231772666543011776457842198325818305317308611504154303826769571758983146441805108479147024769408485761516072557760930780184968296432041095431026185217072400533159804579<178> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3744638015 for P41 x P178 / April 22, 2013 2013 年 4 月 22 日)
2×10228-9 = 1(9)2271<229> = 7 × 67079 × 27649389631<11> × 14953532387089<14> × 7621123414713403493595817<25> × 21862144647452648628754324490351<32> × 232777414945570927129146899543094866460759970481<48> × 265621627235735765223488265754097391375294230951839331294306239549076699946655228380622537914079<96> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=2677535880 for P32 / February 23, 2013 2013 年 2 月 23 日) (Erik Branger / GGNFS, Msieve gnfs for P48 x P96 / November 5, 2017 2017 年 11 月 5 日)
2×10229-9 = 1(9)2281<230> = 11 × 29443513651<11> × 83612742449947707619177722086883671291<38> × [738542014700266737459722948903430850950926246705546080521181866619298591684930386654230684982373799692282841663296033515491609182813190646042337756388452948679255433291455744323141<180>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=985093159 for P38 / March 12, 2013 2013 年 3 月 12 日) Free to factor
2×10230-9 = 1(9)2291<231> = 23 × 25673 × 179369 × 16937339857<11> × 842668317324842426444256289<27> × 12726696096034447280977151199991<32> × 10395864511535000750036540704178935427985278945404095869106914987504340458949073593800482203951072775008262450997048357574813437685227276099381159244487<152> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=2079365318 for P32 x P152 / February 23, 2013 2013 年 2 月 23 日)
2×10231-9 = 1(9)2301<232> = 11 × 1171 × 4336139609<10> × [35807760399877191799035887691222591262449831925530904039525935109583249625948656331426718547427746760817505738029336740400457675513251113149379608649141789427927729281486923326660479257192201620174196777862765579662879<218>] Free to factor
2×10232-9 = 1(9)2311<233> = 31 × 7103 × [90829408745963768148851235052885423242337404004668631609542537682850953481718310754656142565839967664730486436898539008960321172789325727884174337967147002856584905060560508281371342413246560971511355946828464120112810125662487<227>] Free to factor
2×10233-9 = 1(9)2321<234> = 11 × 359 × 13859 × 1782287929859<13> × [2050374071403966081792244116314643020503391832986952696296060790469936441251164251256337156481865382277768837542156938982426617616265363389172027815186076237639803244732471594869470911187358651929904737859400687739<214>] Free to factor
2×10234-9 = 1(9)2331<235> = 72 × 71 × [574877838459327392929002586950273066973268180511641276228801379706812302385743029606208680655360735843633227939062949123311296349525725783271054900833572865766024719747053751077895947111238861741879850531762000574877838459327392929<231>] Free to factor
2×10235-9 = 1(9)2341<236> = 11 × 4231 × 52701936412020105945433619<26> × 8153943775668070754613857920847454014671838749663844086503175695681914634585745478524828758517649571407271845601015548835430779018187239503152889418805888453034680885378180791859353609402056557080224254529<205>
2×10236-9 = 1(9)2351<237> = 17 × 47 × 809 × 138516311711<12> × 20249123156459507263<20> × 16509792015242501180521<23> × [6681684295692350573871201660739767375316809829479364006101107817367240075495441827499734253815748550300991692954764872270982814049639243938052741869687447140252726822989730924217<178>] Free to factor
2×10237-9 = 1(9)2361<238> = 112 × 192271 × 264761251 × 115792347481<12> × 454176619499<12> × 6709809624562729291<19> × 75870342686722243940865708418671161<35> × 12128009818557011040474758012831596650793206563110990869340025174803497576202785043087556119199386274175687178670547167774647774786292307032260979<146> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=3849124566 for P35 x P146 / February 24, 2013 2013 年 2 月 24 日)
2×10238-9 = 1(9)2371<239> = 69263 × 3177809 × [90865894598114589213853492814917344070209810342473719072214586278727444968688383650455956610609624012475898195882127033566954540365892004954157757114958588471863732933797130003333330338287437169112005823972714412040269211136073<227>] Free to factor
