Table of contents 目次

  1. About 588...889 588...889 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 588...889 588...889 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 588...889 588...889 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 588...889 588...889 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

58w9 = { 59, 589, 5889, 58889, 588889, 5888889, 58888889, 588888889, 5888888889, 58888888889, … }

1.3. General term 一般項

53×10n+19 (1≤n)

2. Prime numbers of the form 588...889 588...889 の形の素数

2.1. Last updated 最終更新日

December 11, 2018 2018 年 12 月 11 日

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

  1. 53×101+19 = 59 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  2. 53×104+19 = 58889 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  3. 53×108+19 = 588888889 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  4. 53×1013+19 = 5(8)129<14> is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  5. 53×1016+19 = 5(8)159<17> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 3, 2004 2004 年 12 月 3 日)
  6. 53×1044+19 = 5(8)439<45> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 3, 2004 2004 年 12 月 3 日)
  7. 53×10439+19 = 5(8)4389<440> 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 / June 3, 2006 2006 年 6 月 3 日)
  8. 53×10608+19 = 5(8)6079<609> 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)
  9. 53×101201+19 = 5(8)12009<1202> 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 12, 2006 2006 年 9 月 12 日)
  10. 53×102725+19 = 5(8)27249<2726> 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: Ray Chandler / Primo 4.0.1 - LX64 / January 1, 2013 2013 年 1 月 1 日)
  11. 53×105210+19 = 5(8)52099<5211> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 21, 2004 2004 年 12 月 21 日)
  12. 53×1059389+19 = 5(8)593889<59390> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / May 18, 2010 2010 年 5 月 18 日)
  13. 53×10118216+19 = 5(8)1182159<118217> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / June 10, 2010 2010 年 6 月 10 日)
  14. 53×10198529+19 = 5(8)1985289<198530> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / July 25, 2010 2010 年 7 月 25 日)

2.3. Range of search 捜索範囲

  1. n≤175000 / Completed 終了 / Serge Batalov / June 14, 2010 2010 年 6 月 14 日
  2. n≤200000 / Completed 終了 / Serge Batalov / April 2, 2011 2011 年 4 月 2 日

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

Cofactors are written verbosely to clarify that they are integers. 補因子はそれらが整数であることを明確にするために冗長に書かれています。

  1. 53×103k+19 = 3×(53×100+19×3+53×103-19×3×k-1Σm=0103m)
  2. 53×106k+3+19 = 13×(53×103+19×13+53×103×106-19×13×k-1Σm=0106m)
  3. 53×106k+5+19 = 7×(53×105+19×7+53×105×106-19×7×k-1Σm=0106m)
  4. 53×1015k+2+19 = 31×(53×102+19×31+53×102×1015-19×31×k-1Σm=01015m)
  5. 53×1016k+14+19 = 17×(53×1014+19×17+53×1014×1016-19×17×k-1Σm=01016m)
  6. 53×1018k+2+19 = 19×(53×102+19×19+53×102×1018-19×19×k-1Σm=01018m)
  7. 53×1022k+12+19 = 23×(53×1012+19×23+53×1012×1022-19×23×k-1Σm=01022m)
  8. 53×1028k+7+19 = 281×(53×107+19×281+53×107×1028-19×281×k-1Σm=01028m)
  9. 53×1028k+10+19 = 29×(53×1010+19×29+53×1010×1028-19×29×k-1Σm=01028m)
  10. 53×1033k+15+19 = 67×(53×1015+19×67+53×1015×1033-19×67×k-1Σm=01033m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 16.19%. 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 16.19% です。

3. Factor table of 588...889 588...889 の素因数分解表

3.1. Last updated 最終更新日

May 24, 2021 2021 年 5 月 24 日

3.2. Range of factorization 分解範囲

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

n=203, 211, 213, 214, 216, 218, 223, 224, 227, 228, 229, 232, 234, 235, 239, 241, 243, 244, 245, 246, 248, 250, 254, 256, 258, 259, 260, 261, 262, 263, 264, 265, 266, 268, 269, 270, 271, 273, 275, 276, 277, 280, 281, 282, 287, 288, 291, 292, 293, 294, 295, 296, 297 (53/300)

