Table of contents 目次

  1. About 255...551 255...551 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 255...551 255...551 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 255...551 255...551 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 255...551 255...551 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

25w1 = { 21, 251, 2551, 25551, 255551, 2555551, 25555551, 255555551, 2555555551, 25555555551, … }

1.3. General term 一般項

23×10n-419 (1≤n)

2. Prime numbers of the form 255...551 255...551 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. 23×102-419 = 251 is prime. は素数です。
  2. 23×103-419 = 2551 is prime. は素数です。
  3. 23×105-419 = 255551 is prime. は素数です。
  4. 23×106-419 = 2555551 is prime. は素数です。
  5. 23×1012-419 = 2(5)111<13> is prime. は素数です。
  6. 23×10186-419 = 2(5)1851<187> is prime. は素数です。 (Makoto Kamada / PPSIQS / November 9, 2004 2004 年 11 月 9 日)
  7. 23×10435-419 = 2(5)4341<436> is prime. は素数です。 (discovered by:発見: Makoto Kamada / November 9, 2004 2004 年 11 月 9 日) (certified by:証明: Makoto Kamada / PPSIQS / January 1, 2005 2005 年 1 月 1 日)
  8. 23×101746-419 = 2(5)17451<1747> is prime. は素数です。 (discovered by:発見: Makoto Kamada / November 9, 2004 2004 年 11 月 9 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / July 30, 2006 2006 年 7 月 30 日) [certificate証明]
  9. 23×103447-419 = 2(5)34461<3448> is prime. は素数です。 (discovered by:発見: Makoto Kamada / November 9, 2004 2004 年 11 月 9 日) (certified by:証明: Ray Chandler / Primo 4.0.1 - LX64 / March 17, 2013 2013 年 3 月 17 日) [certificate証明]
  10. 23×1018798-419 = 2(5)187971<18799> is PRP. はおそらく素数です。 (Erik Branger / PFGW / April 29, 2010 2010 年 4 月 29 日)
  11. 23×1070209-419 = 2(5)702081<70210> is PRP. はおそらく素数です。 (Bob Price / PFGW / March 16, 2015 2015 年 3 月 16 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了
  2. n≤50000 / Completed 終了 / Erik Branger / May 1, 2013 2013 年 5 月 1 日
  3. n≤100000 / Completed 終了 / Bob Price / March 16, 2015 2015 年 3 月 16 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. 23×103k+1-419 = 3×(23×101-419×3+23×10×103-19×3×k-1Σm=0103m)
  2. 23×106k+1-419 = 7×(23×101-419×7+23×10×106-19×7×k-1Σm=0106m)
  3. 23×1016k+4-419 = 17×(23×104-419×17+23×104×1016-19×17×k-1Σm=01016m)
  4. 23×1018k+7-419 = 19×(23×107-419×19+23×107×1018-19×19×k-1Σm=01018m)
  5. 23×1021k+20-419 = 43×(23×1020-419×43+23×1020×1021-19×43×k-1Σm=01021m)
  6. 23×1028k+25-419 = 29×(23×1025-419×29+23×1025×1028-19×29×k-1Σm=01028m)
  7. 23×1035k+25-419 = 71×(23×1025-419×71+23×1025×1035-19×71×k-1Σm=01035m)
  8. 23×1041k+11-419 = 83×(23×1011-419×83+23×1011×1041-19×83×k-1Σm=01041m)
  9. 23×1044k+18-419 = 89×(23×1018-419×89+23×1018×1044-19×89×k-1Σm=01044m)
  10. 23×1046k+32-419 = 47×(23×1032-419×47+23×1032×1046-19×47×k-1Σm=01046m)

— 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 23.03%. 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 23.03% です。

3. Factor table of 255...551 255...551 の素因数分解表

3.1. Last updated 最終更新日

March 29, 2024 2024 年 3 月 29 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=208, 212, 224, 227, 228, 229, 230, 232, 233, 235, 237, 243, 244, 245, 246, 247, 248, 250, 253, 254, 255, 256, 259, 262, 264, 265, 266, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 285, 287, 288, 289, 290, 291, 292, 295, 297, 300 (53/300)

3.4. Factor table 素因数分解表

23×101-419 = 21 = 3 × 7
23×102-419 = 251 = definitely prime number 素数
23×103-419 = 2551 = definitely prime number 素数
23×104-419 = 25551 = 32 × 17 × 167
23×105-419 = 255551 = definitely prime number 素数
23×106-419 = 2555551 = definitely prime number 素数
23×107-419 = 25555551 = 3 × 7 × 192 × 3371
23×108-419 = 255555551 = 3623 × 70537
23×109-419 = 2555555551<10> = 12473 × 204887
23×1010-419 = 25555555551<11> = 3 × 23099 × 368783
23×1011-419 = 255555555551<12> = 83 × 39569 × 77813
23×1012-419 = 2555555555551<13> = definitely prime number 素数
23×1013-419 = 25555555555551<14> = 34 × 7 × 45071526553<11>
23×1014-419 = 255555555555551<15> = 523 × 109841 × 4448557
23×1015-419 = 2555555555555551<16> = 107 × 318677 × 74946409
23×1016-419 = 25555555555555551<17> = 3 × 573119 × 14863437643<11>
23×1017-419 = 255555555555555551<18> = 37747 × 6770221621733<13>
23×1018-419 = 2555555555555555551<19> = 89 × 28105619 × 1021650061<10>
23×1019-419 = 25555555555555555551<20> = 3 × 7 × 27763 × 43832842881937<14>
23×1020-419 = 255555555555555555551<21> = 172 × 43 × 421 × 48846891605753<14>
23×1021-419 = 2555555555555555555551<22> = 5915683 × 431996703602197<15>
23×1022-419 = 25555555555555555555551<23> = 32 × 48119 × 59010082770620881<17>
23×1023-419 = 255555555555555555555551<24> = 388081 × 658510866431377871<18>
23×1024-419 = 2555555555555555555555551<25> = 311 × 105239 × 78081513848192719<17>
23×1025-419 = 25555555555555555555555551<26> = 3 × 7 × 19 × 29 × 71 × 1307 × 6311 × 495613 × 7609211
23×1026-419 = 255555555555555555555555551<27> = 2683 × 175005989027<12> × 544266673711<12>
23×1027-419 = 2555555555555555555555555551<28> = 17441477 × 497839267 × 294315353489<12>
23×1028-419 = 25555555555555555555555555551<29> = 3 × 12713 × 103069 × 6346201 × 1024410778361<13>
23×1029-419 = 255555555555555555555555555551<30> = 1301 × 39901 × 4922936680959385924351<22>
23×1030-419 = 2555555555555555555555555555551<31> = 181 × 761393 × 12854683 × 1442568686024009<16>
23×1031-419 = 25555555555555555555555555555551<32> = 32 × 7 × 440435421931<12> × 921006165213981667<18>
23×1032-419 = 255555555555555555555555555555551<33> = 47 × 18211 × 298575160390032626476113403<27>
23×1033-419 = 2555555555555555555555555555555551<34> = 59 × 17317 × 148933 × 361549 × 46451800867465001<17>
23×1034-419 = 25555555555555555555555555555555551<35> = 3 × 20389 × 417799721345751067659940091153<30>
23×1035-419 = 255555555555555555555555555555555551<36> = 811 × 498048191 × 39351941777<11> × 16077811714163<14>
23×1036-419 = 2555555555555555555555555555555555551<37> = 17 × 179 × 26561 × 31618331784729304470783862037<29>
23×1037-419 = 25555555555555555555555555555555555551<38> = 3 × 73 × 19195837 × 1293787343463061150799212687<28>
23×1038-419 = 255555555555555555555555555555555555551<39> = 18539 × 13784754062007419793708158776393309<35>
23×1039-419 = 2555555555555555555555555555555555555551<40> = 61 × 2297 × 5897 × 3092882124841206775578323199499<31>
23×1040-419 = 25555555555555555555555555555555555555551<41> = 33 × 2459 × 3373 × 18103049 × 6303691714022983037843291<25>
23×1041-419 = 255555555555555555555555555555555555555551<42> = 43 × 233 × 1125001 × 22672950584579401240268780810029<32>
23×1042-419 = 2555555555555555555555555555555555555555551<43> = 364265563 × 57427695734419<14> × 122164724542969028383<21>
23×1043-419 = 25555555555555555555555555555555555555555551<44> = 3 × 7 × 19 × 113 × 408959 × 258648167525557<15> × 5358519449147972771<19>
23×1044-419 = 255555555555555555555555555555555555555555551<45> = 761 × 925034987 × 985451521837<12> × 368389502503043935289<21>
23×1045-419 = 2555555555555555555555555555555555555555555551<46> = 12281 × 65539 × 512977 × 8436771554077<13> × 733630876901517041<18>
23×1046-419 = 25555555555555555555555555555555555555555555551<47> = 3 × 149 × 467977 × 1496892671<10> × 81613618278922154575618528999<29>
23×1047-419 = 255555555555555555555555555555555555555555555551<48> = 3174585221<10> × 12402314537<11> × 6490760657690871512396524763<28>
23×1048-419 = 2555555555555555555555555555555555555555555555551<49> = 109 × 2932 × 9437 × 317088960961009<15> × 91265893511623675152767<23>
23×1049-419 = 25555555555555555555555555555555555555555555555551<50> = 32 × 7 × 2153 × 4127047079<10> × 164501255229744817<18> × 277518607712954063<18>
23×1050-419 = 255555555555555555555555555555555555555555555555551<51> = 419 × 3221 × 349939 × 541113329646337859296826629812356773691<39>
23×1051-419 = 2(5)501<52> = 1361 × 16249 × 42242293 × 133090747411<12> × 20554419416619204719897033<26>
23×1052-419 = 2(5)511<53> = 3 × 17 × 83 × 251 × 159933227 × 150391965919990707968598201862931746511<39>
23×1053-419 = 2(5)521<54> = 29 × 439 × 1433 × 42821 × 432626173963<12> × 756148373090724280799394295219<30>
23×1054-419 = 2(5)531<55> = 3617 × 12558578927<11> × 16135471067<11> × 3486700704798374446734040415267<31>
23×1055-419 = 2(5)541<56> = 3 × 7 × 3571 × 8275997 × 555887419 × 326956450243<12> × 226557843617839681688789<24>
23×1056-419 = 2(5)551<57> = 7565643343828029384250508263<28> × 33778430193122311819476911177<29>
23×1057-419 = 2(5)561<58> = 491 × 2250022956936547361479<22> × 2313219716022972890423909948313659<34>
23×1058-419 = 2(5)571<59> = 32 × 2839506172839506172839506172839506172839506172839506172839<58>
23×1059-419 = 2(5)581<60> = 912973 × 33476212175009<14> × 64495375260439<14> × 129647010451139966320354237<27>
23×1060-419 = 2(5)591<61> = 71 × 83777651 × 335120976789364140858871<24> × 1282027040523810937216098661<28>
23×1061-419 = 2(5)601<62> = 3 × 7 × 19 × 263 × 32687 × 7450434815184193767809810718512466621019089974076329<52>
23×1062-419 = 2(5)611<63> = 43 × 89 × 246527 × 270870914236317518796101653266266222577854062941368219<54>
23×1063-419 = 2(5)621<64> = 5526179552333212452287<22> × 462445262835618960264574606140897870107873<42>
23×1064-419 = 2(5)631<65> = 3 × 561935435363201<15> × 31684525201318312667873<23> × 478443268908002103347684629<27>
23×1065-419 = 2(5)641<66> = 203879378578373<15> × 1253464461867180869818273402502490040606180794312787<52>
23×1066-419 = 2(5)651<67> = 135280088858914644452225905897<30> × 18890847700586429389410311817354101383<38>
23×1067-419 = 2(5)661<68> = 33 × 7 × 223 × 55836493 × 10859267370941598788517967747594993438174131264291429481<56>
23×1068-419 = 2(5)671<69> = 17 × 107 × 1493 × 77929 × 335273 × 2392055081179208777<19> × 1505649763127411541916757546145217<34>
23×1069-419 = 2(5)681<70> = 156219296018130249224674804160159<33> × 16358770143599718794296214336868234689<38>
23×1070-419 = 2(5)691<71> = 3 × 3728144059<10> × 34182027548238195539541085253<29> × 66845713995268094829260420527171<32>