2×10239-9 = 1(9)2381<240> = 11 × 29 × 1129 × 469612421 × 745129424382149<15> × [1586989604211293719256393061868902054281317326541957631547618146925342000761304182939828812915912315130898474358317595428610817432820115267330006686703314259747406820634360631973978530605837328954148732709584329<211>] Free to factor
2×10240-9 = 1(9)2391<241> = 7 × 285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285713<240>
2×10241-9 = 1(9)2401<242> = 11 × 349 × 304771 × 93734266231<11> × 1471254785401<13> × 73840807917265651<17> × 9330299401088090082419381<25> × 423052294565063818989209209<27> × 772059816355857820858864679<27> × 873870402323341186158674119921819<33> × 630329912016843287920050857950107178395080345561250290567010329520494515121200711<81> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=1653429595 for P33 x P81 / February 24, 2013 2013 年 2 月 24 日)
2×10242-9 = 1(9)2411<243> = 367 × 2089 × 55681 × 8640887 × [542200781636152375697917357160244885208982443376772500767620870435426981448720442377628460950319587737827925114356544698277803032734738702036128949581999850907360305461451405217869982518410631917571602023446963494367575735031<225>] Free to factor
2×10243-9 = 1(9)2421<244> = 11 × 579566051 × 313714341108261046473576454908988135645333342373744072497127996577877226597280767603452704964974185173903186716880664596038973617897749877316085551426099349255738552253782404832090797910076030629713647285703106481332154181304553640631<234>
2×10244-9 = 1(9)2431<245> = 178681 × 1056481 × 1411365834585499640863<22> × 75067219559759552114944199240002535137402423917105321547232473745026850857336652373386749186062194721966902540422840488666939766323276407166155629030634853566901145199984672399344419210465118398803498696275369937<212>
2×10245-9 = 1(9)2441<246> = 11 × 19 × 1121179553161615656525233026602389<34> × [853509856065954892791450465242003365556625174792592845194852266582146061652624839098609282178176257019876678419181170264627726312888244870313415872806694265695018945410736404889843774715430144254841370787683691<210>] (KTakahashi / GMP-ECM 6.4.3 B1=1000000, sigma=1118666610 for P34 / March 8, 2013 2013 年 3 月 8 日) Free to factor
2×10246-9 = 1(9)2451<247> = 7 × 607 × 33870311327<11> × [13897096588597170589922902162273587959247121466827309875950342328819242888206475924915199880370841311217937441530763328015844048748530490449638099523109014265365985566549847711459998328243015395105968262006080191613009254405866281617<233>] Free to factor
2×10247-9 = 1(9)2461<248> = 11 × 31 × 37878459991<11> × 1548400500096822345304322717655299489084050863699033760825317673908977609624510376905380352073433016063028274576417025698679520172707062493755240768073882041114076449962842539650388149567851657854820332327876134605311609933711173111261<235>
2×10248-9 = 1(9)2471<249> = 983 × 219703769 × 404861470920204441079<21> × 31154558996803410256841018564527<32> × [73419414006257883306928527139956241706530545679838251648298358964776109815168325979328191393299261043368539465660172592849686184201910068717889788451272100227483009016068420334633065201<185>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3351234005 for P32 / March 8, 2013 2013 年 3 月 8 日) Free to factor
2×10249-9 = 1(9)2481<250> = 11 × 2699 × 166446777059<12> × 2796132883591<13> × 1186656896729788030226845245557932895809<40> × 17249651805609900313140937875873892656269<41> × 27702959464879963162109317423046198060749<41> × 594462149213050964205884891166673538623249<42> × 429383502452797800283861528254208060163917424733094624319531<60> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3989451853 for P40, B1=3000000, sigma=3857853388 for P41(2770...) / March 13, 2013 2013 年 3 月 13 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1078907450 for P41(1724...), Msieve 1.50 gnfs for P42 x P60 / March 27, 2013 2013 年 3 月 27 日)