3.4. Factor table 素因数分解表

53×101+19 = 59 = definitely prime number 素数
53×102+19 = 589 = 19 × 31
53×103+19 = 5889 = 3 × 13 × 151
53×104+19 = 58889 = definitely prime number 素数
53×105+19 = 588889 = 7 × 84127
53×106+19 = 5888889 = 33 × 218107
53×107+19 = 58888889 = 281 × 209569
53×108+19 = 588888889 = definitely prime number 素数
53×109+19 = 5888888889<10> = 3 × 13 × 191 × 197 × 4013
53×1010+19 = 58888888889<11> = 29 × 2030651341<10>
53×1011+19 = 588888888889<12> = 7 × 743 × 113226089
53×1012+19 = 5888888888889<13> = 3 × 23 × 135197 × 631273
53×1013+19 = 58888888888889<14> = definitely prime number 素数
53×1014+19 = 588888888888889<15> = 17 × 83 × 417355697299<12>
53×1015+19 = 5888888888888889<16> = 32 × 13 × 67 × 751229606951<12>
53×1016+19 = 58888888888888889<17> = definitely prime number 素数
53×1017+19 = 588888888888888889<18> = 72 × 31 × 89 × 193 × 22569829103<11>
53×1018+19 = 5888888888888888889<19> = 3 × 329007751 × 5966312213<10>
53×1019+19 = 58888888888888888889<20> = 35153 × 1675216592862313<16>
53×1020+19 = 588888888888888888889<21> = 19 × 953 × 25849 × 167677 × 7503599
53×1021+19 = 5888888888888888888889<22> = 3 × 13 × 47 × 253427327 × 12677028079<11>
53×1022+19 = 58888888888888888888889<23> = 12517 × 4704712701836613317<19>
53×1023+19 = 588888888888888888888889<24> = 7 × 71 × 2124609547<10> × 557696402171<12>
53×1024+19 = 5888888888888888888888889<25> = 32 × 654320987654320987654321<24>
53×1025+19 = 58888888888888888888888889<26> = 349 × 168736071314867876472461<24>
53×1026+19 = 588888888888888888888888889<27> = 5113 × 111360113993<12> × 1034255646521<13>
53×1027+19 = 5888888888888888888888888889<28> = 3 × 132 × 13327 × 90011 × 118411 × 81772140781<11>
53×1028+19 = 58888888888888888888888888889<29> = 2683 × 207457 × 105799738467398271419<21>
53×1029+19 = 588888888888888888888888888889<30> = 7 × 223 × 16561 × 16840969 × 1352623173182761<16>
53×1030+19 = 5888888888888888888888888888889<31> = 3 × 17 × 12841 × 4536807547<10> × 1982047149354257<16>
53×1031+19 = 58888888888888888888888888888889<32> = 120078113 × 61180675733<11> × 8015954369141<13>
53×1032+19 = 588888888888888888888888888888889<33> = 31 × 18996415770609318996415770609319<32>
53×1033+19 = 5888888888888888888888888888888889<34> = 35 × 13 × 3287077 × 567118554870944149877123<24>
53×1034+19 = 58888888888888888888888888888888889<35> = 23 × 97 × 409 × 1601 × 40310589560442874257537191<26>
53×1035+19 = 588888888888888888888888888888888889<36> = 7 × 281 × 293 × 11354969 × 16386399377<11> × 5491511425363<13>
53×1036+19 = 5888888888888888888888888888888888889<37> = 3 × 4957 × 395998176914053452282219681856559<33>
53×1037+19 = 58888888888888888888888888888888888889<38> = 326405309 × 180416455447080025554636088621<30>
53×1038+19 = 588888888888888888888888888888888888889<39> = 19 × 29 × 1068763863682193990723936277475297439<37>
53×1039+19 = 5888888888888888888888888888888888888889<40> = 3 × 13 × 61 × 7329229 × 595871357 × 12029432117<11> × 47117581591<11>
53×1040+19 = 58888888888888888888888888888888888888889<41> = 149 × 3079 × 185267 × 692850179375183056547936753777<30>
53×1041+19 = 588888888888888888888888888888888888888889<42> = 7 × 424001327250702907<18> × 198412077321733576592461<24>
53×1042+19 = 5888888888888888888888888888888888888888889<43> = 32 × 229 × 51748407725491<14> × 55215165353052770459937839<26>
53×1043+19 = 58888888888888888888888888888888888888888889<44> = 4013 × 14674529999723122075476922224991001467453<41>
53×1044+19 = 588888888888888888888888888888888888888888889<45> = definitely prime number 素数
53×1045+19 = 5888888888888888888888888888888888888888888889<46> = 3 × 13 × 4667681 × 32349500961430525597399897507381287871<38>
53×1046+19 = 58888888888888888888888888888888888888888888889<47> = 17 × 3257 × 9281 × 1195673 × 2367931 × 330532363747<12> × 122454980248841<15>
53×1047+19 = 588888888888888888888888888888888888888888888889<48> = 7 × 31 × 317 × 2663 × 2216444129<10> × 1450395385487912148927777280163<31>
53×1048+19 = 5888888888888888888888888888888888888888888888889<49> = 3 × 67 × 501271 × 2507689 × 13773458719<11> × 1692185759629789241610049<25>
53×1049+19 = 58888888888888888888888888888888888888888888888889<50> = 10752283 × 3298799699441195489<19> × 1660262380176485445205147<25>
53×1050+19 = 588888888888888888888888888888888888888888888888889<51> = 739 × 3329 × 239372980092884845924419833288913837876474419<45>
53×1051+19 = 5(8)509<52> = 32 × 13 × 1459 × 1165527063251<13> × 3765014076529339<16> × 7861460561971407767<19>
53×1052+19 = 5(8)519<53> = 167 × 14011 × 78134629 × 322109995359186827336502074359471996393<39>
53×1053+19 = 5(8)529<54> = 7 × 515067336524795608742933<24> × 163332011489208868386559634819<30>
53×1054+19 = 5(8)539<55> = 3 × 5387 × 8707635732559824321347<22> × 41847052807226106255642564467<29>
53×1055+19 = 5(8)549<56> = 83 × 2659762210397118455939<22> × 266754931187012601304719940252097<33>
53×1056+19 = 5(8)559<57> = 19 × 23 × 479 × 10039 × 2541639593<10> × 2591150823447679301<19> × 42551933205159487009<20>
53×1057+19 = 5(8)569<58> = 3 × 13 × 2221 × 1101236552042737127660087<25> × 61736154855446249525095147613<29>
53×1058+19 = 5(8)579<59> = 71 × 499 × 3965856561418753<16> × 913040169703852921<18> × 459036879291487520557<21>
53×1059+19 = 5(8)589<60> = 72 × 592 × 347769748425739267<18> × 9927535658504333494476174160217048443<37>
53×1060+19 = 5(8)599<61> = 33 × 409156351 × 533065160425124777181914815781771882809595353321157<51>
53×1061+19 = 5(8)609<62> = 89 × 1866239 × 1103332147509852948581<22> × 321343722490917900971861572396339<33>
53×1062+19 = 5(8)619<63> = 17 × 31 × 3847 × 172049 × 257305087109999<15> × 6561453166308501629891899557641911631<37>
53×1063+19 = 5(8)629<64> = 3 × 13 × 281 × 829 × 148512813557<12> × 21926131499689<14> × 199059066204226788437870936206463<33>
53×1064+19 = 5(8)639<65> = 359 × 49019191643784740097637<23> × 3346360816993614953790702346101339322483<40>
53×1065+19 = 5(8)649<66> = 7 × 109 × 257 × 5748979083815524879870233019<28> × 522378110656275874065734192259041<33>
53×1066+19 = 5(8)659<67> = 3 × 29 × 728264322721541<15> × 92944794796829466582075448827225219628992044839267<50>
53×1067+19 = 5(8)669<68> = 47 × 12799 × 49282981339841092466869<23> × 1986380718175649059629509064098448911077<40>
53×1068+19 = 5(8)679<69> = 4271 × 29759 × 3730172089977087017722556953<28> × 1242100072305533309985810443475217<34>
53×1069+19 = 5(8)689<70> = 32 × 13 × 16547659 × 55466237720565729836683461223<29> × 54838078261045641511833984944681<32>
53×1070+19 = 5(8)699<71> = 1129 × 2741 × 88195945999353907520556011<26> × 215765378670882693727673163957842094791<39>
53×1071+19 = 5(8)709<72> = 7 × 10949 × 212633 × 26514500951240233781<20> × 1362845863711392305683905690435328510601951<43>
53×1072+19 = 5(8)719<73> = 3 × 719 × 2171293 × 92347603165931<14> × 29425049589630370660657<23> × 462723920953204436611363667<27>
53×1073+19 = 5(8)729<74> = 9697 × 493408889 × 71486859077<11> × 172172101114549247911098526761304968708170293928429<51>
53×1074+19 = 5(8)739<75> = 19 × 2237 × 13147 × 21269 × 49549587224890628757013562795184520972109482524621376411816441<62>
53×1075+19 = 5(8)749<76> = 3 × 13 × 283 × 142117205582990823131<21> × 3754357786990020696302411950707766140279854825165687<52>
53×1076+19 = 5(8)759<77> = 2725732791139691371<19> × 21623846397854740432531045757<29> × 999118805914652301317447479687<30>
53×1077+19 = 5(8)769<78> = 7 × 31 × 233 × 4013 × 2902341725781357583013967727100136759054013957855304987577821344336573<70>
53×1078+19 = 5(8)779<79> = 32 × 17 × 23 × 151 × 1128667 × 419055457115109314790079851167<30> × 23431485253274463520022226409514083229<38>
53×1079+19 = 5(8)789<80> = 89209 × 10682802835522217<17> × 562354460792178941012377<24> × 109882702364219365064229799447570369<36>
53×1080+19 = 5(8)799<81> = 383 × 23433124166539<14> × 111566858321982467377<21> × 588124387864359253689921572029875156845777861<45>
53×1081+19 = 5(8)809<82> = 3 × 13 × 67 × 2557 × 31209873851407<14> × 28240423755099153711251387017524961447270896517250076371121047<62>
53×1082+19 = 5(8)819<83> = 263 × 2925984664841200192944677627<28> × 76525392543354864447510303840891461792474968064843789<53>
53×1083+19 = 5(8)829<84> = 7 × 422309 × 550513 × 380607811 × 950735493016461960237611043590906229478901146570429830821240321<63>
53×1084+19 = 5(8)839<85> = 3 × 9873967 × 1573989528646067483<19> × 126304433483466176985753990087744404042099705449211168778983<60>
53×1085+19 = 5(8)849<86> = 52541 × 175067 × 6402222099829371983420008923940695394643962909226217786208391504574124299287<76>
53×1086+19 = 5(8)859<87> = 443 × 9001 × 36793 × 4013965836196383789993920220979544356972590115738433655970511795097974324411<76>
53×1087+19 = 5(8)869<88> = 33 × 13 × 811 × 2179 × 10120669987<11> × 938077880397239164142789661345371859926627002252542549894617367045613<69>
53×1088+19 = 5(8)879<89> = 1567 × 285465042967769505037<21> × 23809057250126505138035549<26> × 5529288246970863313600408377307539544159<40>
53×1089+19 = 5(8)889<90> = 7 × 60378491 × 1393327039706642005745506030069286212935115985707296444095083199859766733556275597<82>
53×1090+19 = 5(8)899<91> = 3 × 5897229313825441449973864698721439<34> × 332861901496860607555339372758486087133691279567835861517<57> (Makoto Kamada / GGNFS-0.70.3 / 0.29 hours)
53×1091+19 = 5(8)909<92> = 281 × 4495663 × 17881965103<11> × 30111325271<11> × 69102325406111<14> × 1252839726556988112044594452716952689183542349241<49>
53×1092+19 = 5(8)919<93> = 19 × 31 × 113 × 1028141 × 1364427553793<13> × 234565544709592041400347911<27> × 26888850934482632471969033477415652203202039<44>
53×1093+19 = 5(8)929<94> = 3 × 13 × 71 × 1223 × 173350526137<12> × 529702203487223703007275499<27> × 18937690026585875712463325605702669385128109458069<50>
53×1094+19 = 5(8)939<95> = 17 × 29 × 30135484293233944555519<23> × 3963768350951859104542916561001162854839415963409113623861314968382467<70>
53×1095+19 = 5(8)949<96> = 7 × 3560059 × 1568511667109<13> × 1061507705848988696999<22> × 14192771800152499469334783233046528884093250660012871183<56>
53×1096+19 = 5(8)959<97> = 32 × 83 × 3119 × 16822831 × 150244402704356279440314955928916906180494447100966813599707335530296503086087667083<84>
53×1097+19 = 5(8)969<98> = 18859 × 3500039190680569413326057<25> × 892158037428433240908641773985797204502720646531592898996726887174003<69>
53×1098+19 = 5(8)979<99> = 3037 × 162131461 × 17020649343187069<17> × 70265986427052411186864670575727394409480447078165445858328042905680733<71>