23×1071-419 = 2(5)701<72> = 193 × 2209780236519110023<19> × 599209834366350408439545216766673797624045085530409<51>
23×1072-419 = 2(5)711<73> = 505327 × 849970507 × 731584399699<12> × 6141749501418979229<19> × 1324196486787441550603911029<28>
23×1073-419 = 2(5)721<74> = 3 × 7 × 151 × 1915802873<10> × 4206668256726648156571279989231473383247479400509672316820797<61>
23×1074-419 = 2(5)731<75> = 3782838822453200226091<22> × 67556554098655940558102850773641311346071852011404061<53>
23×1075-419 = 2(5)741<76> = 157 × 1019 × 854149 × 138157091932474353967691<24> × 135364464704863707325703925826061578864183<42>
23×1076-419 = 2(5)751<77> = 32 × 2839506172839506172839506172839506172839506172839506172839506172839506172839<76>
23×1077-419 = 2(5)761<78> = 59773904929<11> × 4275369927046038239861094412113333716704676554787370692034573861119<67>
23×1078-419 = 2(5)771<79> = 47 × 201413 × 5146721603<10> × 180282672207769<15> × 88587771371885769443<20> × 3284290246635154425993672541<28>
23×1079-419 = 2(5)781<80> = 3 × 72 × 19 × 56533 × 161849871294976815220563997810210648304148553985996725209925457994022379<72>
23×1080-419 = 2(5)791<81> = 4822343131993<13> × 5695297450406965919346877277<28> × 9304880635697377006549323705495042837091<40>
23×1081-419 = 2(5)801<82> = 29 × 4160579 × 12400721 × 20100397 × 18432358411249<14> × 4610001616758912652175248753732570600995348797<46>
23×1082-419 = 2(5)811<83> = 3 × 409 × 3011 × 24798409 × 2533139518648051<16> × 110115151223458919260827480025540856424069862626503837<54>
23×1083-419 = 2(5)821<84> = 43 × 467 × 14125963677418681972277<23> × 401107732011293584759752041<27> × 2246057506432236142943585553403<31>
23×1084-419 = 2(5)831<85> = 17 × 1798997449<10> × 41548293457554583125256499983<29> × 2011187991703650139491366804688697409884243609<46>
23×1085-419 = 2(5)841<86> = 32 × 7 × 15502261 × 26166746836288739455853809904056725041956379071225307740957511873724246444157<77>
23×1086-419 = 2(5)851<87> = 444894067859<12> × 21073527836033880533<20> × 17645368602277999748213<23> × 1544758990229676840728735197561741<34>
23×1087-419 = 2(5)861<88> = 197 × 131713 × 98489619294757030584054276276031614636806104287257838273870247094910579326260691<80>
23×1088-419 = 2(5)871<89> = 3 × 97 × 472457 × 842449 × 5188278928202180309<19> × 710885301557712953437<21> × 59822365171218130003634027101268669<35>
23×1089-419 = 2(5)881<90> = 5544228173385146743<19> × 53667967793787402103<20> × 1123766013904415224351<22> × 764281218103442845254625904369<30>
23×1090-419 = 2(5)891<91> = 104009 × 25792486939801<14> × 810326987272693855699006249<27> × 1175603535390381256665541111254018081322187111<46>
23×1091-419 = 2(5)901<92> = 3 × 7 × 59 × 2207 × 54727677959295851693<20> × 57321999591787030752000505137767<32> × 2979088009290194109421868260703077<34>
23×1092-419 = 2(5)911<93> = 4049 × 8466425530010681<16> × 20586189970025591563935578417<29> × 362127478754468637606630108448809902603939287<45>
23×1093-419 = 2(5)921<94> = 83 × 739 × 41664175873543791766071955843219517673762256966521928942653790624835834089628699733530423<89>
23×1094-419 = 2(5)931<95> = 37 × 100987 × 1684477 × 9166511 × 9150027143592211<16> × 296053994661314623<18> × 2766359484800575700651113258359209439569<40>
23×1095-419 = 2(5)941<96> = 71 × 359 × 28051 × 8734069 × 40923009317637369937389264787402658826411127417234572174543162085502108165671361<80>
23×1096-419 = 2(5)951<97> = 1422389644919<13> × 6812650574353990031664211<25> × 263724592771979662360135990788314623954269019305157169675939<60>
23×1097-419 = 2(5)961<98> = 3 × 7 × 19 × 22850633821<11> × 2802942444361025939353483783500539517225018133007194280576056998705010672012247962469<85>
23×1098-419 = 2(5)971<99> = 107581 × 5164769570561369<16> × 19666811616720743<17> × 1534534531449019271<19> × 15240112614739024177525438956110021713406803<44>
23×1099-419 = 2(5)981<100> = 61 × 131 × 2203 × 1792477 × 232624837407667<15> × 63453285056766714913<20> × 5486633027002811349728879168483756237981892874385261<52>
23×10100-419 = 2(5)991<101> = 3 × 17 × 2903 × 187610847713<12> × 920047328971375258743453934764817762525861175632566620020614913487150062860501669059<84>
23×10101-419 = 2(5)1001<102> = 1773984844307959<16> × 144057349968651591319096737527999897254573295101350041843671409641096320388796497420889<87>
23×10102-419 = 2(5)1011<103> = 251 × 283 × 394128495162559040957<21> × 91282459776034937200842990224229883034573427614387524002899602628024800022371<77>
23×10103-419 = 2(5)1021<104> = 32 × 7 × 123653 × 65880308774918912757421<23> × 49794857479199522322454493509828025367153697822682629604775111427205238529<74>
23×10104-419 = 2(5)1031<105> = 43 × 331 × 231484319018054156363<21> × 3208723329525191001326970397<28> × 24173249163729029623468956384605830732689420352552777<53>
23×10105-419 = 2(5)1041<106> = 21149 × 2738140374212107<16> × 44067429331662452701<20> × 1001433380722889083415523034210546116321354360997277222451224908757<67>
23×10106-419 = 2(5)1051<107> = 3 × 89 × 304585559 × 183954605179<12> × 12361526776253110052746469951419<32> × 138191705900215663268288927238977959384385858170547267<54> (Serge Batalov / Msieve-1.36/QS for P32 x P54 / 36.85 minutes on Opteron-2.8GHz; Linux x86_64 / July 28, 2008 2008 年 7 月 28 日)
23×10107-419 = 2(5)1061<108> = 2003 × 430303257467<12> × 592724597779<12> × 41914848608189<14> × 11934628119101910654730588146710073974978684841959233855336548973321<68>
23×10108-419 = 2(5)1071<109> = 3079 × 1299770600963<13> × 28682292336636262666919<23> × 22263583571745667541607573463283802041198902041936776548693578962480677<71>
23×10109-419 = 2(5)1081<110> = 3 × 7 × 29 × 1588231 × 162865673 × 162227623858369783073481064680199557922703760006549529214021090727331768020684971247900509953<93>
23×10110-419 = 2(5)1091<111> = 52498139 × 68759837 × 1171236310664623846065075156444685421318659<43> × 60445232405964426967246594540875308055954431145200123<53> (Serge Batalov / Msieve-1.36/snfs for P43 x P53 / 1.05 hours on Opteron-2.2GHz; Linux x86_64 / July 28, 2008 2008 年 7 月 28 日)
23×10111-419 = 2(5)1101<112> = 50503 × 51606294371<11> × 980540359662911059402947399484435549537567277419031741411420199999998415888303319035071686481027<96>
23×10112-419 = 2(5)1111<113> = 32 × 787 × 7489 × 118259 × 40308349 × 209586721 × 26147647855970763959<20> × 18442451548724322864913094787908945388503571719542041647483718877<65>
23×10113-419 = 2(5)1121<114> = 1279 × 199808878464077838589175571192772131005125532099730692381200590739292850317088002779949613413256884718964468769<111>
23×10114-419 = 2(5)1131<115> = 12671 × 3204884250067103630129<22> × 725788414881940170954537007<27> × 86706579727612278786969624143583485674657111291579725893503327<62> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=3525223640 for P27 x P62 / July 28, 2008 2008 年 7 月 28 日)
23×10115-419 = 2(5)1141<116> = 3 × 7 × 19 × 1367 × 1579339 × 29666653310722707056360109766344073970913006763621248737108715041683646099644074388005011597262390594373<104>
23×10116-419 = 2(5)1151<117> = 17 × 192406883 × 20871150723274008192701347204335976081<38> × 3743427330215324631982859564971087424753593345379490493751515455230261<70> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P38 x P70 / 2.23 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / July 28, 2008 2008 年 7 月 28 日)
23×10117-419 = 2(5)1161<118> = 64307574638820961007411<23> × 471651373439991329726887<24> × 29397002682338724150501923810687<32> × 2866150826244968311090718055706237174189<40> (Makoto Kamada / Msieve 1.36 for P32 x P40 / 2.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / July 28, 2008 2008 年 7 月 28 日)
23×10118-419 = 2(5)1171<119> = 3 × 1314697287759179<16> × 19957056746293231<17> × 22465119194553960775289171<26> × 14452170797656566311544000085947212614451406070178604674566123<62>
23×10119-419 = 2(5)1181<120> = 1049 × 65353 × 705109488726641<15> × 5286737545614239318426275923343816810380238130013379762680648892161085257250064699696100670180463<97>
23×10120-419 = 2(5)1191<121> = 99421130947<11> × 6089080818545329013<19> × 3143628060985604177503897<25> × 1342838339677980376532468690094755859324728427482654720532995358953<67>
23×10121-419 = 2(5)1201<122> = 33 × 72 × 107 × 242689 × 2785847 × 774795187 × 552729096969604125117866209022368136492287800707<48> × 623498064629031326448330932831149966744250542153<48> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 snfs for P48(5527...) x P48(6234...) / 2.99 hours on Pentium 4 2.GHz, Windows XP and Cygwin / July 28, 2008 2008 年 7 月 28 日)
23×10122-419 = 2(5)1211<123> = 691 × 471799103 × 2594746223723<13> × 302103168179579019577060688029143299855857260988374914121559914012548409228859742310654874712717969<99>
23×10123-419 = 2(5)1221<124> = 1453 × 1801 × 9391 × 6693819476983<13> × 637191652502528066422659078234237565527319133<45> × 24380919769593584418550698024252096421356470057475816983<56> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P45 x P56 / 4.15 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / July 28, 2008 2008 年 7 月 28 日)
23×10124-419 = 2(5)1231<125> = 3 × 47 × 3643631 × 17073588094550355706752106093964111<35> × 155830978679555689187019330766573207<36> × 18696194936136122483576503549609207686186338653<47> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=742209908 for P35 / July 19, 2008 2008 年 7 月 19 日) (Serge Batalov / Msieve-1.36/QS for P36 x P47 / 20.96 minutes on Opteron-2.8GHz; Linux x86_64 / July 28, 2008 2008 年 7 月 28 日)
23×10125-419 = 2(5)1241<126> = 43 × 249348569303014160413787592148654698519463<42> × 23834716483005383332708850249577163177780742690701649474076750209456743894544822939<83> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs for P42 x P83 / 1.59 hours on Cygwin on AMD 64 X2 6000+ / July 28, 2008 2008 年 7 月 28 日)
23×10126-419 = 2(5)1251<127> = 530501 × 6820659093058393981<19> × 2615877950701771798181<22> × 269994737351567375083787870401796709357338444984916029976813777197010788026221091<81>