2×10250-9 = 1(9)2491<251> = 2543 × 13171079344375766257<20> × 85278490159880029079594718311362273<35> × [7002010647500233894961094521060434564973766360115262045842386600910571941754951224197352039408668660352822470833468741726325288609709053617284094317157721301633952077261193920920031715479448617<193>] (KTakahashi / GMP-ECM 6.4.3 B1=1000000, sigma=3306969877 for P35 / March 8, 2013 2013 年 3 月 8 日) Free to factor
2×10251-9 = 1(9)2501<252> = 11 × 3479550778619<13> × 434127710531353409<18> × 9471996598096448989<19> × [1270735288406997147462761946385157011326986768173809549808692874815957704176926728539832956882172826851214224267903294286965674967541420263658243699947084820864232951683672732035364083005626732879970699<202>] Free to factor
2×10252-9 = 1(9)2511<253> = 7 × 17 × 23 × 2801 × 5569 × 69031 × 6437329607927<13> × [105418045543912644605647256608094957319644839840839255469744737596895844729054658307289307123287528514416561353403959666055085047082947719866282150448202620002023057461845236469950211763714700116117506748402521326648981850231<225>] Free to factor
2×10253-9 = 1(9)2521<254> = 11 × 2861 × 146047441 × 6418052236286452639<19> × 677988384430458787830340882824964629374923394530590759145705122694684397786888383770941426990707460432059126469793491634644239656761484317517870250762172958282657543769586371815109565522946589047688817032784186478913345079<222>
2×10254-9 = 1(9)2531<255> = 449 × 354031 × 1653448463861271791768367734608857167<37> × 20334292653330078457898777272167556873<38> × [37421623947027132897210729680572240068509381546126060412601661240912591900144520595914578956988961448962411384175895508330091596150017002514755038724832579252133755474148479<173>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1346847334 for P38 / January 3, 2016 2016 年 1 月 3 日) (Cyp / GMP-ECM 6.4.4 B1=11000000, sigma=56109252 for P37 / April 3, 2017 2017 年 4 月 3 日) Free to factor
2×10255-9 = 1(9)2541<256> = 11 × 9419449909<10> × 3583937936941<13> × 3936234234259<13> × 126985727337543105060894659<27> × 701518139464301201735603534389<30> × 15359480924760300113244204589288451765747744672842035510135941307506756142314010619194229898374697566708033513294628480477333286880276107158204106028154865010031561<164> (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=4119460737 for P30 x P164 / January 3, 2016 2016 年 1 月 3 日)
2×10256-9 = 1(9)2551<257> = 151 × 199 × 223 × 487 × 9929 × 11433625562699084002500881<26> × [53985443248521204543481246597193045469654235264114338866169785725971295213722388415705822235181743107560241768441378812679762848917534026321529477085436651400636435842096033617937124797319175732352928000050497772692391<218>] Free to factor
2×10257-9 = 1(9)2561<258> = 11 × 1687683839<10> × 10773237120402491344933604108428143701731458116912252910529777361823858655899482238164740652103748788589414120817339995763378177482102547892076969862966248276186650254353820246649774420111740975308242068091630175396742767421962507861532104069749179<248>
2×10258-9 = 1(9)2571<259> = 7 × 569 × 1399 × 67273 × 15350826363552752506514202090047017<35> × [347559705228016422973215656545677177907601564318713720558782349307797786582371155225540622932683166276299353344423806506212968264130043266858532429705713658003250665522820255897882673085150647401051027673884419103<213>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=392809040 for P35 / January 3, 2016 2016 年 1 月 3 日) Free to factor
2×10259-9 = 1(9)2581<260> = 112 × [165289256198347107438016528925619834710743801652892561983471074380165289256198347107438016528925619834710743801652892561983471074380165289256198347107438016528925619834710743801652892561983471074380165289256198347107438016528925619834710743801652892561983471<258>] Free to factor
2×10260-9 = 1(9)2591<261> = 64183921 × 784668634433<12> × 10752149730337455534186481475497<32> × [369336436425916207885973250699379218705847119268347217376326741678389076230815160947573060707129188929013022071324485186106728324213404985202241074980428266595651887069305951469911758869860776892442470957467471<210>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=2750592195 for P32 / January 3, 2016 2016 年 1 月 3 日) Free to factor