53×1099+19 = 5(8)989<100> = 3 × 13 × 61 × 67919261 × 99835297 × 104157208797321413909728207463<30> × 3504874880368197865600562776321431847683421350161921<52> (Makoto Kamada / GGNFS-0.70.8 / 0.40 hours)
53×10100+19 = 5(8)999<101> = 23 × 491 × 120331 × 174533 × 28263217 × 20134338577<11> × 100762164561348650916977<24> × 4330245346732795868373830798852378158636792907<46>
53×10101+19 = 5(8)1009<102> = 72 × 10139 × 12397859 × 89683691 × 48776640113<11> × 21855971169264413030077169549855570868975794347668860944302538475705467<71>
53×10102+19 = 5(8)1019<103> = 3 × 2043971 × 4195297 × 316008998813<12> × 1685837176619620275313<22> × 429694294822034983697840099134670328346957991604291524821<57>
53×10103+19 = 5(8)1029<104> = 17597 × 35327 × 660234879222823531615373589467<30> × 143479384203030468046198093958135532280512482215395035709729983593<66> (Max Dettweiler / GGNFS via factLat.pl snfs / 0.35 hours on Core 2 Duo E4500 (2.2Ghz), 32-bit Windows, Cygwin / April 25, 2009 2009 年 4 月 25 日)
53×10104+19 = 5(8)1039<105> = 191 × 1013 × 31153 × 1103029 × 3306427 × 234505819 × 139345437839<12> × 2107326162673<13> × 389015285048294938891940291366613890345426904005369<51>
53×10105+19 = 5(8)1049<106> = 32 × 132 × 89 × 3430934531<10> × 52617417479355293<17> × 240975105956071911351886484920661947365374400485205201468003727939096486007<75>
53×10106+19 = 5(8)1059<107> = 2539 × 23399 × 39246889775375307127821459821<29> × 25256206294607461185960920791380183401226405805343740583978930919848369<71>
53×10107+19 = 5(8)1069<108> = 7 × 31 × 197 × 2399 × 1225983469<10> × 4683737401610164689233282572782720186364392224422923334019148477770128316656093515198268831<91>
53×10108+19 = 5(8)1079<109> = 3 × 3919 × 43271 × 5340515626437476280999439<25> × 2167488090490173890462877355606207720161878119853999685328664851990789686133<76>
53×10109+19 = 5(8)1089<110> = 12917 × 14321 × 6102212322648969953669626693<28> × 52168823326169855172881182426610333087041113013430107512982132704223924289<74>
53×10110+19 = 5(8)1099<111> = 17 × 19 × 536777 × 394136903 × 5915033442876753729798779<25> × 1456909700384697444980506942454288599711450922395727730788657014714807<70>
53×10111+19 = 5(8)1109<112> = 3 × 13 × 4013 × 153359 × 15233720632293220949<20> × 16105875532236197082349346401140574946033826688551208176031097491275535009190077697<83>
53×10112+19 = 5(8)1119<113> = 386672227 × 184980971587742311<18> × 24261531333473826408839<23> × 33934786031848053077425615907366054681037300149686444192736313283<65>
53×10113+19 = 5(8)1129<114> = 7 × 47 × 289531175486154600675813449406456787961<39> × 6182186873256482269014449455225313046649108060530092150465438847951149881<73> (Ignacio Santos / GGNFS, Msieve snfs / 1.06 hours / April 25, 2009 2009 年 4 月 25 日)
53×10114+19 = 5(8)1139<115> = 34 × 67 × 1721 × 1979 × 5221883167<10> × 6805051639168721<16> × 163762338583210367191<21> × 127058407204914243037270087<27> × 430894409767738765705964965437967<33>
53×10115+19 = 5(8)1149<116> = 11558232263<11> × 40510266287<11> × 302477825779<12> × 206358822281429953398125923<27> × 2014931384907428956771142800140968401119017796125464078457<58>
53×10116+19 = 5(8)1159<117> = 22419653 × 17579751683282694343723<23> × 39077826451099586894123<23> × 38235021393388129958999552921046839773637940828761207704376784397<65>
53×10117+19 = 5(8)1169<118> = 3 × 13 × 59 × 131 × 3459575258879<13> × 1672766654677514777<19> × 922970064861157287036355835839364279<36> × 3657629278054723987235307833499770126426083567<46> (Makoto Kamada / Msieve 1.41 for P36 x P46 / April 24, 2009 2009 年 4 月 24 日)
53×10118+19 = 5(8)1179<119> = 6932155488143<13> × 8495032892671621964812576770049606021008482495810497303719449948733897693297086864008236375458477178231223<106>
53×10119+19 = 5(8)1189<120> = 7 × 281 × 122111145041<12> × 533710242503<12> × 35145772660259616219583<23> × 4113731018789437033473190175627<31> × 31773069460948353816154434410162725919869<41> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=1873602012 for P31 / April 22, 2009 2009 年 4 月 22 日)
53×10120+19 = 5(8)1199<121> = 3 × 653 × 1218916529<10> × 2466181058729646871397018515478744623642697180962412407297264085551470918726012673572586479243231255930837199<109>
53×10121+19 = 5(8)1209<122> = 7507 × 23914464969103<14> × 328024494814439443050208433302400111249720911942406219339353008265581105497789107040723813075935867904909<105>
53×10122+19 = 5(8)1219<123> = 23 × 29 × 31 × 273932137479115188362599<24> × 4502254408284188192537778277<28> × 23092598999104297688126348950481909095221768607019136768796877913559<68>
53×10123+19 = 5(8)1229<124> = 32 × 13 × 4423 × 11379693345176802860124888913795387531162646092181098587007095560867510524606010324602532003240421357837892618207638179<119>
53×10124+19 = 5(8)1239<125> = 83921329 × 701715399298417794228316962054889393957153477501397635026596026486769399098635448074099123107176828537699741252773641<117>
53×10125+19 = 5(8)1249<126> = 7 × 1433 × 18307 × 208997227 × 259096480001<12> × 59220205689122677232267433479807231450569316879608139454156923439896513496829464464691482884307671<98>
53×10126+19 = 5(8)1259<127> = 3 × 17 × 317 × 2142846283<10> × 169985901877301709594320880512772392533385220857440244277987409689411908709696223955706253512283951867154937537149<114>
53×10127+19 = 5(8)1269<128> = 11597 × 19883711 × 111454369586241493795989262133<30> × 2291359122139660070004532148593740477997269226745862992180785711814881329696447413242999<88> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=2191162748 for P30 / April 22, 2009 2009 年 4 月 22 日)
53×10128+19 = 5(8)1279<129> = 19 × 71 × 673 × 941 × 5903 × 921784063808351<15> × 12421340045339931728781770009<29> × 10198734659319124820400947026165352095142553000316341381362596248248760401<74> (Ignacio Santos / GGNFS, Msieve snfs / 2.59 hours / April 25, 2009 2009 年 4 月 25 日)
53×10129+19 = 5(8)1289<130> = 3 × 13 × 14643271666013<14> × 989072199016289802344803962923<30> × 10931462574095153368015708621042439<35> × 953727634216619886094497007674560185474261384299191<51> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=3274009842 for P30 / April 22, 2009 2009 年 4 月 22 日) (Makoto Kamada / Msieve 1.41 for P35 x P51 / April 24, 2009 2009 年 4 月 24 日)
53×10130+19 = 5(8)1299<131> = 97 × 3312111581501<13> × 1271121747386539<16> × 98252130102177803<17> × 21238910222340390665954881<26> × 382125981660833345278868179<27> × 180837604891909980515848530736439<33>
53×10131+19 = 5(8)1309<132> = 7 × 97738343 × 17703811623274986542609<23> × 48618725314158859858307753045210207726884844615861587846310076208919212530005063745709509326414258521<101>
53×10132+19 = 5(8)1319<133> = 32 × 4643518973<10> × 79593488079649<14> × 48429621795706069003<20> × 9801800613944284483825203726457<31> × 3729487427193358725267514399562862082318669990920751080263<58> (Makoto Kamada / Msieve 1.41 for P31 x P58 / April 24, 2009 2009 年 4 月 24 日)
53×10133+19 = 5(8)1329<134> = 262918391 × 6902507297954552900544343980154530186562139765296085565049<58> × 32449313991032259990721014237413613972619180694610646930008757342471<68> (Ignacio Santos / GGNFS, Msieve snfs / 4.06 hours / April 25, 2009 2009 年 4 月 25 日)
53×10134+19 = 5(8)1339<135> = 379 × 1307 × 27011 × 44012688661595418101936834495679255490917159915500366891612081274224804369901225574876216642282442577338282302175931372354283<125>
53×10135+19 = 5(8)1349<136> = 3 × 13 × 313 × 1549 × 3049 × 74143 × 186300199 × 1309189589<10> × 315255488283846235436795881<27> × 10488199912154755864745774983<29> × 1708307093986891448752835264729085167873848025113<49>
53×10136+19 = 5(8)1359<137> = 896561 × 25627855753<11> × 27385866116897<14> × 93586836099717041427108289838291357933950217423756553739593722078855100436818932695724579721153796926904289<107>
53×10137+19 = 5(8)1369<138> = 7 × 31 × 83 × 563 × 36467916497685454043561178729676819<35> × 1592488069431850510302639201300386274192150371140061427937716746570830122530356070413043274127267<97> (Robert Backstrom / GMP-ECM 6.2.1 B1=2328000, sigma=2561432034 for P35 / April 25, 2009 2009 年 4 月 25 日)
53×10138+19 = 5(8)1379<139> = 3 × 568606156271<12> × 421748910868721<15> × 633237938276842858605725159374066027361003<42> × 12926461350690842029880554414352022638905256637045133099332495876548231<71> (Ignacio Santos / GGNFS, Msieve snfs / 5.99 hours / April 25, 2009 2009 年 4 月 25 日)
53×10139+19 = 5(8)1389<140> = 657413 × 20410696260847223<17> × 3823221382006965053370031871<28> × 1147909912481955400864275487581850051490198848660755509554577765803385411796416171962164541<91>
53×10140+19 = 5(8)1399<141> = 577153 × 11923297 × 3492350119576818700587648285417907<34> × 626497419541031597886693211292085596727199999<45> × 39111905731165024668312789845345170825587785659453<50> (Robert Backstrom / GMP-ECM 6.2.1 B1=882000, sigma=3328769994 for P34, GGNFS-0.77.1-20060513-pentium-m gnfs for P45 x P50 / 3.36 hours / April 26, 2009 2009 年 4 月 26 日)
53×10141+19 = 5(8)1409<142> = 33 × 13 × 349 × 48072954790560648567652706462002864422476011142041068815981264246148041117795972937647563562877157273846226409104473415202482378540958611<137>
53×10142+19 = 5(8)1419<143> = 172 × 6379 × 2008796784103<13> × 24838614894526801<17> × 2068776505732953917580438564404929945073177<43> × 309461026129065613336287718747252395686825797638200927646978423349<66> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 gnfs for P43 x P66 / 9.15 hours, 0.45 hours / April 26, 2009 2009 年 4 月 26 日)
53×10143+19 = 5(8)1429<144> = 73 × 79473050106862706275240784169605362262487122995225933<53> × 21603263304638811935007782608993962985407454791157017884866832547047245476678698092370731<89> (Serge Batalov / Msieve-1.41 snfs / 6.28 hours on Phenom II X4 940/openSUSE/x86_64 / April 25, 2009 2009 年 4 月 25 日)
53×10144+19 = 5(8)1439<145> = 3 × 23 × 3347 × 6111936759569<13> × 30640070353597<14> × 70182313997449<14> × 1940136399326423063282783178301205687477619526249111882137772299752626865214823286295311297673328939<100>
53×10145+19 = 5(8)1449<146> = 4013 × 2086472299<10> × 2895230432243<13> × 57968818127543191603945489<26> × 600768533553563816773369126147<30> × 69753630841413122154141893581212807753891601974141248210480679263<65> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=3838722880 for P30 / April 23, 2009 2009 年 4 月 23 日)
53×10146+19 = 5(8)1459<147> = 19 × 541 × 1172317 × 235060575725579<15> × 9237495928744902899345213964123421<34> × 22506262284520226043638845786993481451478146780791861537970684431898609724245820689195797<89> (Ignacio Santos / GGNFS, Msieve snfs / 8.46 hours / April 25, 2009 2009 年 4 月 25 日)