23×10127-419 = 2(5)1261<128> = 3 × 7 × 13789 × 636704041316348681226905897<27> × 7221520930973206646401819070774877612779<40> × 19194065806847188314532804326356425958335559911996902133<56> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P27 x P40 x P56 / 5.25 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / July 28, 2008 2008 年 7 月 28 日)
23×10128-419 = 2(5)1271<129> = 2455552249163861923<19> × 183984724928350103604095598822455287<36> × 565658580426499955089656149121889215128319053548001037907750693173909533651<75> (Serge Batalov / Msieve 1.36 snfs for P36 x P75 / 2.60 hours on Opteron-2.2GHz; Linux x86_64 / July 29, 2008 2008 年 7 月 29 日)
23×10129-419 = 2(5)1281<130> = 347 × 1399 × 59004638297548789745241165391<29> × 145724632415306209970889384614530979<36> × 612236216310466332533975530312917979837581554624783714920903<60> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P29 x P36 x P60 / 5.18 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / July 28, 2008 2008 年 7 月 28 日)
23×10130-419 = 2(5)1291<131> = 32 × 71 × 277948867834776050128261<24> × 143886337798122774492204380111972546928102340506164485376163221174708562938966521913153958023974489436269<105>
23×10131-419 = 2(5)1301<132> = 99346240247<11> × 7986204722527<13> × 322102022461686981918401415703343265883900031646517409870060408370459288256425719298820852737754814070199879<108>
23×10132-419 = 2(5)1311<133> = 17 × 238821139 × 8808018954562471117146096945029<31> × 71463683796511502389022158956810349650260869065339396811634714922502034368591135000665584113<92> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=1462786881 for P31 x P92 / July 20, 2008 2008 年 7 月 20 日)
23×10133-419 = 2(5)1321<134> = 3 × 7 × 19 × 1406343509201398365268977301<28> × 131983281958163855510539651678444328449<39> × 345065940183956376607582992204291886943136677148509477565980637101<66> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 snfs for P28 x P39 x P66 / 10.59 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / July 28, 2008 2008 年 7 月 28 日)
23×10134-419 = 2(5)1331<135> = 83 × 61675709953442697785653352579529799727020527376375559085086927<62> × 49922126545103830085717272367270909155555235254621911382926371134183211<71> (Serge Batalov / Msieve-1.36 for P62 x P71 / 4.5 hours on Opteron-2.8GHz; Linux x86_64 / July 28, 2008 2008 年 7 月 28 日)
23×10135-419 = 2(5)1341<136> = 62083001408959<14> × 41163531040024290464925523676119946561430210658463788419004795008343324024212007823813752945617222412764516567969896049889<122>
23×10136-419 = 2(5)1351<137> = 3 × 587 × 5081 × 7220707395104081979889441231486340266276055853078025872679218893<64> × 395546029374132684362629681712347760388410687843986837692961179827<66> (Serge Batalov / Msieve 1.36 snfs for P64 x P66 / 6.60 hours on Opteron-2.2GHz; Linux x86_64 / July 29, 2008 2008 年 7 月 29 日)
23×10137-419 = 2(5)1361<138> = 29 × 2052587 × 4430448401<10> × 969031894951745856162844371744941588788758132954253283037158087316184420756676984361145865406314258892963961083165353137<120>
23×10138-419 = 2(5)1371<139> = 17609003514447728631938833758128093<35> × 145127778153873886153305871603820300439044982225316042826202236046692596812484867625963184012287196067307<105> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=1309995126 for P35 x P105 / July 28, 2008 2008 年 7 月 28 日)
23×10139-419 = 2(5)1381<140> = 32 × 7 × 1221884077<10> × 3307384099<10> × 185108549203839883<18> × 2746579189500310771626838549<28> × 582944350776654841809718096403461<33> × 338676012281352254540742951033008260118077<42> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=2750317490 for P33 x P42 / July 20, 2008 2008 年 7 月 20 日)
23×10140-419 = 2(5)1391<141> = 499 × 3697 × 588763883 × 7640370262711621<16> × 30794968480433199508456241834816636283881536809507688107214579916612054111683297868413578399611604274594401619<110>
23×10141-419 = 2(5)1401<142> = 21277 × 50620069 × 21416740057201493<17> × 95792077670044720909433<23> × 1156562859407044272850177719398961834468629004105856810405225464938680643055575113299805483<91>
23×10142-419 = 2(5)1411<143> = 3 × 457 × 1187 × 1862017 × 1106770699<10> × 14886815158650811<17> × 5679777058284628909237<22> × 90120329918021210025522587874225969383422776918955539590797414147589275199993658523<83>
23×10143-419 = 2(5)1421<144> = 557 × 171012781 × 136207903799352110227<21> × 538844847458477932858080232424621<33> × 36554051399146403713935390141869213541499333355306590438897345084105764804979409<80> (Serge Batalov / GMP-ECM 6.2.1 B1=2000000, sigma=2258810441 for P33 x P80 / July 28, 2008 2008 年 7 月 28 日)
23×10144-419 = 2(5)1431<145> = 11328951549049208258659188667017358765383634275585517<53> × 225577410627202540610471998982892547446702289733649826841945206400113122054353971517703547003<93> (Serge Batalov / Msieve-1.36 for P53 x P93 / 7.02 hours on Opteron-2.8GHz; Linux x86_64 / July 28, 2008 2008 年 7 月 28 日)
23×10145-419 = 2(5)1441<146> = 3 × 7 × 171906473 × 273973539056672514893<21> × 577311161603154375393851<24> × 44756408382685268080864898217009682764993066093031781022746934316923663239585416033847062229<92>
23×10146-419 = 2(5)1451<147> = 43 × 6841 × 346043 × 34758835800516322384363626653111027<35> × 41510532436848216902506677855337901<35> × 1739977716010306568378337706839472575468221244846012298568319529657<67> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=380832070 for P35(4151...) / July 28, 2008 2008 年 7 月 28 日) (Serge Batalov / pol51+Msieve 1.36 gnfs for P35(3475...) x P67 / 5.00 hours on Opteron-2.2GHz; Linux x86_64 / July 29, 2008 2008 年 7 月 29 日)
23×10147-419 = 2(5)1461<148> = 125863 × 86808599 × 894223361 × 393430184484011485920049<24> × 664830312160833336498377192003102976167785291763887856226572013628427526186417683195272268537000257807<102>
23×10148-419 = 2(5)1471<149> = 33 × 17 × 151 × 1283 × 75011929299489064304755445730298699<35> × 242428544050253915914646918889394792594740748663<48> × 15803560686756702280080903994808482373671375272389819798509<59> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=1168396302 for P35 / July 28, 2008 2008 年 7 月 28 日) (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P48 x P59 / 42.02 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / July 30, 2008 2008 年 7 月 30 日)
23×10149-419 = 2(5)1481<150> = 59 × 509 × 1373 × 4236889 × 118477049 × 12347063472457399933114922895563200268458198457812016259766823991188396203827156301834791871822809256308932390202793145850249557<128>
23×10150-419 = 2(5)1491<151> = 89 × 28429 × 2755710854535299<16> × 3391430191131833<16> × 13272715735240788679347421<26> × 8142493385171795465398251479424044028219502430085702379680190093911921381134738317469453<88>
23×10151-419 = 2(5)1501<152> = 3 × 7 × 19 × 828705755470883248206443600902260497750813<42> × 77288001192943139407705039988537472974515304633897945114412907051296370165896505908384922416246634351671973<107> (Serge Batalov / Msieve 1.36 snfs for P42 x P107 / 14.25 hours on Opteron-2.2GHz; Linux x86_64 / July 29, 2008 2008 年 7 月 29 日)
23×10152-419 = 2(5)1511<153> = 251 × 15727 × 30313 × 103850550449<12> × 534229782631<12> × 19790119266604017679102945476566143<35> × 1945142794525748056047069045389871786110518491818897667080431528816127400819396477203<85> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P35 x P85 / 43.36 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / July 29, 2008 2008 年 7 月 29 日)
23×10153-419 = 2(5)1521<154> = 157 × 1511 × 71889401 × 6594980699<10> × 10359967718793949674331<23> × 126119780815898289136469561<27> × 50235185876494027386262953460826258885293<41> × 346173000949072010309520257023196154046249<42> (Serge Batalov / Msieve-1.36/QS for P41 x P42 / 16.5 minutes on Opteron-2.8GHz; Linux x86_64 / July 28, 2008 2008 年 7 月 28 日)
23×10154-419 = 2(5)1531<155> = 3 × 91411 × 125717 × 99479243282099<14> × 340181494077011694290357817506041<33> × 69952169448817622365476237996541279017803003027<47> × 313131860083472179775867830221927950460921636582587<51> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 snfs for P33 x P47 x P51 / 57.77 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 2, 2008 2008 年 8 月 2 日)
23×10155-419 = 2(5)1541<156> = 113 × 6650487823450193<16> × 142450464161059263155679700679<30> × 2387203880597113428673111753170712166636318290144431855398417184974145469199823087283804233308276862223956841<109> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=2480463531 for P30 x P109 / July 22, 2008 2008 年 7 月 22 日)
23×10156-419 = 2(5)1551<157> = 109 × 1949 × 615887 × 79671967 × 568072473549876077847951681943235841700911865100362592901083<60> × 431555511214783572160697906549520112228842379475734051031125209152188991775173<78> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P60 x P78 / 60.42 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / August 1, 2008 2008 年 8 月 1 日)
23×10157-419 = 2(5)1561<158> = 32 × 7 × 14776651 × 63748651 × 973336363550106887302722574739<30> × 442420062949587264507358090096128210983570197191636875054556465288607675852564435098117942495764116067637731443<111> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=571795841 for P30 x P111 / July 28, 2008 2008 年 7 月 28 日)
23×10158-419 = 2(5)1571<159> = 203982161 × 171689635527179533850177211158120096687991880816145824295203094123<66> × 7297079191886613832743568747111087572188527660082593836965018158316475096972563946317<85> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.36 for P66 x P85 / 35.26 hours on Athlon 64 X2 6000+ / August 1, 2008 2008 年 8 月 1 日)
23×10159-419 = 2(5)1581<160> = 61 × 62207219 × 1841593051318439<16> × 274927478843071052517148883273<30> × 1330156950130039397064004388659279184341745294810159416063773478769991675234897872467629348943160242174487<106> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=2573143363 for P30 x P106 / July 22, 2008 2008 年 7 月 22 日)
23×10160-419 = 2(5)1591<161> = 3 × 421 × 1303290019<10> × 16757517846851<14> × 33410740941589932192257971<26> × 141201378282839605551482507237147623978827958693229<51> × 196384032376405294052137230651200422806370915812525870825887<60> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 gnfs for P51 x P60 / 34.78 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / July 30, 2008 2008 年 7 月 30 日)