2×10261-9 = 1(9)2601<262> = 11 × 149 × 2671 × 14731 × 22811 × [1359566954268198523363938087519273204877651503652803999264784371771680069036358397387780445475460800028836891680453332728030389193758682741453389076629820872475492403967360114157873503209270125271431823879735300980285826584053706207401018404860679<247>] Free to factor
2×10262-9 = 1(9)2611<263> = 31 × 6664753 × 33205956919<11> × 302399086562383<15> × [9640238264789281228505954077997726963105534051424596036589373702609437236231423725659130042158407054149634740637101908857482966860506782090714912854461650475589882645895868490744133277551835475226805739260791410059738257771646081<229>] Free to factor
2×10263-9 = 1(9)2621<264> = 11 × 19 × 334330410011042651<18> × 922116385565207219<18> × 39342206138861604053894048521182809<35> × 78897525007002763405113174315057366900952737584003113661896841415801287132227676009375664159476457154281576145997303451260190374016123190279810828902090878766699583227801241896321799374918719<191> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=766980720 for P35 x P191 / January 4, 2016 2016 年 1 月 4 日)
2×10264-9 = 1(9)2631<265> = 7 × 31271 × 5651863840077911<16> × 181376534143927438439961518553578163439<39> × [8912866397740866047966769631312252895197276745374456406463992262745847277183619958329145396144893039122525228666099111873106106854938389633459032443713743945329547575551533718752813667579624556265365340607<205>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2273066438 for P39 / August 12, 2016 2016 年 8 月 12 日) Free to factor
2×10265-9 = 1(9)2641<266> = 11 × 173429 × 85518997384056450449159<23> × 440538337932835334200971885532314841<36> × 255528239767038244756928354591633703783019<42> × 1089006263704776347153460561204591640159923219694222261727328110076120356793753601889393048089264075471835910248292886450731394040973022627434103876990989074749<160> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=890808902 for P36 / January 4, 2016 2016 年 1 月 4 日) (Cyp / GMP-ECM 6.4.4 B1=11000000, sigma=1964691542 for P42 x P160 / April 2, 2017 2017 年 4 月 2 日)
2×10266-9 = 1(9)2651<267> = 4622408794902407<16> × [43267484308302637606957949575287584916621603406837549542453113338820701748443157491382328738636902755501483345247411477398924131355152720271540461931268986411933809543320552693514266017879999677415584964184895114498348142942480120976445455739155204113<251>] Free to factor
2×10267-9 = 1(9)2661<268> = 11 × 29 × 9857209 × [636041345627248870665737553157994240321870300337206446577595739804734817140598463723988158562579836565620769956346361251714243131226761492027073375918567850405896987880268095408800709025563538746173177341339612746500212628144812180077026903064717552606043921<258>] Free to factor
2×10268-9 = 1(9)2671<269> = 17 × 1831676627311<13> × 44588204437222463730384574559564152831<38> × [14404967634934445974752362587561000149181450606591082149586762425422889889819127011402351328984201320680136248082301724606807316049891089702257182735991655590084271716152515519979931984467581881721711104457882999396503<218>] (Cyp / GMP-ECM 6.4.4 B1=11000000, sigma=426321629 for P38 / April 2, 2017 2017 年 4 月 2 日) Free to factor
2×10269-9 = 1(9)2681<270> = 11 × 71 × 139 × 4633199622217279<16> × 3673340270406636896404847401<28> × [108248525490368228569256491374188291681740598369289885016863947069938759247104026428167579040699604626242179409129290926446728282451576230502681547390956339928317543155066570924380309688809474205004118999357545772971418831<222>] Free to factor
2×10270-9 = 1(9)2691<271> = 7 × 300176549781749384010709969711<30> × 951820806528761795756661862318094874357966547078573823776067287281851512393983512773791575073732645369191631368883570215506607471544446233814315738796161260238523740898422454942576966899509190570770818354191371626336489266475020888154782783<240> (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=1828521062 for P30 x P240 / January 4, 2016 2016 年 1 月 4 日)