53×10147+19 = 5(8)1469<148> = 3 × 13 × 67 × 281 × 8020244914067615507037613586718595482604618420202421902108522387908376116800188611948318752376754182671216718064330535781112081106769586081213<142>
53×10148+19 = 5(8)1479<149> = 5651 × 26801 × 108707012291<12> × 773474143085751735235970207<27> × 4624381918247184898467027790292655461967775554945190578975688734704415260947274004961992156153800781647<103>
53×10149+19 = 5(8)1489<150> = 7 × 89 × 181 × 13860095467<11> × 127907351040860227747<21> × 298749405551037697759977109415955797<36> × 9860477861640212173667954263879056032708182342505378235882532507138565347054351<79> (Ignacio Santos / GGNFS, Msieve snfs / 11.63 hours / April 26, 2009 2009 年 4 月 26 日)
53×10150+19 = 5(8)1499<151> = 32 × 29 × 1049 × 21508858606039281669054961626978764263315505330341572849489529852875348859482626726745372856063935690947733067759803676878504574284901471165345901<146>
53×10151+19 = 5(8)1509<152> = 11005133755709399739846139646663420523079<41> × 5351037997001869599349449652602850650625326819936478162439626755570976783012160572839424777050332270827075435391<112> (Sinkiti Sibata / Msieve 1.40 snfs / 17.28 hours / April 28, 2009 2009 年 4 月 28 日)
53×10152+19 = 5(8)1519<153> = 31 × 625913 × 6958847334209<13> × 210814408739207324962612124821<30> × 20688075617540906499953026451261388295816455794590976409066846398452495743997943095566505674959763304867<104> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=2236419490 for P30 / April 23, 2009 2009 年 4 月 23 日)
53×10153+19 = 5(8)1529<154> = 3 × 13 × 151 × 1104819812890349325391<22> × 5337056004796930905390628567<28> × 7961885334239550480336605084633<31> × 21300150554817246934507773260046199194433393097835926658634652295145801<71> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=1149936533 for P31 / April 23, 2009 2009 年 4 月 23 日)
53×10154+19 = 5(8)1539<155> = 37971697959006556067063120880293<32> × 26750290160545884056238066771927664782732542089391686301<56> × 57975545719181940975342922884870737353678736928569607670017493537673<68> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=3638990105 for P32 / April 23, 2009 2009 年 4 月 23 日) (Ignacio Santos / GGNFS, Msieve snfs / 15.78 hours / April 27, 2009 2009 年 4 月 27 日)
53×10155+19 = 5(8)1549<156> = 7 × 1792927 × 3543577 × 2443577634254454687137637845111973397935401399897115454809979896223<67> × 5418819651805614652357594463326606111851486150836128615586608425053563039831<76> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 15.04 hours, 0.56 hours / April 27, 2009 2009 年 4 月 27 日)
53×10156+19 = 5(8)1559<157> = 3 × 179 × 44685583042943812043<20> × 245409655404229865935923126115924253478108340640902509581247220049249609428727409457446715077100214642440526375334467256534947889875779<135>
53×10157+19 = 5(8)1569<158> = 21817969 × 2699100401549240852294220827286393563437957441817287800202158545962224480605361978875709690892350653211070603725254577494765387598125604124237635908681<151>
53×10158+19 = 5(8)1579<159> = 17 × 89803869709<11> × 19946527811963839934482153629736138114375201<44> × 19338468652164063844346333500613745540736302026055121157305398505959820677361605766269700887682845416813<104> (Erik Branger / GGNFS, Msieve snfs / 49.58 hours / April 28, 2009 2009 年 4 月 28 日)
53×10159+19 = 5(8)1589<160> = 32 × 13 × 47 × 61 × 543172787 × 146740646009623<15> × 10377904187206720222921982134102753<35> × 21223730306600451520506577284963975239844497432815229537295512873899546101677447590414810139556667<98> (Erik Branger / GGNFS, Msieve snfs / 35.62 hours / April 28, 2009 2009 年 4 月 28 日)
53×10160+19 = 5(8)1599<161> = 40237 × 51203 × 76558171429<11> × 204704040097<12> × 1823872158981217353941763837536806078314542256882291211623390720958882471141621110941056108695374587342474744601398818839047814323<130>
53×10161+19 = 5(8)1609<162> = 7 × 709718732680925963273434075511<30> × 118535668079661328446835390169781367112696291073297653940264980679589480803529870838577090978612622055485143543597553998658585880057<132> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=275210792 for P30 / April 23, 2009 2009 年 4 月 23 日)
53×10162+19 = 5(8)1619<163> = 3 × 1723 × 2655315417745817<16> × 171350162476640484283<21> × 26342549352212524177658708353759886900127603649<47> × 95053560209664005393787353568489591164108220293809699182000297998744547765379<77> (Ignacio Santos / GGNFS, Msieve snfs / 35.93 hours / April 26, 2009 2009 年 4 月 26 日)
53×10163+19 = 5(8)1629<164> = 71 × 125441 × 543667994926069758106471<24> × 141981755621425466912511299686577381546348961449<48> × 85658249428232845412735044023039818341069505361385323720612300437103972695570075959681<86> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 34.15 hours, 1.07 hours / May 5, 2009 2009 年 5 月 5 日)
53×10164+19 = 5(8)1639<165> = 19 × 7275791921399<13> × 4259900830262339947382269071322731189406204336971245580037338324583558103583280355806356885646210009228050865985198334983490465234779403356022494070869<151>
53×10165+19 = 5(8)1649<166> = 3 × 13 × 150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997151<165>
53×10166+19 = 5(8)1659<167> = 23 × 909518249142631<15> × 101908807772549968092207768219787<33> × 27623734159715430740229212625948447694972356799499723931346911102607938595696028274216199990446929662922041541312235019<119> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=183289767 for P33 / April 23, 2009 2009 年 4 月 23 日)
53×10167+19 = 5(8)1669<168> = 7 × 31 × 5801 × 2171422861<10> × 135266161385821144300657096869448610669383<42> × 1592711769493037551738175961976900809985538358919210031942464262455167074834538118938696628704611091433213992059<112> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 43.70 hours, 1.36 hours / April 30, 2009 2009 年 4 月 30 日)
53×10168+19 = 5(8)1679<169> = 33 × 97871 × 49048796603<11> × 458386770874262077570867<24> × 15411402341570770700756659<26> × 1367038993699028857971861131191<31> × 45066025056904692418507137599401<32> × 104395751098716970128892501976970215911993<42> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=4041292653 for P31 / April 23, 2009 2009 年 4 月 23 日) (Makoto Kamada / Msieve 1.41 for P32 x P42 / April 24, 2009 2009 年 4 月 24 日)
53×10169+19 = 5(8)1689<170> = 9851 × 38047 × 5043595148840315585593<22> × 31152464110448827547829360077099558730718457895031237088310904127147226554013552023052876542623250204039132573785960626801130941041464684909<140>
53×10170+19 = 5(8)1699<171> = 1559 × 2903 × 370723 × 33658580232709090033<20> × 67871489825328151030318753<26> × 15878422731457635314161599067107119872220986892417<50> × 9676095432618857994298840083734799477765342988159463785324899923<64> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 gnfs for P50 x P64 / 18.46 hours, 0.99 hours / April 29, 2009 2009 年 4 月 29 日)
53×10171+19 = 5(8)1709<172> = 3 × 13 × 12517 × 811991 × 41965866407<11> × 3955013221717<13> × 19945568457173<14> × 194033779430545213<18> × 23128602404611901024778204483779271141862203318066047959981787271320406471696008251310554054505593403523943<107>
53×10172+19 = 5(8)1719<173> = 807379 × 603812754341<12> × 28759572858649<14> × 9993027152629419597904559069<28> × 35301764274656969995635746440541350381<38> × 11906324612627081905737388568432204863860375854067088525617352372196014894391<77> (Robert Backstrom / GMP-ECM 6.2.1 B1=1172000, sigma=1695054277 for P38 / April 27, 2009 2009 年 4 月 27 日)
53×10173+19 = 5(8)1729<174> = 7 × 109 × 337 × 32117 × 927467459 × 1355939609<10> × 13693646389597<14> × 42233535190407367625899<23> × 98045660498502488205160495288316797455301845182847830077344500910458853238840815853824831792996948758790713699<110>
53×10174+19 = 5(8)1739<175> = 3 × 17 × 24611 × 190335731164766587<18> × 24649811293360697678224251957551845936540585639257504363540365080187932709810863024825847934510206585477348379835972682442952396800510998042158817248627<152>
53×10175+19 = 5(8)1749<176> = 59 × 281 × 66449 × 3359701150017343<16> × 877747172492967495127142302830627916616575312789<48> × 18126605868851081779459191764965506287093068015187871080859858686135207440387014241240173116363942999017<104> (Warut Roonguthai / Msieve 1.48 snfs / October 12, 2011 2011 年 10 月 12 日)
53×10176+19 = 5(8)1759<177> = 8294092389637679<16> × 71001004235812960813258179375514456464645755202350212011510956903521007234057290715921210098597922376534195650824807751061401434191307207988132563808390018131991<161>
53×10177+19 = 5(8)1769<178> = 32 × 13 × 1259 × 217157 × 408533 × 155122246988641<15> × 7672904306658443636134196446552695609599<40> × 202237566619332517092399359185855046068999439<45> × 1872082966737778087575829276904880609418952516992931569614440023<64> (Rich Dickerson / GMP-ECM 6.3 [GMP 5.0.1][ECM] B1=11000000, sigma=1403904305 for P40 / January 18, 2011 2011 年 1 月 18 日) (Dmitry Domanov / Msieve 1.40 gnfs for P45 x P64 / January 20, 2011 2011 年 1 月 20 日)
53×10178+19 = 5(8)1779<179> = 29 × 83 × 56671 × 397302042061058419<18> × 764648480363550491427385880911<30> × 561805943477853761856674267872978066478843702421886731769<57> × 2529457794411425253963747749161488771720116899521120577840536881597<67> (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=3079772143 for P30 / April 25, 2009 2009 年 4 月 25 日) (Markus Tervooren / Msieve 1.42 gnfs for P57 x P67 / 46.33 hours, 0.17 hours / September 21, 2009 2009 年 9 月 21 日)
53×10179+19 = 5(8)1789<180> = 7 × 4013 × 17839 × 17981 × 65355450688973339109195516472625633024179205179574210025458709602040136358096011438153413550486408411577605057960613680960406007640812179093999545682063307437389801081<167>
53×10180+19 = 5(8)1799<181> = 3 × 67 × 7753 × 467712874948997340147347573908507417<36> × 9277642778843380347719533680822774228073<40> × 870864419203635722315194328196734611935239863623475289867757749407372405846045984600645870268689193<99> (Robert Backstrom / GMP-ECM 6.2.1 B1=746000, sigma=338678068 for P36, B1=2958000, sigma=314658206 for P40 / July 6, 2009 2009 年 7 月 6 日)
53×10181+19 = 5(8)1809<182> = 293 × 176243 × 1440161363226367<16> × 4648807088243344680150847604995364064982182624096839807<55> × 170333936382444592738468589628119896338483495405780157358429917327344492289792089987302875715502391722919<105> (Dmitry Domanov / Msieve 1.40 snfs / December 11, 2012 2012 年 12 月 11 日)