23×10161-419 = 2(5)1601<162> = 34239449 × 2926008353<10> × 3265797762225884596670732499419492287<37> × 781076750339822130193637764085753788800316293642129828413036710971415513493721659905790281056519495473703209<108> (Serge Batalov / Msieve-1.36 snfs for P37 x P108 / 31.00 hours on Opteron-2.6GHz; Linux x86_64 / August 6, 2008 2008 年 8 月 6 日)
23×10162-419 = 2(5)1611<163> = 2243 × 88035909371<11> × 40350728463526367<17> × 320733865742085492309037642934214749246941606585039490117213068319350402055184793684656667112454023243470674154468301427205838088401<132>
23×10163-419 = 2(5)1621<164> = 3 × 72 × 445416381479<12> × 28147772315476835226478494998303<32> × 13866210121634082517759356527935249827409961332736226297692188923203068870905046280504817078100473253861116418240833709<119> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=4056865929 for P32 x P119 / July 23, 2008 2008 年 7 月 23 日)
23×10164-419 = 2(5)1631<165> = 17 × 14783 × 6954611 × 127092897952617830861128387381793123491<39> × 5984338350534202483602163442377911766177<40> × 192248766671982198740268835298401979782919136451461142361013167032834159033<75> (Robert Backstrom / GMP-ECM 6.2.1 B1=4366000, sigma=1627898278 for P40, GGNFS-0.77.1-20050930-k8, Msieve 1.36 gnfs for P39 x P75 / 21.39 hours on Athlon 64 X2 6000+ / August 4, 2008 2008 年 8 月 4 日)
23×10165-419 = 2(5)1641<166> = 29 × 71 × 132745428289<12> × 1240062004353599171<19> × 620307761470091015755690541703303810222293530677225354864980633273<66> × 12155107128456035886009851568901921324819251306725762561321071641847<68> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P66 x P68 / 101.57 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / August 12, 2008 2008 年 8 月 12 日)
23×10166-419 = 2(5)1651<167> = 32 × 643496646045034314863036088356290602835699348302317420935391877062800651<72> × 4412620003991111484688047460906035814232134281081696744784440167395589300355555901131709979989<94> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.36 for P72 x P94 / 88.42 hours on Athlon 64 X2 6000+ / August 3, 2008 2008 年 8 月 3 日)
23×10167-419 = 2(5)1661<168> = 43 × 1913 × 202061459 × 8243229814663<13> × 9719287489760292844376840465897<31> × 25684063928938037339841953821170973102004701<44> × 7471758700860606702764453521083040039688701616397278375982183054061<67> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=3645631555 for P31 / July 23, 2008 2008 年 7 月 23 日) (Serge Batalov / pol51+Msieve 1.36 gnfs for P44 x P67 / 14.00 hours on Opteron-2.2GHz; Linux x86_64 / July 29, 2008 2008 年 7 月 29 日)
23×10168-419 = 2(5)1671<169> = 12227 × 48449 × 181003 × 135110400299347159<18> × 33379385617121485187<20> × 5284789631973670077396236647036681617432818886892737429506025706866423866993604508992392070356286427451032793135107763<118>
23×10169-419 = 2(5)1681<170> = 3 × 7 × 19 × 99115019415880121677092502404222247027<38> × 646208937806761842825739606924013230081780096425955573149216008366271383509656353669041781599017902484058310271913115315734810187<129> (Robert Backstrom / GMP-ECM 6.2.1 B1=3434000, sigma=909235864 for P38 x P129 / August 2, 2008 2008 年 8 月 2 日)
23×10170-419 = 2(5)1691<171> = 47 × 167 × 1233615293<10> × 645304315442331619894177<24> × 8914696587075694200020688570908983<34> × 285490091589476305221345080451232055137<39> × 16070488449447674612650589351851462929548050466307798710623429<62> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=843189100 for P34 / July 28, 2008 2008 年 7 月 28 日) (Serge Batalov / Msieve-1.36/gnfs (with pol51) for P39 x P62 / 2.80 hours on Opteron-2.2GHz; Linux x86_64 / July 28, 2008 2008 年 7 月 28 日)
23×10171-419 = 2(5)1701<172> = 562003853 × 9819478707452999260663842216145669618164917<43> × 463081680659769326936886310127931535214424803461949022560762005197836495742479612235092546488980256930797094956201310351<120> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs for P43 x P120 / 83.31 hours, 1.45 hours / June 23, 2009 2009 年 6 月 23 日)
23×10172-419 = 2(5)1711<173> = 3 × 1787 × 2777 × 1939351 × 885130327055894994012483812383537691844107466498065190359540870163568805840191641404586321809350605151812690044349188759646389505564373756180097153631116880433<159>
23×10173-419 = 2(5)1721<174> = 673 × 853 × 5591061403121<13> × 7006809008629239360483702710486422780612342481<46> × 25181631057758153981933321553668940225037068307<47> × 451255837422041310778962833166372971071264336217045028875777297<63> (Serge Batalov / Msieve-1.38 snfs for P46 x P47 x P63 / 30.00 hours on Opteron-2.6GHz; Linux x86_64 / October 6, 2008 2008 年 10 月 6 日)
23×10174-419 = 2(5)1731<175> = 107 × 30029 × 17725645207<11> × 17177291165701<14> × 2476524846141698449<19> × 217775438960959376674111543630369862266373<42> × 4843422579829178947723125725122614756988629020007020971287741483153442359848736165503<85> (juno1369 / GMP-ECM B1=11000000, sigma=633460790 for P42 x P85 / April 27, 2010 2010 年 4 月 27 日)
23×10175-419 = 2(5)1741<176> = 34 × 7 × 83 × 593 × 298937 × 433884878656891339<18> × 174238196836575116171951716194039677780877331481<48> × 40520232382325820041041111693248572051645991760150802711617140413542220146416937273773247997734889<98> (Wataru Sakai / for P48 x P98 / April 17, 2011 2011 年 4 月 17 日)
23×10176-419 = 2(5)1751<177> = 1693 × 40766729 × 6784935167<10> × 582406709601371<15> × 64712766329852691432002761083917<32> × 771073511127576234777110033082908100809<39> × 18778663554365193587028132136971846756713170062564978859065837339119323<71> (Serge Batalov / GMP-ECM 6.2.1 B1=2000000, sigma=410517240 for P32 / July 28, 2008 2008 年 7 月 28 日) (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=359160519 for P39 x P71 / July 29, 2008 2008 年 7 月 29 日)
23×10177-419 = 2(5)1761<178> = 274316323 × 953867572327<12> × 9766649247370101894911037812901898318341518792550360531740657671866949116174373047351651647382960906385786429572101031571719890169130004538818821902380727331<157>
23×10178-419 = 2(5)1771<179> = 3 × 4973 × 1712953653432237787757594715165597932539416553090391819529161174043538813295499400466221298716774284841849692040723611204206418362863164793589084761415346575209836822545449129<175>
23×10179-419 = 2(5)1781<180> = 311 × 605993 × 9486007 × 14509530323<11> × 29282668291<11> × 62155026673<11> × 348398479188686501<18> × 4498980788192811699189568905957540794386101261910526893<55> × 3453371022627095076155775850110344684731257028691845350307583<61> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona gnfs for P55 x P61 / 47.90 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / August 2, 2008 2008 年 8 月 2 日)
23×10180-419 = 2(5)1791<181> = 17 × 160625847619<12> × 23288197500401<14> × 10538502885230213<17> × 14005677645847267<17> × 452648203174615703323010093477<30> × 818721351585225269696284670558586233<36> × 734691701926879427540330661208791006085582518574130629367<57> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=150552219 for P30 / July 25, 2008 2008 年 7 月 25 日) (Serge Batalov / Msieve-1.36/gnfs + pol51 for P36 x P57 / 1.60 hours on Opteron-2.8GHz; Linux x86_64 / July 28, 2008 2008 年 7 月 28 日)
23×10181-419 = 2(5)1801<182> = 3 × 7 × 631 × 38218677258865332945353153<26> × 454294838445380861908829430532335894799790647942571080873<57> × 111076763740573549384876554306983446287483638099792040452038247251589180414171137440507322501229<96> (Dmitry Domanov / Msieve 1.50 snfs for P57 x P96 / May 27, 2013 2013 年 5 月 27 日)
23×10182-419 = 2(5)1811<183> = 313 × 1120317181099<13> × 2206950016109987<16> × 443909231364586098236860883150221945772101461059<48> × 743897876454947740203526753803629274267949533886154495502577052289072804799376199744276804166813373273981<105> (Dmitry Domanov / Msieve 1.50 snfs for P48 x P105 / May 27, 2013 2013 年 5 月 27 日)
23×10183-419 = 2(5)1821<184> = 701 × 110753 × 6693388357<10> × 34515161731<11> × 142480645176216037054651392316041249381398178354543682593633999670263973842050908503247628534061105003167554925943385733564625900154540552292986813483361701<156>
23×10184-419 = 2(5)1831<185> = 32 × 97 × 1061 × 19040340637648210868379117961880200224083<41> × 533069110183538168764034856646424157448997606332829033<54> × 2718300519021907080423642860825043651728871207807033967846075461947330821337467175953<85> (Erik Branger / GMP-ECM B1=3000000, sigma=1385992420 for P41 / December 11, 2009 2009 年 12 月 11 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P54 x P85 / September 12, 2014 2014 年 9 月 12 日)
23×10185-419 = 2(5)1841<186> = 197 × 1723 × 752893977142793544359694770234762162429346628786279260160549730447588922507241694351887587036998846762834141712323139476228027362131200613837733016594110601434623106185220429352521<180>
23×10186-419 = 2(5)1851<187> = definitely prime number 素数
23×10187-419 = 2(5)1861<188> = 3 × 7 × 19 × 444562846253<12> × 634791206601862391<18> × 218613113840905019830369700950295243<36> × 3508127044763732233458705101032392972305956879<46> × 295935347335276674440034001992761974970606704014448447660915363148825502679<75> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3924512080 for P36, Msieve 1.50 gnfs for P46 x P75 / April 23, 2013 2013 年 4 月 23 日)
23×10188-419 = 2(5)1871<189> = 43 × 683 × 1123 × 11003 × 129491 × 13776430890486919<17> × 1998967854737700046309<22> × 4118359186990383026851<22> × 65615481280730819870909029109781563549335597<44> × 730790082739108945520358150329693309160286713343015176689118525792073<69> (Serge Batalov / pol51+Msieve 1.36 gnfs for P44 x P69 / 13.6 hours on Opteron-2.6GHz; Linux x86_64 / July 31, 2008 2008 年 7 月 31 日)
23×10189-419 = 2(5)1881<190> = 4729 × 1272630683<10> × 7444620502877365715218426198631<31> × 57038889121656280657495968841620376120423123850690340295652077054982030328799444308548646486997318715596520717436416034053736175856530927182860803<146> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=1793952661 for P31 x P146 / July 25, 2008 2008 年 7 月 25 日)