2×10271-9 = 1(9)2701<272> = 11 × 59 × 89 × 2450009 × 1182429877859735774079630829<28> × 119523201500793948527674534090914971306763109162702840258747843941556387069245067069221647832992144795855456532038896426944841621329411057020914120551770788807011597650022640926377718933661239959176603339874115703772815342568025053771<234>
2×10272-9 = 1(9)2711<273> = 2753 × 11421199 × 56804159 × [111977805281966630603635195742694808826276883265444379712565911066119303364205610204131925158567936078236746136505444956063655340706165024399514463367901550434229037940833030240102540929307402201983676850604824671185339405555361635350194819800096050363367<255>] Free to factor
2×10273-9 = 1(9)2721<274> = 11 × 379 × 22739 × 657445181 × [32089813456592198533977501143202386691802484820642938623386798724329170783372706208189980629420010469722721897890201150722637457433954726755472410071578407379156341607261144831416683971878315800276701439244238045155319480040545959322707066614761205388309321<257>] Free to factor
2×10274-9 = 1(9)2731<275> = 23 × 72953 × 11919526508728967250504940941726030875149515560643868982948521352937775899790156735813826531554860514720913226442992778554864686555191281581530455284194290665997583911976680638338322648471112133541607193195857487757156334721759512825112535229650537362053829773666070889<269>
2×10275-9 = 1(9)2741<276> = 11 × 1229 × 2741 × 14419 × 9331515058239601891<19> × 375371203915038209221914289<27> × [106863190368292113107022518944706220107847985325413306944165534070548104417215875104276744506702119760264126851197544012527215041825302928758459080467374517435804096439699240743555886657214206943663394726230321692032109<219>] Free to factor
2×10276-9 = 1(9)2751<277> = 74 × 3572377 × 3749959 × 100039046510106553<18> × 621562046391327781485236682416069729656488096617848120257632062764638376513239357563888476860720560224358992389008021689528168122831333369859394072597608607754141530640939041206624762654658389500555894675110490155419118635456999820802935042529<243>
2×10277-9 = 1(9)2761<278> = 11 × 31 × 61 × 1049 × 2729 × 8656987323900911<16> × 38797163603269008861840704176698202186758028401979719960245863357591331925989877664254499128120290467122221534489908153908628440967734135752247086808239216831700066907376035984367079365880850660743354002016236427559648664023927852741544175822082853561<251>
2×10278-9 = 1(9)2771<279> = 2578323914304679<16> × 77569772707916682349448453798288896662341990461720669859990837453686919352464309144444652098192402618104420592485170285823990849617288346622166963246614324271820252874242269148238889459481514702490802550869799196845032423844808029087453026084628674574501665991729<263>
2×10279-9 = 1(9)2781<280> = 11 × 585694036259<12> × 786490671059894220121891708130099651<36> × 47195812448489109345659636640323209151<38> × [8363141913561617862857864576766178538724767154188272111377304892946759235669359319501111990873938666396194892553523172439741475874539621331011484790467567010260502225755735425669480119421075459<193>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=693823286 for P36 / January 18, 2016 2016 年 1 月 18 日) (Cyp / GMP-ECM 6.4.4 B1=11000000, sigma=3626901239 for P38 / April 2, 2017 2017 年 4 月 2 日) Free to factor
2×10280-9 = 1(9)2791<281> = 719 × 40390295291150316130355729239063<32> × 688690475827929879238415246685092101374123730362160882562857597595142894167021900554972883431737169464985276009726218657854850951315237050276711151233030621040918049128689262583641369659423920623879654707526011301958782465273252785601154715116303<246> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3354912037 for P32 x P246 / January 5, 2016 2016 年 1 月 5 日)
2×10281-9 = 1(9)2801<282> = 112 × 19 × 1282031 × 7054809522983242966333083239<28> × [9618496808174956865098855220504230194879079466704690398458549120738387668931162564210615290601062638945969410235674557156721957945583470305368185403278786845662139456286806399636701346992729834817219832451584055933091073545460043048959069574701<244>] Free to factor