53×10182+19 = 5(8)1819<183> = 19 × 31 × 88883 × 48676801 × 1909934179<10> × 44909803185561712575377489171512594879<38> × 2694125231951175852624904324678327290468308136743054314646170986495012520044492807970631334790960472860374888200542723067<121> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=11000000, sigma=3646388374 for P38 / January 19, 2011 2011 年 1 月 19 日)
53×10183+19 = 5(8)1829<184> = 3 × 132 × 313525843121228417<18> × 3469107172146883252031<22> × 8038653128004913635470223675890713077591034477<46> × 1328467855967764884021265231529515948155546983268589438361051105440036980079613101480144416458713<97> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=761703653 for P46 / April 23, 2009 2009 年 4 月 23 日)
53×10184+19 = 5(8)1839<185> = 3570571 × 2272384007<10> × 2393510226170387<16> × 152937048474146144538304996869595333<36> × 597217258688036676171387508287998767084972633927<48> × 33199658864400082603893441773353482637236315580934201587427733438557861<71> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=11000000, sigma=3640547026 for P36 / January 19, 2011 2011 年 1 月 19 日) (Dmitry Domanov / Msieve 1.40 gnfs for P48 x P71 / January 21, 2011 2011 年 1 月 21 日)
53×10185+19 = 5(8)1849<186> = 72 × 902829978413473489444924337<27> × 13311632175405183534967107570874937014132001247606973952111223566548486506432888017839423416087662945400355395097519522519423359320799623493647770043920548953<158>
53×10186+19 = 5(8)1859<187> = 32 × 12547 × 252766620829<12> × 75886207539634421<17> × 232428550344764604099332747485313915067865339<45> × 11697118980019449831167863246663311895695297844557316111440541051951869225648033338635044661069754040490609793<110> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P45 x P110 / November 3, 2016 2016 年 11 月 3 日)
53×10187+19 = 5(8)1869<188> = 7321 × 55786707677<11> × 144189030451384347979850386170617801260861566274931789334515254541198062946517225792597836594847884336650788027040032563064297856759509117447071628707979977133530322145722517<174>
53×10188+19 = 5(8)1879<189> = 23 × 149 × 9133 × 1021637597731<13> × 29078929780665430520713512844261283<35> × 643666395509113163554290290988549439459048058041177<51> × 983942401058070351599558503204902675754844350912910853845166431059245258357732551999<84> (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=1241649351 for P35 / April 25, 2009 2009 年 4 月 25 日) (Robert Backstrom / Msieve 1.44 gnfs for P51 x P84 / June 1, 2012 2012 年 6 月 1 日)
53×10189+19 = 5(8)1889<190> = 3 × 13 × 381181 × 1890738045310576852074564977329988351713715534194259398856686243072087<70> × 209510669633689530535928051322848872898733253543389021708070065889120663421372122513377077630086617651858174351533<114> (Ignacio Santos / GGNFS, Msieve snfs / August 6, 2010 2010 年 8 月 6 日)
53×10190+19 = 5(8)1899<191> = 17 × 9030767258774743<16> × 383583386474261498769543417440237420042364019196560588070819348721018100018451633622859069127957672393253728421618883438420675033513101953792811644738434616583909902273409919<174>
53×10191+19 = 5(8)1909<192> = 7 × 2939 × 9281161402879<13> × 289132267042019139658590673019357<33> × 10666866194765111497479208943782071594321661029391739223722554877106913319364559945036795750954746506208661585455768910994186498145902988274831<143> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=3000000, sigma=4209317769 for P33 / January 19, 2011 2011 年 1 月 19 日)
53×10192+19 = 5(8)1919<193> = 3 × 50917482587<11> × 45346311841468819589552951241702768145726819056106421268431<59> × 850164980128810393064917194842564196232419766587115961430651991559753632332316859367392383848370550774581042232907367068679<123> (matsui / Msieve 1.48 snfs / February 17, 2011 2011 年 2 月 17 日)
53×10193+19 = 5(8)1929<194> = 89 × 14243 × 476308962166363018339<21> × 97533346570587085006508626150961498766146271648119052044720528023443950258218246115560813815745124060877141512421934015103219101904577898755107966644562980231512997913<167>
53×10194+19 = 5(8)1939<195> = 285029662361<12> × 237666183667050370931<21> × 4265546019261343047945983746912979<34> × 2037986381238047661211739099652131129212450743883141917946588295407384024750315890053816689152359562661517483962891574865553202201<130> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=11000000, sigma=3034660976 for P34 / January 20, 2011 2011 年 1 月 20 日)
53×10195+19 = 5(8)1949<196> = 34 × 13 × 25951 × 6741108811<10> × 798807315484773786106083395471<30> × 40020040194252306342776629924366714161501093035240199502391871405295913297825890367123716177967704294723670730999957297653020507953068707764259704023<149> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=633471676 for P30 / April 24, 2009 2009 年 4 月 24 日)
53×10196+19 = 5(8)1959<197> = 298128395003<12> × 27913268210687<14> × 62510512638626489<17> × 35185515469066280073861700339946057262331008075400003741<56> × 3217379950846685362761206160385882043229249449542389854966873122001670528691831389461707177562636401<100> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P56 x P100 / October 20, 2017 2017 年 10 月 20 日)
53×10197+19 = 5(8)1969<198> = 7 × 31 × 877 × 2016361 × 1534637280296163799590453278654487927123068041204484280329882668362634788584617226332569031757358688658838571458412071170780459912630912670375459477293726025265998849320481558438956769661<187>
53×10198+19 = 5(8)1979<199> = 3 × 71 × 87424468960331558703235771<26> × 19750653502922749744625229280562727394089621601681<50> × 16011767813038998152523371361240413599302006081965673664903638316470881533500041367759429821958576693533158335989521047103<122> (Jo Yeong Uk / GMP-ECM 6.4.4 B1=11000000, sigma=8259005656 for P50 x P122 / March 21, 2018 2018 年 3 月 21 日)
53×10199+19 = 5(8)1989<200> = 191 × 367 × 631 × 2897 × 414154471091467<15> × 1109669680513934529799681542071894844271452656655571319527907875508943470558965243558805636667142101372212113843263294877136457491116914696529779021472899078562221986662281773<175>
53×10200+19 = 5(8)1999<201> = 192 × 134789 × 23765153 × 39853057 × 320495311303165535602444090245792286865527452470616096560243<60> × 39870141007055613317761578874832819150667811960278186650167934533057155387230983243145006692879144331663822471741743247<119> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs / September 27, 2012 2012 年 9 月 27 日)
53×10201+19 = 5(8)2009<202> = 3 × 13 × 405683 × 62635489579154110232271623867118103<35> × 5942394329616350083543134914418678468815254638488449610157480904899597258932565815669787572083517683998758043054391994015670908338456661773435238069120916598499<160> (Wataru Sakai / GMP-ECM 6.2.3 B1=3000000, sigma=303242967 for P35 / June 20, 2010 2010 年 6 月 20 日)
53×10202+19 = 5(8)2019<203> = 2854678590966455857<19> × 20628903399227148852235095793125856952836972129557823323336715016270506263289839510225646595696540865171744597385238038947781753885158432385498437684708120476762046447638988564475184777<185>
53×10203+19 = 5(8)2029<204> = 7 × 281 × 6991094456219571760445366554492296155281<40> × [42823664738654024146753494596611162996197643707455475080552632365269730895208935483894078392027330205442062850153313457655994824376155448514431058020416853642407<161>] (Dmitry Domanov / ECMNET for P40 / July 1, 2009 2009 年 7 月 1 日) Free to factor
53×10204+19 = 5(8)2039<205> = 32 × 113 × 4931 × 106031 × 80522381 × 78406560485739517133849<23> × 1754185578785297999300817145151437432033207222550657121395777868027560331008506157635994381698346431466570274947685892318968021335311623130575438262059108599699713<163>
53×10205+19 = 5(8)2049<206> = 47 × 197 × 317 × 946474730253881<15> × 15947952781883519<17> × 5893032166055217751510000561<28> × 8420794288736398704499222545435687464025833710301228005343071<61> × 26785772730178987921182557831235743663167052364206528013347199524391764791403407<80> (Markus Tervooren / Msieve 1.48 for P61 x P80 / December 10, 2010 2010 年 12 月 10 日)
53×10206+19 = 5(8)2059<207> = 17 × 29 × 12528143 × 1713847868093<13> × 10609272425840892326334191<26> × 5243748681556153981241899450270556988908895870754775843847719445512266963532543404500340680593046242345140717399334020692988821724189534570485738593204893535297<160>
53×10207+19 = 5(8)2069<208> = 3 × 13 × 419557 × 54266615209<11> × 11090434008429949<17> × 15099045892584566217708469463<29> × 39604724869727488616794225499398102849378553089205398896498011721931696445079918556746820666755210217849489354902130319876912084493258919632174721<146>
53×10208+19 = 5(8)2079<209> = 51357889931<11> × 11841060582919322283639313802969<32> × 96835719745119502114133639892545642590497609279589740567205770747407925799281756271578814646457784646501577579948464336312316268708406997812209128513972375533910141251<167> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2892106737 for P32 / November 21, 2012 2012 年 11 月 21 日)
53×10209+19 = 5(8)2089<210> = 7 × 193 × 2131 × 121447 × 137301304687<12> × 50165769690247<14> × 25022678661191441<17> × 18834647593731399751633018803354721<35> × 518841048811895344330022166150216464171197717212269097672078198066007567906723524882959622815335905312943668595490930115563<123> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1418661596 for P35 / November 21, 2012 2012 年 11 月 21 日)
53×10210+19 = 5(8)2099<211> = 3 × 23 × 269 × 2647 × 3383868951223<13> × 35421301332930557713761492929497633699798751168747529392054935216594477220833234325927178375168983883636075129791595447919966784732308365293848323089400809590409210132498772231385095499640329<191>
53×10211+19 = 5(8)2109<212> = 487 × 156971 × 35666258660257<14> × 8500096737484501190631368771184048532729<40> × [2540993480397853921853906421106724466491207225464665125916594955712069168638455078380714215608693106513476283406648200799481730822240676019603509432869<151>] (Serge Batalov / GMP-ECM B1=3000000, sigma=3592708182 for P40 / May 26, 2014 2014 年 5 月 26 日) Free to factor
53×10212+19 = 5(8)2119<213> = 31 × 2100523 × 5559311 × 1533232391167149037<19> × 198875916428173045618079<24> × 5334983436796576754273814526503249725058423536064420521078660133953300373441007050194559515276424783479869364978337370130559503775813921854506639921863485401<157>
53×10213+19 = 5(8)2129<214> = 32 × 13 × 67 × 1459 × 4013 × 30389 × 1972967 × 324112153 × 136048743937<12> × [48531326431869436672006276717696126131308016347768014464322249983310673094457730677893649022847588144293180005770381276459462003084256102694110831668910807306744951675079171<173>] Free to factor