23×10190-419 = 2(5)1891<191> = 3 × 6339730275679<13> × 12792851948053<14> × 195602254069818692747759<24> × 1909300086506850731960797981529<31> × 281240505231691045431673953403297956191867654635205427832610932115298960894880673037587466283371769257125561881<111> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=1977751987 for P31 x P111 / July 25, 2008 2008 年 7 月 25 日)
23×10191-419 = 2(5)1901<192> = 536749 × 1049437 × 2222514223<10> × 164646728337905536231<21> × 640556862356338194459757<24> × 18183469352047122005819738271467857341848407<44> × 106445086486657196807532944997246788012201790725070046199662462071658155594075770621<84> (Wataru Sakai / GMP-ECM B1=11000000, sigma=3307947160 for P44 x P84 / March 20, 2009 2009 年 3 月 20 日)
23×10192-419 = 2(5)1911<193> = 619 × 219492527 × 70051078765660177<17> × 14847157048924522258978645156542935050723<41> × 4573409132228565872555633028253292497592650037720722346539<58> × 3954365007136706245065879248211547282618420345588469697117163938083<67> (Eric Jeancolas / GMP-ECM 7.0.4 B1=11000000, sigma=1:410129142 for P41 / October 16, 2020 2020 年 10 月 16 日) (Eric Jeancolas / cado-nfs-3.0.0 for P58 x P67 / October 17, 2020 2020 年 10 月 17 日)
23×10193-419 = 2(5)1921<194> = 32 × 7 × 29 × 12097 × 19421 × 41175707 × 173256341 × 3380474941<10> × 278067141973787440159<21> × 21981471799923293466345117222099732721965408577228738681<56> × 403908641845404554074623864588276528765475625934389912775099413193825340298976493<81> (Robert Backstrom / Msieve 1.44 gnfs for P56 x P81 / May 7, 2012 2012 年 5 月 7 日)
23×10194-419 = 2(5)1931<195> = 89 × 149 × 293 × 967 × 262403331781593574766113562024732715006041761541629645347256899192602329339316450676257<87> × 259206335328679478628934062972172053952198882671875357817752938738556941931038271583585904166740073<99> (matsui / Msieve 1.49 snfs for P87 x P99 / March 7, 2011 2011 年 3 月 7 日)
23×10195-419 = 2(5)1941<196> = 158597 × 7029942179561563<16> × 313306481963429959<18> × 138881901627091563659<21> × 337159954666957756609533851017<30> × 425452593547811250316631268573489297907292332462667<51> × 367228525511343637108246350268855498271898118507609664399<57> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=2243790911 for P30 / July 28, 2008 2008 年 7 月 28 日) (Serge Batalov / pol51+Msieve 1.36 gnfs for P51 x P57 / 11.25 hours on Opteron-2.2GHz; Linux x86_64 / July 29, 2008 2008 年 7 月 29 日)
23×10196-419 = 2(5)1951<197> = 3 × 17 × 111269 × 15738683 × 286136049862320331122365857250657763669680217897674430509382519538001671631498287363858485200268182599863446176319573397436116071664826094146438561528396326002250104696081746276914163<183>
23×10197-419 = 2(5)1961<198> = 571 × 9202769 × 129188341993<12> × 3906973282439474368465492315145429702148715153943549<52> × 96353375036382575187024736566286325819047685430408646611727484519982808622588657890132674726321377988708252258768473717691257<125> (Bob Backstrom / Msieve 1.54 snfs for P52 x P125 / March 13, 2021 2021 年 3 月 13 日)
23×10198-419 = 2(5)1971<199> = 330048488040326643281297069715026424433630199177<48> × 515268873558507774234780986872212218799351367544094804445562015097943<69> × 15027047896934639118130321753833927516048042040409791293930953426741283723690424241<83> (Wataru Sakai / Msieve for P48 x P69 x P83 / 993.45 hours / November 14, 2008 2008 年 11 月 14 日)
23×10199-419 = 2(5)1981<200> = 3 × 7 × 431 × 822166237785966937833596339772273380167<39> × 8016571463986106513104624218307848381307<40> × 2765643382267819668781591954418791280834022267016280940169<58> × 154897452662266545680968239519414846256501968007596611529641<60> (Wataru Sakai / Msieve for P39 x P40 x P58 x P60 / 904.98 hours / September 6, 2009 2009 年 9 月 6 日)
23×10200-419 = 2(5)1991<201> = 71 × 8219 × 22343 × 269641 × 1003835581792243363<19> × 7523809296967452778311389696840923658342739112697<49> × 9624545237021308165729653104119056247397785319621658469344430527745515126041941365175901900022200631269293941622570943<118> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs for P49 x P118 / October 25, 2012 2012 年 10 月 25 日)
23×10201-419 = 2(5)2001<202> = 2988863 × 973147927 × 878618727559415971162579178802003919642728904733726907752634758646623980752425250334684209524262481901266117832666763701000401068216877308909289233589750406520062976172934806000111668551<186>
23×10202-419 = 2(5)2011<203> = 33 × 251 × 73583 × 17408653 × 168570085040992581290901100088365918597306710944099353175342680061635834360218208031<84> × 17463234108965043537727961582592240239052654307761962979291516807509632409758252376284680536826720032227<104> (Bob Backstrom / Msieve 1.54 snfs for P84 x P104 / September 4, 2021 2021 年 9 月 4 日)
23×10203-419 = 2(5)2021<204> = 1117 × 1987 × 115142137211280465170229389670078228068639331823169111109208762757185607773516016846996775169107504759250056231915488074253261939200846484943338303969334945523501486409898699449535479072140603968569<198>
23×10204-419 = 2(5)2031<205> = 269 × 519083 × 821441 × 11681641 × 5576046527800175467<19> × 342050020359093561601286858304641760696208556355893811572444571488139163606114103638505610291128753201610435366617915381180309729639324806466679452271147867931460219<165>
23×10205-419 = 2(5)2041<206> = 3 × 72 × 19 × 128993 × 54876812999<11> × 1947164275524543669958152471971076364561<40> × 663829843743440059714201038185203556289984740199145364999743052203632840243793268622510698476400382349723793136174470533854770554901867639532009041<147> (Ignacio Santos / GMP-ECM 6.3 B1=11000000, sigma=2226666516 for P40 x P147 / October 18, 2010 2010 年 10 月 18 日)
23×10206-419 = 2(5)2051<207> = 2713 × 136460875743368436468039800764978718182426096519<48> × 1891127944075136600947156079884343635375799078183<49> × 365011432156981300194557482878693141473795570979941747323473588085351470073199474067268202720196676149562951<108> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs for P48 x P49 x P108 / February 10, 2014 2014 年 2 月 10 日)
23×10207-419 = 2(5)2061<208> = 59 × 2344823180844101724484764569<28> × 18472395400845109725571932712033484790393440271433858951920140836886754216151798451567879194903960244987513152501999292795668574014092308638240909289077748829996503197680587779381<179>
23×10208-419 = 2(5)2071<209> = 3 × 2564453159<10> × 3842321896031<13> × 668849703694884621128792173<27> × [1292549000836215671937440437359260923588817666985824359881230530923527932845126351155684304665331038679222155194042532610680771682859259275855137309786564500401<160>] Free to factor
23×10209-419 = 2(5)2081<210> = 43 × 26141 × 61493 × 3585749 × 24920642058722213885987518922442258658297965018081085835688851774484060085902314787789014693<92> × 41374225725959089172619849307804058274445520260972617752123068045619736425330129914977545281892020277<101> (Bob Backstrom / Msieve 1.54 snfs for P92 x P101 / July 6, 2021 2021 年 7 月 6 日)
23×10210-419 = 2(5)2091<211> = 181 × 196853 × 20539724594141181097384256686626363643033880273825836151124916033404131742075451065583<86> × 3491966734909215520850143416230787804606166100271062955572720854301801179653426104999924591641240785114838426294731929<118> (Bob Backstrom / Msieve 1.54 snfs for P86 x P118 / August 13, 2020 2020 年 8 月 13 日)
23×10211-419 = 2(5)2101<212> = 32 × 7 × 215471 × 1139484537066127765646410679258040672302364437207750686472939110097902357133<76> × 1652142540169503544332550476328805023220104444897271881540543896850434771527128916304471781207176976321688519086655580100520255339<130> (Bob Backstrom / Msieve 1.54 snfs for P76 x P130 / July 18, 2020 2020 年 7 月 18 日)
23×10212-419 = 2(5)2111<213> = 17 × 261337 × 19760318989<11> × [2910995625323095147576847660451948854104305605726546189807638100328238123559074889676525334356224065040706024190434905030364652305077791945692235383498474020560427466283086070016888896276479983971<196>] Free to factor
23×10213-419 = 2(5)2121<214> = 3761115007342845342895871001660166582199<40> × 679467538367300788677373441149844186278354736608663621809358336480642713200027099494468432848575265499726218033237654963461599212242711332098207448146854449919992542469812249<174> (Serge Batalov / GMP-ECM B1=11000000, sigma=2672796980 for P40 x P174 / November 8, 2013 2013 年 11 月 8 日)
23×10214-419 = 2(5)2131<215> = 3 × 179 × 331 × 5299333102283128793439548324163542805806467<43> × 3075479946399207799265115740619401464707098256405357721<55> × 8821631829369193355720495488053467153090969578307398494865624798270613568372863985463372451727534007869625839919<112> (Bob Backstrom / GMP-ECM 7.0 B1=60170000, sigma=1:2202612864, Msieve 1.54 snfs for P43 x P55 x P112 / February 10, 2020 2020 年 2 月 10 日)
23×10215-419 = 2(5)2141<216> = 433 × 6060240877183<13> × 25243043228602189379118537877245770726270407922087740151681<59> × 3858032064028258889421625798911865252014416129384098819788712887499701119717295660201296247274088010347016765219995324122282965535764679391089<142> (Bob Backstrom / Msieve 1.54 snfs for P59 x P142 / October 28, 2020 2020 年 10 月 28 日)
23×10216-419 = 2(5)2151<217> = 47 × 83 × 991 × 241651 × 2735565545230845668211848717947107365747644332734689929025090563197601916820493035118842705908278656391815537349841154845321649953408586373103726168888493245671148962930241876214816131859990753325035665111<205>
23×10217-419 = 2(5)2161<218> = 3 × 7 × 101693 × 1775094947<10> × 7124470785031247<16> × 2986469925622460153249514513561998125873<40> × 316841914679732533050674916715037004666720710778714534753686463871297432261715196686066158360935778472084676162175468813397944479851777821647817931<147> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2423009179 for P40 x P147 / April 19, 2013 2013 年 4 月 19 日)
23×10218-419 = 2(5)2171<219> = 229 × 4861 × 208433 × 443590496466904165170264613677688132118233202295646662099904327138244017765587342295299419241666577<99> × 2482993087680026254972445559137589312830423241595173372042872704116611934306860025801565367663708472031191919<109> (Bob Backstrom / Msieve 1.54 snfs for P99 x P109 / December 9, 2019 2019 年 12 月 9 日)