2×10282-9 = 1(9)2811<283> = 7 × 47 × 9161 × 274081 × 81733135731857<14> × 156826077774521<15> × 11082453446713001558366975510255201<35> × 17043544807155358749335810758859705084041447801183270506147065596120315931349414784507810014937936569478211073812085911586146711948386971179438259475644052381879609710164528789312818918579581137020965414349327<209> (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=3457518148 for P35 x P209 / January 5, 2016 2016 年 1 月 5 日)
2×10283-9 = 1(9)2821<284> = 11 × 11436899 × 158975069919024219923440944803466235193489233242491533921754648544314169585495318108677726525186750200541089137727090025173622834142525712766911889156476609771423339331913150742887719667876596778390874850063656400059300880581194414515841941230588975051875353784114191983492919<276>
2×10284-9 = 1(9)2831<285> = 17 × 223125019548577<15> × 34177366217590244071<20> × 408172614501710440917234632822958168913<39> × 3779639225709002256008119838674781599801379546411613844476933255227134229001516838595851658439623662873776898211463474624888867094120859542436084314410169706666760667833952305869483318679787539613294922839654513<211> (Cyp / GMP-ECM 6.4.4 B1=11000000, sigma=563419499 for P39 x P211 / April 1, 2017 2017 年 4 月 1 日)
2×10285-9 = 1(9)2841<286> = 11 × [181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181<285>] Free to factor
2×10286-9 = 1(9)2851<287> = 449 × 1319 × 340903 × 610271 × 1168039 × 4402954231223333297<19> × 31563400673045295263863433988414310210224344473390465421098441075631573751974481752730464849453538316063588982404086966606970901733914353785748343201326902577750934399271288555319147359501014018780140886118509061394634982777511906889758208222159<245>
2×10287-9 = 1(9)2861<288> = 11 × 109 × 191 × 221989 × [3934105394751703444626328560037497678508257070975479528136563838767847241953458725862319291253006661365872597168348712170926542303990480883111013577758062003783628577935173166544748284782769818178714408708046409266214686164025834763335877484606423362890121143224312778751420091<277>] Free to factor
2×10288-9 = 1(9)2871<289> = 7 × 742838020907687<15> × 3571748270128343<16> × 5161450180596084997182863<25> × [20863407876096062245370164763338799314202683894676621862525526254887551721307795856234066019555163460090305776143176679761505287991313799830247005908970981513010331632483532539382269411663958385204852264864264663105792222025060026911<233>] Free to factor
2×10289-9 = 1(9)2881<290> = 11 × 132151 × 179360039 × 1655037869610109<16> × 339796914837353671<18> × 309856047284156248609<21> × 10474541799871706797789<23> × 1862887011933096493737922871<28> × [22559645693525217481918050095091087858337438574274274084764517909645708462754711288851821974727105508333705340921806953973930718659286616697674076431602724857785235901271741<173>] Free to factor
2×10290-9 = 1(9)2891<291> = 7079 × 937943 × 108363613659104859450826605721009<33> × 277970147504092593147260198465280772647454878134673618726060775486789146622975697958098312688905566704093381638502602420142864038691211474526209145849107791460386259281533964566044085268733353691727214912582324889437362734633762836141381761905560167<249> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=516802799 for P33 x P249 / January 5, 2016 2016 年 1 月 5 日)
2×10291-9 = 1(9)2901<292> = 11 × 80586301189<11> × 82436786869203409<17> × [27368754369362303011873248004420190784880914061468369772632021766648551191221783146854658019120548489971955852650126270709810398181317903342020100332603256136747565186370584993194160607154284644064133882466052437732872941833629348815383007089173886992191707360881<263>] Free to factor
2×10292-9 = 1(9)2911<293> = 31 × 366521 × 794023 × 764014703 × 17248534783<11> × 70864818887<11> × 1948394423089<13> × 15546105351487<14> × [78370616916986418193670918983956346747390686079389966668047541113298907181198987048207305462383319601783969175305257482076693809281576665165870979744116559887470884561267161562931498646935056424140593553084698831608428852063<224>] Free to factor