53×10214+19 = 5(8)2139<215> = 18371 × 19584538047640970902409<23> × [163676839676049597425049410437887055581041629156493459613952156513944263873911819290700256468608971137979699724038869122588201474104566849054805876564950579635834379010771775578456765945851<189>] Free to factor
53×10215+19 = 5(8)2149<216> = 7 × 47221 × 1332283 × 21798141940706552012847325771916531<35> × 40584334693224583909044125231917481<35> × 1511561239267999287811058881760452683429463623353170121398087999595290751722933107831998537483607279497080463861053759164450349833373099<136> (Serge Batalov / GMP-ECM B1=3000000, sigma=2996072668 for P35 / January 9, 2014 2014 年 1 月 9 日) (Serge Batalov / GMP-ECM B1=3000000, sigma=2930894750 for P35 / January 9, 2014 2014 年 1 月 9 日)
53×10216+19 = 5(8)2159<217> = 3 × 283 × 48463 × 40697198551349229781<20> × [3516825827561496232731892882083746740178685631222699095896235642891873349064039069308114109448380287086809467901115642234889919367977075817817559042724922844104039080233029709156276505804587<190>] Free to factor
53×10217+19 = 5(8)2169<218> = 4253 × 663001 × 805413863 × 3216085788313<13> × 96991767770476269459467<23> × 369191102343354125563549<24> × 225159858928044977120859177528655377230361787783643813781294013278391395983004587778737931773930489828158198321575011666519224764103338959269<141>
53×10218+19 = 5(8)2179<219> = 19 × 167 × 97162097399<11> × [1910145311796756461822631285545582476697342117606946537560119143765341651747783232049702882579418567685516785086424000014887112839994133006788717046200637101295131591680693888952036518402529404273902291107<205>] Free to factor
53×10219+19 = 5(8)2189<220> = 3 × 13 × 61 × 83 × 691933733467<12> × 120784087402691<15> × 13929140945227875048449514477176102811848204379237043<53> × 25619005474393456279163185995359371360921277261810487912918890220947432726837327129973330474086050960263555374692099737662707709862918787<137> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P53 x P137 / March 10, 2021 2021 年 3 月 10 日)
53×10220+19 = 5(8)2199<221> = 43627 × 4489189 × 300683862351758915462391139620931161813107531729592153826456048687775833244137339167543327823336349966177685549704961003530079349937810397841974627288838392984625534238975999443634805214352690567671441508344463<210>
53×10221+19 = 5(8)2209<222> = 7 × 2767 × 210869 × 7193297 × 44242369537<11> × 5529288520801<13> × 2300816346720928660787791<25> × 30525013613925696965761734468007<32> × 10829929985639582701673419322868264622074601643944151851640209<62> × 107724461016875307851244608422041625825543237405653555649770620677<66> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2732152245 for P32, Msieve 1.49 gnfs for P62 x P66 / November 24, 2012 2012 年 11 月 24 日)
53×10222+19 = 5(8)2219<223> = 33 × 17 × 2957 × 11784526031215803622813427572959987236977427<44> × 368177487777333387771027802279764674907520624181068681269980980978848890232949723599135175045376234117449983928274035587682668637764105781784559729277989299905507279482754189<174> (Bob Backstrom / Msieve 1.54 snfs for P44 x P174 / June 22, 2019 2019 年 6 月 22 日)
53×10223+19 = 5(8)2229<224> = 827 × 27997 × 28183 × 393503633 × 585244054874062819423<21> × [391871226053753649059431697970512768178741870220839791863958298124384032333429627093797821957762977285406398417695757892780263378528863642745653408986943321650480477012550689271107823<183>] Free to factor
53×10224+19 = 5(8)2239<225> = 659 × 1811323 × 5593268497<10> × 12177431867<11> × [7243203181259068919916520034636899321155522047159142437530019705428988395831245561042844105500268979717709711795648739379935834539446167661456415729291913042367260807715223838796137584490385750923<196>] Free to factor
53×10225+19 = 5(8)2249<226> = 3 × 13 × 883 × 1527349 × 3461184127<10> × 88518468264268023564917<23> × 930826781184951699243961<24> × 1149925007150117522324893<25> × 5642046998075218888787798681<28> × 5136607994888678941350600111352461019309<40> × 11780389760118713821533110004193072752480565748778947324590292755451<68> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1414789021 for P28, B1=1000000, sigma=448328688 for P40 / November 22, 2012 2012 年 11 月 22 日)
53×10226+19 = 5(8)2259<227> = 97 × 10831 × 11273 × 106735337 × 46584918219734275170505236719384396506268800512080386142754329113666437034869390135257402404419819243194613835822768932871607048611894830477383005780415391107094466819759534335576654143234654440817905896459527<209>
53×10227+19 = 5(8)2269<228> = 72 × 31 × 1015277 × 281066641 × [1358569107620769494912746262476582508984530061203191064589411993830895012105594527924692253220444119643426364649087164077499176358430733051831355942577370093905123705280043793431806611594807370970548032621602083<211>] Free to factor
53×10228+19 = 5(8)2279<229> = 3 × 151 × 6498043463<10> × 3009086564565667441<19> × 1292045837902658641488924243281<31> × [514564645201610900042110754243109514196670210349237517324326495661177740453815672387732585708335770476140580274940056900746771546522074501378626648621641892847393121331<168>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=3767127668 for P31 / November 20, 2012 2012 年 11 月 20 日) Free to factor
53×10229+19 = 5(8)2289<230> = 4651 × 137428043994126823776288620369<30> × [92132245337432823303540570962786963560242072659691596795967149956491750633635852727057845012258572112028143356361744296936178477212781934191582782898914347456655098236443620753264491491931700351931<197>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=4071731325 for P30 / November 20, 2012 2012 年 11 月 20 日) Free to factor
53×10230+19 = 5(8)2299<231> = 28901 × 379645261 × 54572358779<11> × 169990702043341710577<21> × 4886412761034868835327<22> × 701785782277807468086932243207<30> × 1687135248139191242350559551224024984665348535304429421075735056517714254104220837941386274997480369546795206461643315476402401167783427<136> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=1618565347 for P30 / November 20, 2012 2012 年 11 月 20 日)
53×10231+19 = 5(8)2309<232> = 32 × 13 × 281 × 709 × 606048882728593<15> × 10645153168711643<17> × 39159340919167904635979122800863917207577331372138943988931502687452849445434241256083986403338931794977680626774220900101628336731773141867197803286862483525889117471672426856147807494031706027<194>
53×10232+19 = 5(8)2319<233> = 23 × 80722247 × 3291479783328483206711<22> × 121340354397766391804134027<27> × [79417430318865785392347860477159902572137928901339294984963855597401328047426699555259328273233699572656721313249601630878918579843876430976948015106204282262465694199591186477<176>] Free to factor
53×10233+19 = 5(8)2329<234> = 7 × 59 × 71 × 755437 × 2291664830139086923<19> × 11600470607764156191160208124961599049232465510936607563537804955830166626002280369439633591686044207052095464520232376321672575496457134732269548538305151180177642520549046117083265522907153362111496763493<206>
53×10234+19 = 5(8)2339<235> = 3 × 29 × 593 × 1601 × 10193 × 7043478571529258279<19> × 14421388802015928979237<23> × [68860754155469239386779694329946726567605991018286474057706105326808724187870374205956219860732589470620665252690989633177720540548870853603858361161316329443458142549124271039196261<182>] Free to factor
53×10235+19 = 5(8)2349<236> = 22436383 × 195501353 × 64746781865343031<17> × 363654776706491191<18> × [570194815133954629455213618282738173169573363537292525149087093765979667664794370596901214098082443684327269316819913843609046696405008937557012998080358447159440971586159527428513346591<186>] Free to factor
53×10236+19 = 5(8)2359<237> = 19 × 11875087283454541721822025107730136093<38> × 2610014672478872184790227495580788896387047421049588572208909960435671208519301722922970129552461344152408015885640490585469187687580693912948017175750646069419989953494726583983792035209334556177567<199> (Serge Batalov / GMP-ECM B1=11000000, sigma=1730829493 for P38 / November 8, 2013 2013 年 11 月 8 日)
53×10237+19 = 5(8)2369<238> = 3 × 13 × 89 × 2777317 × 20717819 × 10334242506412224251<20> × 2853189458737698058384578197647428245299781899624820165774074825060741638697740568873516174862233429349916381822724414318499780849865952542480807101750785045937254241055990259119384638254763388003080483<202>
53×10238+19 = 5(8)2379<239> = 17 × 409 × 1845721383149792983591349<25> × 4588756229749121818805687132279078240220774512414085339008876731542336142812571259487394958557161130103485229941911173994703256065892554528552444662765335933002923139297245782597028503908800813302102842738995437<211>
53×10239+19 = 5(8)2389<240> = 7 × 92993 × 99510701 × 513950257427<12> × [17688629608418102592208142938163179666410292644582269246372413237853820550244689771697074168824290515925810623883438538589084955624093160489211353527933503737738638041219366281644288317583718224741307462821556485657<215>] Free to factor
53×10240+19 = 5(8)2399<241> = 32 × 1487 × 444523 × 989887056442075962752280388659342270414579960868326894588040758296456792063766160549833121113006841758420760813258080590020490087000002522400313842861981086485345841700974458495612361323624430163557173799606388449269447860613314621<231>
53×10241+19 = 5(8)2409<242> = 84130817 × [699968109056743011171386685676532641884232372174501632248369689419382304214267750292843214501160601933639713600890014997582739377045261415788805294603152241929243227114850066045226791139908802845560015052378356065279728460130000745017<234>] Free to factor
53×10242+19 = 5(8)2419<243> = 31 × 1327 × 2420279 × 128105207 × 148620931 × 183404219 × 5706591061<10> × 3913003684463<13> × 75856398648286332987409893758353714363323690730140157147554984078135616653408540389833897910299054650161295177445943627363951873405349762982066560134840037307872229998196921417897206187<185>
53×10243+19 = 5(8)2429<244> = 3 × 13 × 359 × 11239 × [37423692270610371403942140144495601431395786557292663789613701145893192043671336206457517273094051230073304024410906757768474120779971799637949220047568888069324150310548400565727318645244461164502822071559662335514725756524546601182351<236>] Free to factor
53×10244+19 = 5(8)2439<245> = 4165188735276958847721222676363<31> × [14138348255417805994663292123114962135085631860915288045171250131192220108663053275529995182181048068200797649591095264501549384901015814904445501705617476587022155504724330270053687125165329754670408637689884934603<215>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=862714314 for P31 / November 20, 2012 2012 年 11 月 20 日) Free to factor