23×10219-419 = 2(5)2181<220> = 61 × 24490171 × 10041339639623<14> × 23418084885848026987341656371<29> × 7274793015437106662077348706625607131389140196513210617513310302617756208144586827087038650810333941947804991123110325000269247333493200830221098790074907726802939758237<169>
23×10220-419 = 2(5)2191<221> = 32 × 131743 × 27138730218947609987071369422359<32> × 794192432467647113255649892024686918358082712525691527066954319640714329388748023641627544426127492884648344078183078382424541085640001317023679281793604430766290083423723290263937647<183> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4083776301 for P32 x P183 / April 19, 2013 2013 年 4 月 19 日)
23×10221-419 = 2(5)2201<222> = 29 × 35150669 × 367069247 × 98477605245857<14> × 7571146603450875229<19> × 633231591163192451029<21> × 33800607542046934571183<23> × 42797610149019534571889085324971032041746921256146359358874909461317639946978475791045920259463845591946517285289890402762235623<128>
23×10222-419 = 2(5)2211<223> = 245846970487876113156463210918610971236245057<45> × 10394903587724226971520068733146725758613204755924974993464870535219011890479787829555353596561462210125250618091028750257478861138302592864269858347782313182322294791341907693343<179> (matsui / Msieve 1.52 snfs for P45 x P179 / June 14, 2013 2013 年 6 月 14 日)
23×10223-419 = 2(5)2221<224> = 3 × 7 × 19 × 151 × 31858882933<11> × 13313889235164755363906620743916215862991301026653389435139914501087568544600269905355285179035291802150740321964458752512297022739771027519119682721898143351512671315315318553927920833223866392301732059583803<209>
23×10224-419 = 2(5)2231<225> = 944233 × 217992167 × 239280884975665593315209<24> × [5188684418124658330260209315510090174213810950365888309605032159342748798811649474698296994465057160084959536085332245783181472382642901230970683742924647309249281544084007957686564561049<187>] Free to factor
23×10225-419 = 2(5)2241<226> = 389 × 43499 × 1315818083<10> × 62986915305110387<17> × 1822259662575449146337981363768377872498163127463346657879492925713226249048725931188680058877053507141059643567849367175803187185666134889561266023858539159266362370499177467034818283192459521<193>
23×10226-419 = 2(5)2251<227> = 3 × 31799 × 602185355202289203049176958104002309<36> × 444856990657722188272565822067742119861982172457815744125645524489917404710781914210303400435008357277699846257440715395424279129684298493546044812212782122252598338026010889993653040087<186> (Bob Backstrom / GMP-ECM 7.0 B1=45540000, sigma=1:3303093375 for P36 x P186 / August 4, 2018 2018 年 8 月 4 日)
23×10227-419 = 2(5)2261<228> = 107 × 43391289323549<14> × 10793715817142274354649383509<29> × [5099504912175920312988822732798222979877276114984854831860975509835433649288805844282582688373882347701834130092632699871807350530890553158772942650405995700263202569588803758794131773<184>] Free to factor
23×10228-419 = 2(5)2271<229> = 17 × 202017461 × 70978413707660648175187<23> × [10483859874441509167213316753489375087278291723716738822303753591666358193608606572890664367235901199648865395328155032228174837990675561874766742589552569704132404465148915537579853554918693646529<197>] Free to factor
23×10229-419 = 2(5)2281<230> = 33 × 7 × 131 × 1673463161<10> × [616788219701565513748781763602859316708746741034888488827350494891054551131471087558698463533822930748404861771953230004604153920570343992982872363136314103764931664141213496801686848560705579354593765999826702041249<216>] Free to factor
23×10230-419 = 2(5)2291<231> = 43 × 344820370190773<15> × 50387050698417049<17> × 777498606344285902207<21> × [439952104449421663922317612000647736186072600851919279748761428101026003524666331070147587984062378035547687062675375834853970153718711294281683008976689329507964481891428013263<177>] Free to factor
23×10231-419 = 2(5)2301<232> = 157 × 383 × 1084477167912931538462845313<28> × 8252034288680930236190745497699216347<37> × 619162405683930861981000463733925949741<39> × 2318554941298555747247043538931856258217975052715196915999<58> × 3308137046356397841917360053644286904020924109990685242135286445429<67> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3299242912 for P28 / April 18, 2013 2013 年 4 月 18 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3938295577 for P39, B1=3000000, sigma=3543359446 for P37, Msieve 1.50 gnfs for P58 x P67 / April 22, 2013 2013 年 4 月 22 日)
23×10232-419 = 2(5)2311<233> = 3 × 6997 × 8831 × 438329 × 570525968771230246912789933953131<33> × [551272960760471665750741573200857036368141471207815153191145398774665301479647549841737177622398301564850900536889134967245630604381465537498581540302076050924725005236876769533615318469<186>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1507775340 for P33 / April 19, 2013 2013 年 4 月 19 日) Free to factor
23×10233-419 = 2(5)2321<234> = 3631 × 2443501 × 159562359250524148411<21> × [180516168736534101341866857367016933980004108695256282366952590987660875677788224948404559592097512746834096961492470627087620483589704667712654746135865075967054620562522330883898714155777554151555911311<204>] Free to factor
23×10234-419 = 2(5)2331<235> = 823 × 5720386459<10> × 36554890193<11> × 628705665370327<15> × 2613161005950175231<19> × 5499560772460908334189840684450891961<37> × 1643512794700088151869152905431210983529625438106553801717276962454383583816622334898675114388072733718357346723235641339517222935806074284043<142> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1893217051 for P37 x P142 / April 19, 2013 2013 年 4 月 19 日)
23×10235-419 = 2(5)2341<236> = 3 × 7 × 71 × 9859 × 5780147 × 54224927 × 170866875779748740888262563<27> × 278414647835202950993499044598751<33> × [116596898406566942245916273715964457021341872466901881152971665544534128584413659158131638084230507551447256271806535358216668508152805892790079017369096207<156>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1514416900 for P33 / April 19, 2013 2013 年 4 月 19 日) Free to factor
23×10236-419 = 2(5)2351<237> = 20248041897191661286997<23> × 2582682477972797710036351621981<31> × 4886875553677209543066311092085637745061037872950945072481587555137096811839865653568064737261731669298468077774003982090929666408803920214998783178839134070002952114530733695754929343<184> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2361744558 for P31 x P184 / April 18, 2013 2013 年 4 月 18 日)
23×10237-419 = 2(5)2361<238> = 14339917 × 348676572679<12> × 209205098436862700220721<24> × 81442422903012665071981882663<29> × [29998046280899521072118212982295921496280050727287434870303505576623435466935783823063733047367932074059154912611821732701792197290975373080416756488572772216350316059<167>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3326016518 for P29 / April 18, 2013 2013 年 4 月 18 日) Free to factor
23×10238-419 = 2(5)2371<239> = 32 × 89 × 31904563739769732279095574975724788458870855874601192953252878346511305312803440144264114301567485088084339020668608683589956998196698571230406436398945762241642391455125537522541267859619919545013177971979470106810930780968234151754751<236>
23×10239-419 = 2(5)2381<240> = 33349 × 400416587 × 104219539409077<15> × 1920450557379587<16> × 15350654858654024251<20> × 6228898641999895233505712708090409560444095261397699806577653834506610134460645633367359331666712817177642620624478848452584526796371945175499580229077382594441452701882725737573<178>
23×10240-419 = 2(5)2391<241> = 741973 × 286564543 × 12019178116424442087850529455006591861616020324291993965774877631940741665427263793575198360402345507333456244374703745778259376742243864884894508485980909101528869215181363523596910714499207897224464017888855304451158086044509<227>
23×10241-419 = 2(5)2401<242> = 3 × 7 × 19 × 257 × 1423979 × 327748101283<12> × 55832827791723735842999267<26> × 9564139768768460294025123167205378851318508526614351516113496365553377821240813375277805275419161496201907413443705054816547201428820412932440315336781231881331420032450528094595591428017873403<193>
23×10242-419 = 2(5)2411<243> = 1583039 × 7897633 × 477436298891275453859920261302899887<36> × 42813558778923755662736811546665628301277591572678265454758430601315007571770424607489883005815085712266438185776646399400488847526065410153328101750886662833954631314689395614767143872718561679<194> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3488323360 for P36 x P194 / April 16, 2013 2013 年 4 月 16 日)
23×10243-419 = 2(5)2421<244> = 283 × 40709 × 27898766071870889223474065799033541<35> × [7951031269245441893985053701553541517296361833628090142609252113405511736980838304408566463772438418380029507768436920117480719742952010985474904033778651505810302723019981805867405834852293023372358613<202>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4228977265 for P35 / April 19, 2013 2013 年 4 月 19 日) Free to factor
23×10244-419 = 2(5)2431<245> = 3 × 17 × 30973526518457<14> × [16177987492645994581550107741696811274344715263207780996832657157230769723434580653647167290739875370798954359218577892888558065954596538741884692578688411466854813313623036035051972006284133748254434897079100067823302111083702093<230>] Free to factor
23×10245-419 = 2(5)2441<246> = 60761 × 823222493279<12> × [5109085673961347923402372659537787686179384655785826699812290969832295734060880408884591697420863140752893932976579202476063890019879563878332009298762391960847234921993051958756845970587917322975046534959913446021328714849242729<229>] Free to factor
23×10246-419 = 2(5)2451<247> = 2861 × 5650231 × 27472317085115675039<20> × 5214343729140958543089057829<28> × [1103586345298594438994117690381297515129737943477258496722973333236721840727488145962980545196799078206813250605973826826604021953825705995875064232563912344614165792820986607186295607113031<190>] Free to factor
23×10247-419 = 2(5)2461<248> = 32 × 72 × 14262019 × 32887097 × [123549270990139120460002754463112063156106495306438417905251862636197119989579262266654855856327604271714481555040212734508939341909583360346920539145064622917407880091163149702723738412535369857534816538755053902804003000236892677<231>] Free to factor