2×10293-9 = 1(9)2921<294> = 11 × 803729 × 1113401 × 10835333140274411<17> × 1875140423097031903302298890663309938156005050475998290790156528883980947898603303276397410270795585475159192488401237111134291320370858330210075115052510913880120609801872349886062104140529374830237721583718275246768290142976528870333784964448015427831820612440599<265>
2×10294-9 = 1(9)2931<295> = 7 × 2663 × 7559 × 125641 × 1363489 × 110638585460240037999677689897<30> × [748870643815706531203720030776092178701178119690704725873169049181682826951130424570303039528278820553094150528586309118932782905164128846396866284044843815446450617935730579314695195275582024006235139099043054916169206316144634519776866579324913<246>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=284310333 for P30 / January 5, 2016 2016 年 1 月 5 日) Free to factor
2×10295-9 = 1(9)2941<296> = 11 × 29 × 479 × 447469363521059399993792381<27> × [292509848543355357576368193049005039234682827937152143563823182267982958965959888355302987336465312737285403510698120717407705831449531423565017120953710220407823840236355898351891267987943348791756337776683951018158899134972485231296862543379444381975189689079011<264>] Free to factor
2×10296-9 = 1(9)2951<297> = 23 × 1500898521839<13> × 3461188108129<13> × 182424328340719279728653534822689313<36> × 15733159088611012458258732031016608991<38> × 241266318091160506009346817765229924264153216438847<51> × 2417298264291629073059405689900752859062131460731202611780379874748487275435903860466868667744889036463985426462233537412974245119832624094802422607<148> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2421418283 for P36 / January 5, 2016 2016 年 1 月 5 日) (Cyp / GMP-ECM 6.4.4 B1=11000000, sigma=986272515 for P38 / April 1, 2017 2017 年 4 月 1 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1776300619 for P51 x P148 / April 4, 2017 2017 年 4 月 4 日)
2×10297-9 = 1(9)2961<298> = 11 × 6221 × 4021468606549268990149<22> × 70790058192958480233691<23> × 6208669870220788584938325313331<31> × 16535662100820857887831410039339185445719409444185614719323677936388316909733728104411452368814335522758714796744833221790953896034715942189419181082056485078881371516964532183143274568805546591537272466291581612379109<218> (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=775124140 for P31 x P218 / January 6, 2016 2016 年 1 月 6 日)
2×10298-9 = 1(9)2971<299> = 4601127202861774463<19> × 1122400976708521425147599<25> × 47492189663501875031533687<26> × 3375159998549829799576944166951<31> × 927386998343108617526569637695650205703<39> × [26051945324820768022769051561424555859392668686806684077528855636251137069115679643692747826733500155652667440986752851589738165596062584614392848589051823371713<161>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=82741410 for P31 / January 6, 2016 2016 年 1 月 6 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=26081982 for P39 / January 18, 2016 2016 年 1 月 18 日) Free to factor
2×10299-9 = 1(9)2981<300> = 11 × 19 × 131 × 91331188914514166086915750148288352458019389<44> × [79982192083610693268830657361526890003540951052587911453259382997378522968048407505366803899295110813194414661526724727730215962879702332728672507860994979845306074861135671443001075798685797063024745931425972330693311059885459636873442977006004731761<251>] (Markus Tervooren / GMP-ECM 6.4.4 B1=43000000, sigma=3914020616 for P44 / January 22, 2016 2016 年 1 月 22 日) Free to factor
2×10300-9 = 1(9)2991<301> = 7 × 17 × 253321 × 2715487 × 480856246517384364439<21> × 246686635936416232016946462606733391<36> × 205969648511358802550356092907539098757808461832709882908212534676571535784095579548409117347831130039122817219331638922290430171511836255644966758351985556465263468041611227114608166559550129222958275864726084690624711581159455743<231> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3305585675 for P36 x P231 / January 6, 2016 2016 年 1 月 6 日)
plain text versionプレーンテキスト版

4. Related links 関連リンク