53×10245+19 = 5(8)2449<246> = 7 × 39087019121<11> × [2152299817659562348495287910266431160736223288808520011165242935921762970401852970889387024027367096469360027464218256291525275254488601988066834760944474197683010981403821003445277899297091476051906530009449859887845401578330478288687<235>] Free to factor
53×10246+19 = 5(8)2459<247> = 3 × 67 × 6727806433<10> × 2278583036179<13> × 3118847617632547<16> × 126503517408354377<18> × 1400470655850621696350575187<28> × [3458821773858420363385823528566944430650131714340364866279148687648386655776054587038873864651266302905829248093773032428969187825974039595767807982760121257158059<163>] Free to factor
53×10247+19 = 5(8)2469<248> = 131 × 647 × 4013 × 116833 × 145757 × 1154751529<10> × 3569740181565718002071137215977<31> × 164809478774078763104962559788600467123991<42> × 14965331278509232286670639743454859591896464396400806320968931871748707222094017751935787860248817814236311278134334519172571165378486737319827744603<149> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=4219447995 for P31 / November 20, 2012 2012 年 11 月 20 日) (Serge Batalov / GMP-ECM B1=11000000, sigma=2104215373 for P42 / May 27, 2014 2014 年 5 月 27 日)
53×10248+19 = 5(8)2479<249> = 40933 × 50881296683265419494298969<26> × 42140641599307298274730876079835433386709<41> × [6709659335213395653225786238249025632792580949080901462929168162933939923423491314796314222494434014010907153895439862698586256261287833749731762698717602490049486272842294501273<178>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1893284577 for P41 / November 21, 2012 2012 年 11 月 21 日) Free to factor
53×10249+19 = 5(8)2489<250> = 33 × 13 × 766386608244001<15> × 691576107414992186771095861<27> × 31654711193626434851368598387839583536537653420748281352501186692626497429564114005729420842105439224545346606312768156896659025689562776624036974440223556419206755118381646890588942066628952640279087009099<206>
53×10250+19 = 5(8)2499<251> = 409781 × 19672573552477511<17> × 2586181290944158375038495565279<31> × [2824628904155215356982184093858537775770124606556535454165996390211070694722843374813315814424883700045985457430275192046422323087141587709068550490576251131961790486595984308449872282766585290501501<199>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3733942265 for P31 / November 21, 2012 2012 年 11 月 21 日) Free to factor
53×10251+19 = 5(8)2509<252> = 7 × 47 × 223 × 4149122683<10> × 34979485391<11> × 415700853055175353959977<24> × 26845887669394161079675077774701<32> × 49850161892219261129620074499751170709<38> × 4696082526223998988693596455021504072266239513164531199323400460531<67> × 21169077312006256612747471007564802726174895890716551205653664100233<68> (Jason Parker-Burlingham / GMP-ECM for P32 / January 2, 2021 2021 年 1 月 2 日) (Ignacio Santos / GMP-ECM B1=3000000, sigma=1:1754173392 for P38 / March 2, 2021 2021 年 3 月 2 日) (Eric Jeancolas / cado-nfs-3.0.0 for P67 x P68 / March 3, 2021 2021 年 3 月 3 日)
53×10252+19 = 5(8)2519<253> = 3 × 24551 × 13142856407<11> × 66076426184723<14> × 56206113725487690656125100053105531<35> × 1638034530624081226868656448926115639888436533091408657308277441567211705180734387183909879600530925844917250543060896451330915624467318804495335282503769578661113544264681566653346095563443<190> (Jason Parker-Burlingham / GMP-ECM for P35 x P190 / January 2, 2021 2021 年 1 月 2 日)
53×10253+19 = 5(8)2529<254> = 5119 × 9817 × 48518232874379462928702488872213<32> × 24152632035922878500702324287181546184158289591853073150015656312834053084452650915691083315218227340969571653024036654133807663339697093045590886720808083898631185590127069977524406823786599923909790960186108928611<215> (Jason Parker-Burlingham / GMP-ECM for P32 x P215 / January 2, 2021 2021 年 1 月 2 日)
53×10254+19 = 5(8)2539<255> = 17 × 19 × 232 × 517782943 × 2056258837<10> × [3237051764921822830554613982596230943851212664689776409045845109552634931009592985501028384476681977837522391411425691048910717438036292924602132342303770347966491387174226485480087131737410956593219994380262460603369997666037729737<232>] Free to factor
53×10255+19 = 5(8)2549<256> = 3 × 13 × 17107 × 7540448277623<13> × 1170570924067698258018973008987428043746423269627582729626564957918190824693908281026012104983164866960837357978585960617191282826052061389114015735547736638081308947596446390109196516657951037493275880381481429136644093211675957771941091<238>
53×10256+19 = 5(8)2559<257> = 415979 × [141566975469648441120558703417453498587401981563706073837594899956221080604763434906302695301659191663254368342846366977392822447500688469583533997843374037845393370552092506806566891330785661989881433651431656138624519239886842578324600253591861341291<252>] Free to factor
53×10257+19 = 5(8)2569<258> = 7 × 31 × 349 × 242551 × 1955203 × 2836356869<10> × 66971253687364919<17> × 86318517603499762839567167773617734441580133604352166315535923790725212035266155535795698705485172599759175540756791697704378140830794111723596251353243582226140991090773666474433755492814237202415498756071009406251<215>
53×10258+19 = 5(8)2579<259> = 32 × 24251 × 11334727 × 337768891 × 10417019747715127832083949<26> × [676529905812707774075775758260583627635809534374977733717801363915136985658592757189945864274820894059574197948440207343157025948388651488286401185352318954877492910478892314793880871125791730558738228321276410747<213>] Free to factor
53×10259+19 = 5(8)2589<260> = 281 × 345945353305905307508552159688978917<36> × [605786427254808391327064650454118756526355247992536869952237699969878066739784481881654325608704361321333026839518610635731760117014915498376640230102770702305456544426482296547681681433672693651286557614513370661350658957<222>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:320464187 for P36 / May 23, 2021 2021 年 5 月 23 日) Free to factor
53×10260+19 = 5(8)2599<261> = 83 × 1451 × 8761 × 17911 × 65777 × 4207369024889<13> × 650129189957393<15> × 115196626724334307<18> × [1503454350585992294887914758394329646599275412423572225703273983363065307684653552675402945118305897430746597284889703708513482555846813154683497496084105701861300137578879080995881089155693046463941<199>] Free to factor
53×10261+19 = 5(8)2609<262> = 3 × 132 × 4626306193<10> × 33865540576501<14> × 44694737643496925314621097<26> × [1658733526874125856200419902552785329387300979772966520877737444703796191154562226502743718135201435511056861618354281528932325931653500371471363302796149655251206223475455860084787546180805890260396661063956487<211>] Free to factor
53×10262+19 = 5(8)2619<263> = 29 × 2437 × 125219 × 574547 × 131018288044460792237<21> × 124340617040786419450601872631<30> × [710950071028204768113344691356019043279894571265736559317922841322517532383772527797559236402133384274035533572428426543283974455534212611697742266952945775509610690659143872717093104552984531551283<198>] (Jason Parker-Burlingham / GMP-ECM for P30 / January 2, 2021 2021 年 1 月 2 日) Free to factor
53×10263+19 = 5(8)2629<264> = 7 × 7547 × 1349839917468971<16> × [8258072725350613632840701337027361606617437568839084100216227911133542035913217273988708462819899013331137787149211392022085240269461534310897441760691217547979690705028539715941583520844280108583347003732383185850985185248260553570730185439271<244>] Free to factor
53×10264+19 = 5(8)2639<265> = 3 × 44075295082972913<17> × [44536581304053281483523218416713490579994910145076187080602389931874917128823063740150056916420813144681857773612604640187447921773264202942694008654609549346017939893688959761351107363521373350668320615833470987529543528333731240070321612486678851<248>] Free to factor
53×10265+19 = 5(8)2649<266> = 36651401 × 3302128561690990670182616742883<31> × [486573891954812837762227855484263633114278022299150255483960729850365055694523120897540295870328819618169066511664788233441041093999003573102797621683537724300189954124633136350749868715438872454207700051400162414485012953125083<228>] (Jason Parker-Burlingham / GMP-ECM for P31 / January 2, 2021 2021 年 1 月 2 日) Free to factor
53×10266+19 = 5(8)2659<267> = 5449 × 5737 × 6997 × 11329 × 124483378807823054942783874778717<33> × [1909048157281877221855316016762923611596843376570256369502255840977687067015172047420066516443390523533809633584072404315443565371211358662331711369977938236045181843398127748892387533831178410306943231158039775614106793<220>] (Jason Parker-Burlingham / GMP-ECM for P33 / January 2, 2021 2021 年 1 月 2 日) Free to factor
53×10267+19 = 5(8)2669<268> = 32 × 13 × 2212127 × 738138773989697189178742228763<30> × 30824740043257309980242365886100017476300415705161520039968808172071796966555657915762855565785369146910833383906085273035634029100773332807613381216229877175710350165652039852822433444511179546205336315051847831482596249173754417<230> (Jason Parker-Burlingham / GMP-ECM for P30 x P230 / January 2, 2021 2021 年 1 月 2 日)
53×10268+19 = 5(8)2679<269> = 71 × 2011 × [412442053836917299142665262807298512329293735783394771635503945825347132243708118649462385673786350346957150383376561929730768721951022117010588866087847044697045747605696058221254150684537080486121324888387732883849313906534405060119265790888765934465292222977069<264>] Free to factor
53×10269+19 = 5(8)2689<270> = 72 × 278743 × [43115488423275780908336447207122242651642236820801202430773141325257688461684359595441026826107092056115247472775477322420461543493973264150708709213958032506198481923176611217464005054827322753589704047396514753798806031251586578792745661253826225041389445261727<263>] Free to factor
53×10270+19 = 5(8)2699<271> = 3 × 17 × 229 × 354043 × [1424202322376683217138321008709262344811057320599012285490968187416903264568287492838042907245028417259823212906365075338552294098405789859059173510310778326579121401892871239418829022686956734666841156603108258371624436300959290018425922002584424552309106864837<262>] Free to factor
53×10271+19 = 5(8)2709<272> = 200467 × 793143740105009687<18> × 123740417855490802977133<24> × [2993139717328110480507259155002981598503414024467564534418912452511569074298453049802181801851960737457334792731179161002438629220292627912010249770765982869641242379831367925817670012824008413583669035250333107642260603134377<226>] Free to factor
53×10272+19 = 5(8)2719<273> = 19 × 31 × 461 × 38103914042447842751801804107287729073<38> × 56917727381704430669006575186980735180130497548252749446512056916288993327895556806081523913203744304525811432916613001343150908089886093795714856375899492581179692961225094138635143618257507040073735195723484461452322267132453217<230> (Jason Parker-Burlingham / GMP-ECM for P38 x P230 / January 2, 2021 2021 年 1 月 2 日)