23×10248-419 = 2(5)2471<249> = 22488329 × 1846625839<10> × [6153882959154053143496351364419222170567582630689707838233361809307329710148584429484865317512139890301641466386801699107476417924052054277746804651546538352335031803630336962775068965867257415070616145198920987910043278054017414921<232>] Free to factor
23×10249-419 = 2(5)2481<250> = 29 × 44437335871184743<17> × 1983075799580674527900749884144743225724057608980063151275620319846328233508912214334690569329498833548104950314937270279372145021221228273467252851430839685897045021369310990506322697412059541728075171462587806674667995251437989533<232>
23×10250-419 = 2(5)2491<251> = 3 × 1973 × 28712200062594441173384537<26> × [150373225410428175815735220631842106468349982611935398437779311403328578484167882594415576247440473813772046103982344957382790830014987081611930650726667043522490594526506134892154796560788037287201533764364048594663263017<222>] Free to factor
23×10251-419 = 2(5)2501<252> = 43 × 4877 × 626237597 × 15722717311755910711<20> × 123764864829031417072791140339238368466309579496997229352772750013388743505678313285732354941681502358793679444345957014213456126060847686006586921249689787571860608125012140839004607320968258465147839050837881458689123<219>
23×10252-419 = 2(5)2511<253> = 251 × 40714469 × 80963903 × 3088669177050240254190668334716165493529024715174136863566657736675902831416883990555905681980797904252953343826783041295079801160479924209328199187202960327259591935247116072237548622745526779394447196499489375873289996807725661827543<235>
23×10253-419 = 2(5)2521<254> = 3 × 7 × 25969 × [46860919439763446078668074124194883561821064227779927267778166927152255813351735412654200439636921596180712819782479761685738042163010394363161123529254762648424321958150754022755254993693131472791837072325346806458901649320995464474227614895334099<248>] Free to factor
23×10254-419 = 2(5)2531<255> = 773075594491<12> × 268454124319393299794463863<27> × 168104869035507080923156964399<30> × [7325090426756312853282447269669085469716524174140159225668610624346645648808618832873606712828815249249294811556087046932872357150626332447849628590883149135445455479596004627138054198453<187>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=3413306125 for P30 / March 3, 2016 2016 年 3 月 3 日) Free to factor
23×10255-419 = 2(5)2541<256> = 15771891451<11> × 19209894459310183307717285503<29> × [8434834551257129354101627346792271362905611538068322993900061690182733036243317153016935188852335091797790176389196777470485073606724311366578591912839709143009145027070031273151489282660928034629194574610513961646867<217>] Free to factor
23×10256-419 = 2(5)2551<257> = 34 × 21929 × 11673491 × 56020431811<11> × [22000587344908786538041943016170724186142829624948694017177520581525439107982362913324686650428006824282092860068324092906732587918819009060850979949986992111707910740140575710311109129100109447384705880685284856433681502151411360399<233>] Free to factor
23×10257-419 = 2(5)2561<258> = 83 × 241446546924524501324161<24> × 12752232890774649795154743548877810853151101930844285984028327189596120316953586955158817976063245713650970893943546775515310946827589397832090668297878654420075926737046977372795859581179956419173114713256910010112659214250125790277<233>
23×10258-419 = 2(5)2571<259> = 17137 × 9865211 × 245289404079440943752556476574021411539<39> × 61626196334827774833782703420129420277729196336744940243810859190576811928476480755271739851543671994580360024336719066541342017592601217115144151836631221757157472226829585193466690011117136909076175466330287<209> (Marlon Trifunovic / GMP-ECM 7.0.5-dev B1=3000000, sigma=1:636279787 for P39 x P209 / February 28, 2022 2022 年 2 月 28 日)
23×10259-419 = 2(5)2581<260> = 3 × 7 × 19 × 3861983 × [16584488180665857427142742838959278190517413312651161350023811968471241345197275963522488334114627489927446615909239221776084996761770162487113502065910548397667743242011012848184485547712513864631217705777425077342407786106623833525436038690853230703<251>] Free to factor
23×10260-419 = 2(5)2591<261> = 17 × 668431611439<12> × 4163527807721<13> × 5401544461739428575181870562287178188935755199231209155644195581359549794129081581741875714412459562020433161465277746187280728741025246993294113177964503636951984359730080907483696989594235700547215474476483012655790445493588969251737<235>
23×10261-419 = 2(5)2601<262> = 23817623 × 1762030311781<13> × 238786312428167521<18> × 58831302932691959473<20> × 933755059343192223446744413426213<33> × 4642187428651514531285288713897767499898805276684872457580773723894333355802206189872801344498311478280968497743753431484170605630592083675661080318496127362082384788306513<172> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1038660447 for P33 x P172 / March 4, 2016 2016 年 3 月 4 日)
23×10262-419 = 2(5)2611<263> = 3 × 47 × 56131 × 1098509177<10> × 27982779508459<14> × 6753738571154831<16> × [15553375208701466910324594087065785698822189842086524305576657658093894730561098770919307180737823791193155540909748165394039629469523041550364420912227567961057405426649933818715972207566128040988554589894257039264157<218>] Free to factor
23×10263-419 = 2(5)2621<264> = 193 × 23629 × 66491 × 299534821 × 42674162077<11> × 100387996693169<15> × 45843036687328555551568066803202003<35> × 14326903184364012846754147758836050468822832826505569540714050960729723706481550695363342794277559237332400808020322884860812598174737996431226922823731673747983981562438917675540664027<185> (Marlon Trifunovic / GMP-ECM 7.0.5-dev B1=3000000, sigma=1:3789642081 for P35 x P185 / February 20, 2022 2022 年 2 月 20 日)
23×10264-419 = 2(5)2631<265> = 109 × 1628108759<10> × 162273545583479921020803157<27> × [88741689051681941418903296423023929536860165251996781895751742585228487275278806501778999538996520563166262935750702508428588388491766365280466389323691396150535619355112719470980229727174316904420842266004622659717078222319753<227>] Free to factor
23×10265-419 = 2(5)2641<266> = 32 × 7 × 59 × 6833 × 3687040391863819<16> × 24476493673072673153<20> × 2065456811506392223877<22> × 348688979766356532429011726074111362439<39> × [15481031887960269171053203304659715291393409719457732716496954703133719672688597256952113090440854008601184296485564183757836337879348300484230261602209202727885571<164>] (Seth Troisi / for P39 / December 6, 2023 2023 年 12 月 6 日) Free to factor
23×10266-419 = 2(5)2651<267> = 3820759 × [66886070426204729362819155972819943774405963724892241451385851752375785951313745660366318722420219531133880874338202319370458999260501789187843450883857253377026804243752499321615300927264859038624408280018592001106470090250538062085453585414718791621129612089<260>] Free to factor
23×10267-419 = 2(5)2661<268> = 113 × 18735028834900253<17> × 19145983206800357043339097<26> × 63048512332988566775632487775378986910213223285891090729857028077787868935035740493542025216679543461114139409598586878848017364304517361209999932688460009411867532262368613815623375211945109108756462893511626643527615496147<224>
23×10268-419 = 2(5)2671<269> = 3 × 1579 × 183571 × 2227747 × [13192041249729458924278221479803512275399728092487345692005214705437479741945077050606437538408947964495134063271263289394557740491470150741007647095767092572672560048727946090528188562525398555458104767566914968302275572150691584218163861243326872228279<254>] Free to factor
23×10269-419 = 2(5)2681<270> = 130303 × 11843258686639<14> × 394996822243343<15> × [419243265125589424789196925618299654661840135221353996314227881260371104209782080803441157150710879387314523770777893539694068163531506943119230011878574834766753006388303943787429587540798585825946964857167297283922004545284305330468321<237>] Free to factor
23×10270-419 = 2(5)2691<271> = 71 × [35993740219092331768388106416275430359937402190923317683881064162754303599374021909233176838810641627543035993740219092331768388106416275430359937402190923317683881064162754303599374021909233176838810641627543035993740219092331768388106416275430359937402190923317683881<269>] Free to factor
23×10271-419 = 2(5)2701<272> = 3 × 7 × 91940430485500589<17> × 42232250207373661931<20> × [313411751842514071626342305116482466632179630447788132452437889382230326987618069603367266486795802470056836517047819543559200893386759778943415942088029723975114182577551391403705919402697082086777647692862501372992407794921513907309<234>] Free to factor
23×10272-419 = 2(5)2711<273> = 43 × 439 × 384320410447639<15> × 496881638430101<15> × [70893424093428315141319549649370753077597959309023968558950359760600304885101884815076570449583064071955958997244280043796473783087094682812957351546350885462664324122569881042767765871333610024702927850683337048995236921848839453742372217<239>] Free to factor
23×10273-419 = 2(5)2721<274> = 233 × 8821 × 8244922396085512899889<22> × [150808219037087369418016063591397791394191396328767810837474706145498173421231157701080035742938726345331666214461783444130244099999951327704045076942453965415848580816701139898541985964612325174478156536966446859781468227027984829350199229853563<246>] Free to factor
23×10274-419 = 2(5)2731<275> = 32 × 359 × 719 × 269281 × 8024437 × 2088818156167356142328674161220203606255086201<46> × [2437241482092781449846611525765433104442529165181136388031623280822458303825501483670629211717980515336486615965047113387392280540017992116826770993690036940925590034283631497990136458503310037158050627332705547<211>] (Ignacio Santos / GMP-ECM B1=3000000 for P46 / March 27, 2024 2024 年 3 月 27 日) Free to factor
23×10275-419 = 2(5)2741<276> = 523 × 323812420208027297<18> × 119105721118065099468684254891513<33> × 15534736319112484425754540382498266921451<41> × [815555697632085744012062896682528134556436185671337754595124548790011092557678480751667553338419335300404641300994857312127842325334469002595767392635622348666719205697382376124393167<183>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=4072054522 for P33, B1=1e6, sigma=2045181026 for P41 / March 5, 2016 2016 年 3 月 5 日) Free to factor
23×10276-419 = 2(5)2751<277> = 17 × 911 × 33476419 × 13325752123107744783290521<26> × [369902530824842655554310020406771545348764652517514436446775020178072203915509247628476368557454006068984486925563396927881254991975705673555883994497193525915831922927502426617137842821765788363568699714060678400137347946635128561724081027<240>] Free to factor
23×10277-419 = 2(5)2761<278> = 3 × 7 × 19 × 29 × 68055963581<11> × 2676813599768739604424886791579<31> × [12123558586462555693718800429473414807593456498346788646410011300846983674605586102459146630664482114025676667670823379716047608789565796865990012848866337747806164152572839842432592212584580551765128599757377837554003633535759826219<233>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1739346469 for P31 / March 5, 2016 2016 年 3 月 5 日) Free to factor
23×10278-419 = 2(5)2771<279> = 4423 × 385537 × 59501386735433717<17> × 1251799506628317895243873<25> × 2754883736494994331296720964655957<34> × [730360344586543104724906336375668606738154705039768262560763481810764412797873687952889636529654265132487824708381054018017119683451159858693355996740091534647110867872909960019683617089457602673<195>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1021602843 for P34 / March 5, 2016 2016 年 3 月 5 日) Free to factor
23×10279-419 = 2(5)2781<280> = 61 × [41894353369763205828779599271402550091074681238615664845173041894353369763205828779599271402550091074681238615664845173041894353369763205828779599271402550091074681238615664845173041894353369763205828779599271402550091074681238615664845173041894353369763205828779599271402550091<278>] Free to factor
23×10280-419 = 2(5)2791<281> = 3 × 97 × 107 × 463082797 × 21192609073<11> × 33571352083<11> × 224950616830271<15> × 15106108283903776498096391<26> × [733089282784365423430669372172492335933433884888241913714527660459977878861960260070009877580134386588514047023686048379059943263011854814870948963292664764372540626290335619308659915990482705070615833013041<207>] Free to factor
23×10281-419 = 2(5)2801<282> = 3595887079<10> × [71068848921313848508521408871403426947144008343749093450204962778130540832691024432348576415226067658048267526132612340454296995335529988581033402232583164927453372780273436265921062187936284624235708808684633212742650630814081677550797071499351038313168219361527830544969<272>] Free to factor
23×10282-419 = 2(5)2811<283> = 89 × 3919 × [7326896495481694067666756182228198421276797725731327802482161396238881036367210035681985932995850109537102607451326311618004924311566398088125999683350647108312873771271493689790033445689698287959137579683981397328358689173618457917651417483695266092174269277462880508830662361<277>] Free to factor
23×10283-419 = 2(5)2821<284> = 33 × 7 × 197 × 4457 × 559034431336033<15> × 2716012368255858558057701<25> × [101424847088330868980587104562985582018800514416394137555394038787582659297024430447531826484202191345119201051654477156661875049249509579588905811105307859152545882426366522557953647459788987620872883494277175032551367963522879974997387<237>] Free to factor
23×10284-419 = 2(5)2831<285> = 27158941157747292202741<23> × 285929057360933464020964445533<30> × 32908963192319208520676659687155104166625699106130983026837672865771302722869343049686319054410510217349367855793789290639239384634665378930902026122802847174724588618994031251735099022608836847528475817620065779445310518052762783967<233> (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=1500412629 for P30 x P233 / March 6, 2016 2016 年 3 月 6 日)
23×10285-419 = 2(5)2841<286> = 2068279 × 618772693808251607<18> × [1996848258854830697392787411303872408917126694179025949633882045941832173991898180843159175291636430321591599797800762496113496508101808805437387493028320875482733528918886825001019762790225970338051073153109790772528705140487787072482364604758157307081125956367<262>] Free to factor
23×10286-419 = 2(5)2851<287> = 3 × 409 × 20939 × 994683300989043446672435570329802860646032878426169872005493488831222340749549310077499365489359944087035273204061783204994752894222432645312191452213271326679222078256950889073233977532188740879581230718794005140618443131471136558915695214626643222759710155686662599103919222167<279>
23×10287-419 = 2(5)2861<288> = 2399 × 4783 × 6899687 × 2897189881<10> × 8091763609<10> × 14589088543717<14> × 866540578384697<15> × 2821491403991732098589377426133071350337697<43> × [3860196078625563910308459819220897717061995562935027478873507994931648836393881439046610776690506824959036281027218896650082265847026092517508231697464308955157232669450453843587084637<184>] (Ignacio Santos / GMP-ECM B1=3000000 for P43 / March 28, 2024 2024 年 3 月 28 日) Free to factor
23×10288-419 = 2(5)2871<289> = 16777127 × 539571196811<12> × 666821488589495905186229398262393<33> × 14781083649452189589153516296922323<35> × [28641985118771076256101650357486087460167936867559650175153361879208214831093903729464994462440380831362226711343320810892375210346863675925085060055798237738628074977877813539521178537234299823018797697<203>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=4141482356 for P33, B1=1e6, sigma=2912813422 for P35 / March 6, 2016 2016 年 3 月 6 日) Free to factor
23×10289-419 = 2(5)2881<290> = 3 × 72 × 223 × 14456096561219<14> × 224805549936676375447843<24> × [239886086556695798207643946072860897340073874961590831331997883612500678583876906528776878321808057238820036820317526065104506563639488085052651188748083145069886241029288278988617602894798913437031881570002656778207914160056450888377214239510268963<249>] Free to factor
23×10290-419 = 2(5)2891<291> = 11968474993597<14> × [21352390817733663976530360467585005911739160453476437051434304035885056725884256245795094888645508147658974449544822456995653476963332819640912948367801341771160281231844060022939687126592015459540520454192660971740440094298529551956204969867183244115489222112845040386858171083<278>] Free to factor
23×10291-419 = 2(5)2901<292> = 453073 × [5640494038610898366390306982661857041923830278024855940556059521435961877126987385157702082347779619521700819858070455656275159975446684211055515459000107169386733607068961415832670575283796552775282472262870565130907283275665412760317996339564607812770912315577303338657469228039533487<286>] Free to factor
23×10292-419 = 2(5)2911<293> = 32 × 173 × 19225605101051<14> × 3250156503819137659<19> × 1471730210057663109562717<25> × [6284685606454353476188248153327001615288920283751425211585967315959525441787651671713776992686907235689569738498566726184995971746883047539888466923714165409753402645115886629031329466589207560237785202173520551016150275584177857851<232>] Free to factor
23×10293-419 = 2(5)2921<294> = 43 × 185233 × 3845291381<10> × 22029621247<11> × 351949319123477767907<21> × 1076173010618942572523839488356671681751095528645108448035051592844476832857555557106852790371682028734693772975712443215395909660850328295690101220837372520309813646521684932101481414751431993493343337898202222804541727475462295720508210812891021<247>
23×10294-419 = 2(5)2931<295> = 457 × 227477077 × 24582807900593661303187686185140148553733776362238609515144049883472329176903768822015751895654289288590012734608900969639851101293777873162582429522294485612072713575119394432241442462434504956157980425081207165137849668960338534912769073276301182942045666673845189664132889270035659<284>
23×10295-419 = 2(5)2941<296> = 3 × 7 × 19 × 12671 × 9697759876243<13> × 42776086182050147<17> × 165293611737049889898622944930229961<36> × [73717907325714454485727252329521743811162568382225652930858568031087172506979567793330458457306976145880147161831840667614465375171580963820895291594285739287105652871078044073544643114885883512855439667346825933584711985199<224>] (Marlon Trifunovic / GMP-ECM 7.0.5-dev B1=3000000, sigma=1:4288421775 for P36 / April 15, 2022 2022 年 4 月 15 日) Free to factor
23×10296-419 = 2(5)2951<297> = 20219 × 10412371 × 275433441888928559<18> × 4407165414084870282692159638266434255920033960766527798579718759251984670637982104146670794182679064704902780275685517661001319986984155187417069480338054858344876104440106822507667668791796735603201664614172500267334027397873758517075186143872252014072888313868830961<268>
23×10297-419 = 2(5)2961<298> = 23773 × 44579 × 46217167 × 34113279899<11> × 503712388183<12> × [3036418185166722308977598994037737817404253302078986400016589554125285458742538234852452085222774761198427266148915916453275019945345353114057814042973367283829782638380312043918102678119811214913840234210550951756680947579317972842342303822441489684350572627<259>] Free to factor
23×10298-419 = 2(5)2971<299> = 3 × 83 × 151 × 877 × 116579 × 17775934506727<14> × 1943150313582914250208186511857<31> × 192464339950727191553014411244373230493868580593334030624905491003806727212360623424483512009582503938092129780186712062032197461694906143571650528845193451890447652640703254682224047063911403760483736675517597610847690737494241077980195524577<243> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2479280332 for P31 x P243 / March 7, 2016 2016 年 3 月 7 日)
23×10299-419 = 2(5)2981<300> = 33769 × 103720207 × 96760040789963<14> × 754063134259211075503463160871531382612476313715158353765356440318538733586101462571108067791947392884089829759167907143088931213512582694553041190499729403525067540696870362504321943649348001330372585182120056644175326207229409782104532263175373048961164790124549918189819<273>
23×10300-419 = 2(5)2991<301> = 421 × 1151 × 320669 × 13393733 × 36442963 × 5557739576718070415245927177<28> × [6062579121629400524429096176181512514979335860308943124745253968757957953732436182494537888225151465542589103715820439650167528973279960757327336416971869929525743703299678603114755701291736319836916886132326319078275988306116864076265189718582903<247>] Free to factor
plain text versionプレーンテキスト版

4. Related links 関連リンク