53×10273+19 = 5(8)2729<274> = 3 × 13 × 2125463 × 790798848301961<15> × 100814858233034342462442139751<30> × [891096282884795913951543012753747772474141186545693554058749650782462284732871314054790752919882379470682734684929108776909775872949057517754045019229171530586412926596655163570979865885739192316611481079704318021147677607<222>] (Jason Parker-Burlingham / GMP-ECM for P30 / January 2, 2021 2021 年 1 月 2 日) Free to factor
53×10274+19 = 5(8)2739<275> = 4657 × 12645241333237897549686254861260229523059671223725335814663708157373607234032400448548183141268818743587908286211915157588337747238327010712666714384558490205902703218571803497721470665426001479254646529716317133109059241762698923961539379190227375754539164459714169827977<272>
53×10275+19 = 5(8)2749<276> = 7 × [84126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984127<275>] Free to factor
53×10276+19 = 5(8)2759<277> = 35 × 23 × 57877087508372338869394128498945619<35> × [18205079597313501791138758981998579477239027106959543886331008368772721010634512407849754657642474140054683265860663752690602223023363291069702011787188974450816538548913198650799186866760055952766605440014094792848813875523812118342548279<239>] (Jason Parker-Burlingham / GMP-ECM for P35 / January 2, 2021 2021 年 1 月 2 日) Free to factor
53×10277+19 = 5(8)2769<278> = 7673 × 97381 × 13001239 × 1627579660174097387237<22> × 226656528137199658686875875831<30> × [16432313204919272561743688169020293351539424978564850588827389443656647040396921954689197210256547600000004630219421038202793960571932567686437862757570029550303437278166869549451320979195349093520742562982110841<212>] (Jason Parker-Burlingham / GMP-ECM for P30 / January 2, 2021 2021 年 1 月 2 日) Free to factor
53×10278+19 = 5(8)2779<279> = 9283 × 826667 × 730518766146049<15> × 105046849432624520900940330338285387651517266557914988114750099067341320082342159725351091763190028546015027750537071795377793920565869923024626612834662335797185786093044840094142658111934547574344848353003350963905458304974160540387353161993262774161401<255>
53×10279+19 = 5(8)2789<280> = 3 × 13 × 61 × 67 × 480749 × 76850328081055485430455510111558685990699068522375742117857650028350695829204660799528958020998856167731025783437752495925756247057051368471542237249991895140737117048830869677983589083089999856133039318831378625066830571974553366003800009533487069325276295973506445277<269>
53×10280+19 = 5(8)2799<281> = 1803742783793<13> × 56771135713399<14> × 698002974190057<15> × [823898852431931036039849810890550381188470916805312239855516152657609520405844835163939536581983210051744422771005311974942482479504632911220769078239330453792169889647283155797754312140421632225169867462655144047376564807828312419921190311<240>] Free to factor
53×10281+19 = 5(8)2809<282> = 7 × 89 × 109 × 4013 × 20027366209<11> × 954851026197487<15> × [113003058342810431614799828613416949171847299324704010217049997048525148666082828545067574525682038682414101958799140944289858765026438847234226162252096256685006898628013351160447575906573198838785677292522497220250688304952040041493406783692728113<249>] Free to factor
53×10282+19 = 5(8)2819<283> = 3 × [1962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962963<283>] Free to factor
53×10283+19 = 5(8)2829<284> = 1511 × 825005483485254544397<21> × 47240236229451243739648512643192279775687750124297080611264497779352132153898683159439367844831874325308067583226422906177711690083533663626404337569630251042803978025854561865656125652896373364978207152118374427265488280149540933984918120962365981477452269467<260>
53×10284+19 = 5(8)2839<285> = 317 × 369780429911<12> × 110996031940637<15> × 45260851660017886750560449785924933008835834788632955605361002717422428398096463603012921565041715354799597611772755439454020320676586260520529205925078745984018680860061861188195062739959317992359079355555262752295349754988297790637363353080680372931819031<257>
53×10285+19 = 5(8)2849<286> = 32 × 13 × 122775081061<12> × 2536705975775404515103890721<28> × 161609593132402224112140925584351145199454202918773368579337932256782723303290914988255257902116869882645516405874936969543000449020597048346794624238615648212627832400164505058656256768433462424851983741335422425637084624655874367328614495327857<246>
53×10286+19 = 5(8)2859<287> = 17 × 24917 × 2648959 × 7080117722303<13> × 128973706658887847<18> × 57474048460363349902603396421253656361547287747434648953256946504156119778179134774273195305774012192206327991413962925555630352485699295204967202694741831464872459813963187662903511363626449573419929266468516783185857057104148142099933479440179<245>
53×10287+19 = 5(8)2869<288> = 7 × 31 × 281 × 31481 × 25477391 × 231066030996557<15> × 350308443838487<15> × [148756901789850693995901214588503488524066214954573917775148256128663699087349601563481573904440859183275075012170623239671428421345295966090786412168893301943233959357359760604833370316709418086988582874225443429698065169162795311366946952413<243>] Free to factor
53×10288+19 = 5(8)2879<289> = 3 × 9433 × 3755879434380564061<19> × 119170214227771374803<21> × [464925009049186467875590449337675039242048588369941146389835223954004176878134463263976434580796107737043121334522158473698411807170554687101642993713090765462761024031220243701999340348171596108656462433499536334613531083808863482574437025881917<246>] Free to factor
53×10289+19 = 5(8)2889<290> = 343307 × 2558333666369098763<19> × 6378512289787336867588722331<28> × 10511728101560519796574560081924736207388840680403123537140042599247502119864492069314581668273273447274192017631772913215689306434281559812050564276809920570516213722672704681480724443006627329213155550111134497929486865587439167393365459<239>
53×10290+19 = 5(8)2899<291> = 19 × 29 × 25855805833122110654726541053<29> × 41335546475719331338014957135386458933400710671666476685654824136306350527586956445432601420715411083998933080173642024435149311134839129861660915689353753749720061816088958282883372558146686547870392649085469645581409187223581250033647092889966263267017858763<260>
53×10291+19 = 5(8)2909<292> = 3 × 13 × 59 × 279221053 × [9165762102166499889696266708906358568218389441608534084513886893325108780146872025608423840289306247999677532389325241717041358334093022751865222967761505054150402743907648692089395371324037233415115874624532405203382116928041600302819900464796058670243255785684148809093973318513<280>] Free to factor
53×10292+19 = 5(8)2919<293> = 210323 × 385739 × [725860296988151218007664212999890957775209275730073426980911686688394609253149934339691068249550406401952974861619750792873716749074853494723583854113734564920701157787642325025104385480620997210063458859179471292814839623038874288999312489919615382367249366104135650335787790839337<282>] Free to factor
53×10293+19 = 5(8)2929<294> = 7 × 4460161 × 77525051459<11> × 139046162287<12> × 67839875970231142562227<23> × [25792810603724296422059006924108754636663296918780447121990797038795092423253286092119353621576324011768227692511070935713211684393860276438032738955807692647874214129804739629665526786645919073875533615932894415168785813877956390346489853977<242>] Free to factor
53×10294+19 = 5(8)2939<295> = 32 × 191 × 268607 × 329317 × [38728083560668797248064427396498929228188611739552934181384020647899193294954884671295573889685616550913411719259677541130339883752419761061920206355993132585778122932942826170422331551834101202657433141053223819715870499678685804977532011739384305495042364177391664469775266349149<281>] Free to factor
53×10295+19 = 5(8)2949<296> = 479 × 1583 × 5923323656493133075741<22> × 175479640075457678178972877022933814380651<42> × [74717913093429802642638022778834446354875850733237602664989588346409949711825791995291906087771741059652871588389534993066679088912899537973498010503588515778127423668263591037382119919185511351002462023031710027151838756321047<227>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3296995587 for P42 / May 23, 2021 2021 年 5 月 23 日) Free to factor
53×10296+19 = 5(8)2959<297> = 739 × 32889487 × 609856603 × 118753656230997587<18> × 11486882823130243780513<23> × 595450946170125877114253<24> × [48911267972109235309751889864016916605340685749789643131748107132106626436959876540666753814408866744499552047182121289597628340178828671176815207604721792768646538471472332149677485951771490275154781662771907343537<215>] Free to factor
53×10297+19 = 5(8)2969<298> = 3 × 13 × 47 × 36571 × 64217 × 566201597018712770009<21> × 11640970205548067473091253731440254397<38> × [207550497490103290316935122224292436630064452354834000287380609678076971020277250284017954746785321285870320333496787978227323549007038945726641996322506162520295489433320301471912273128753520796734813230906814714273904162518703<228>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:986772964 for P38 / May 23, 2021 2021 年 5 月 23 日) Free to factor
53×10298+19 = 5(8)2979<299> = 23 × 51197 × 2774353 × 2492960222239<13> × 18170763475181755000397<23> × 372934301964355627207306789979<30> × 794526940050158287364038877130737<33> × 183168187264628419442524401781592645463452389469<48> × 7331954517968522169505853186450336100108068593601652483524007970963048479062356362609394131238570191552990056832503967133180072751510355325463<142> (Jason Parker-Burlingham / GMP-ECM for P30 x P33 / January 2, 2021 2021 年 1 月 2 日) (Ignacio Santos / GMP-ECM B1=11000000, sigma=1:276505730 for P48 x P142 / April 3, 2021 2021 年 4 月 3 日)
53×10299+19 = 5(8)2989<300> = 7 × 2333 × 145601 × 227207 × 9918427361<10> × 22473508763<11> × 572587679764578435591919<24> × 226551604507667921259609080147<30> × 37697423975526923725298432199261133208202262547760633051731259437807868819942664691182703327902021743384371048977194045027126973178030605290463773551993613076198977486141601282652419646679522340942672900956550483<212> (Jason Parker-Burlingham / GMP-ECM for P30 x P212 / January 2, 2021 2021 年 1 月 2 日)
53×10300+19 = 5(8)2999<301> = 3 × 16860456895027<14> × 79684398687264389094413238783481626040801343<44> × 1461064761786459532337690295735488191561383203776355287641567323682964093953928625037622505700750712383776641918121248224843651352907395227986583575193688637330485011312667918640924599652380308591434062939041691194654954082385585780957498820383<244> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1:2386466431 for P44 x P244 / May 3, 2021 2021 年 5 月 3 日)
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