Table of contents 目次

  1. About 588...881 588...881 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...881 588...881 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...881 588...881 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...881 588...881 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

58w1 = { 51, 581, 5881, 58881, 588881, 5888881, 58888881, 588888881, 5888888881, 58888888881, … }

1.3. General term 一般項

53×10n-719 (1≤n)

2. Prime numbers of the form 588...881 588...881 の形の素数

2.1. Last updated 最終更新日

September 16, 2015 2015 年 9 月 16 日

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

  1. 53×103-719 = 5881 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  2. 53×105-719 = 588881 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  3. 53×106-719 = 5888881 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  4. 53×1021-719 = 5(8)201<22> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 3, 2004 2004 年 12 月 3 日)
  5. 53×10309-719 = 5(8)3081<310> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 3, 2004 2004 年 12 月 3 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 4, 2005 2005 年 1 月 4 日)
  6. 53×10816-719 = 5(8)8151<817> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006 2006 年 5 月 31 日)
  7. 53×10858-719 = 5(8)8571<859> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006 2006 年 5 月 31 日)
  8. 53×101115-719 = 5(8)11141<1116> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 13, 2006 2006 年 9 月 13 日)
  9. 53×101419-719 = 5(8)14181<1420> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 8, 2006 2006 年 9 月 8 日)
  10. 53×101689-719 = 5(8)16881<1690> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / August 20, 2006 2006 年 8 月 20 日)
  11. 53×1012009-719 = 5(8)120081<12010> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 9, 2010 2010 年 9 月 9 日)
  12. 53×1018693-719 = 5(8)186921<18694> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 11, 2010 2010 年 9 月 11 日)
  13. 53×1028098-719 = 5(8)280971<28099> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 17, 2010 2010 年 9 月 17 日)
  14. 53×1090965-719 = 5(8)909641<90966> is PRP. はおそらく素数です。 (Bob Price / September 15, 2015 2015 年 9 月 15 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了 / Ray Chandler / September 19, 2010 2010 年 9 月 19 日
  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 / September 15, 2015 2015 年 9 月 15 日

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

  1. 53×103k+1-719 = 3×(53×101-719×3+53×10×103-19×3×k-1Σm=0103m)
  2. 53×106k+2-719 = 7×(53×102-719×7+53×102×106-19×7×k-1Σm=0106m)
  3. 53×108k+7-719 = 73×(53×107-719×73+53×107×108-19×73×k-1Σm=0108m)
  4. 53×1016k+1-719 = 17×(53×101-719×17+53×10×1016-19×17×k-1Σm=01016m)
  5. 53×1018k+4-719 = 19×(53×104-719×19+53×104×1018-19×19×k-1Σm=01018m)
  6. 53×1022k+9-719 = 23×(53×109-719×23+53×109×1022-19×23×k-1Σm=01022m)
  7. 53×1028k+26-719 = 29×(53×1026-719×29+53×1026×1028-19×29×k-1Σm=01028m)
  8. 53×1034k+22-719 = 103×(53×1022-719×103+53×1022×1034-19×103×k-1Σm=01034m)
  9. 53×1041k+2-719 = 83×(53×102-719×83+53×102×1041-19×83×k-1Σm=01041m)
  10. 53×1043k+18-719 = 173×(53×1018-719×173+53×1018×1043-19×173×k-1Σm=01043m)

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 16.28%. 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 16.28% です。

3. Factor table of 588...881 588...881 の素因数分解表

3.1. Last updated 最終更新日

May 8, 2017 2017 年 5 月 8 日

3.2. Range of factorization 分解範囲

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

n=188, 198, 199, 201, 203, 206, 209, 211, 212, 214, 219, 220, 222, 223, 224, 226, 231, 232, 233, 235, 244, 245, 249 (23/250)

3.4. Factor table 素因数分解表

53×101-719 = 51 = 3 × 17
53×102-719 = 581 = 7 × 83
53×103-719 = 5881 = definitely prime number 素数
53×104-719 = 58881 = 3 × 19 × 1033
53×105-719 = 588881 = definitely prime number 素数
53×106-719 = 5888881 = definitely prime number 素数
53×107-719 = 58888881 = 32 × 73 × 89633
53×108-719 = 588888881 = 7 × 89 × 359 × 2633
53×109-719 = 5888888881<10> = 23 × 256038647
53×1010-719 = 58888888881<11> = 3 × 61 × 331 × 972197
53×1011-719 = 588888888881<12> = 97 × 11447 × 530359
53×1012-719 = 5888888888881<13> = 5701 × 1032957181<10>
53×1013-719 = 58888888888881<14> = 3 × 1013 × 19377719279<11>
53×1014-719 = 588888888888881<15> = 72 × 47 × 751 × 340486177
53×1015-719 = 5888888888888881<16> = 73 × 617 × 130745074241<12>
53×1016-719 = 58888888888888881<17> = 32 × 6543209876543209<16>
53×1017-719 = 588888888888888881<18> = 172 × 163 × 1851503 × 6751861
53×1018-719 = 5888888888888888881<19> = 173 × 1386043 × 24558992879<11>
53×1019-719 = 58888888888888888881<20> = 3 × 2203 × 12781 × 65867 × 10584367
53×1020-719 = 588888888888888888881<21> = 7 × 6806327707<10> × 12360113669<11>
53×1021-719 = 5888888888888888888881<22> = definitely prime number 素数
53×1022-719 = 58888888888888888888881<23> = 3 × 192 × 103 × 527919469371208069<18>
53×1023-719 = 588888888888888888888881<24> = 73 × 1607 × 19009 × 264079903482319<15>
53×1024-719 = 5888888888888888888888881<25> = 7121 × 12123434231<11> × 68212931431<11>
53×1025-719 = 58888888888888888888888881<26> = 34 × 299477 × 65092267 × 37295417239<11>
53×1026-719 = 588888888888888888888888881<27> = 7 × 29 × 503 × 5767257429696587851109<22>
53×1027-719 = 5888888888888888888888888881<28> = 1229 × 14737 × 44563 × 7296220891954919<16>
53×1028-719 = 58888888888888888888888888881<29> = 3 × 52905920969387<14> × 371028975017521<15>
53×1029-719 = 588888888888888888888888888881<30> = 1104449 × 199159763623<12> × 2677232520103<13>
53×1030-719 = 5888888888888888888888888888881<31> = 216411202177<12> × 27211571442001605553<20>
53×1031-719 = 58888888888888888888888888888881<32> = 3 × 23 × 73 × 120427 × 248887 × 390063513887852537<18>
53×1032-719 = 588888888888888888888888888888881<33> = 7 × 2719 × 773392758107<12> × 40006081140077851<17>
53×1033-719 = 5888888888888888888888888888888881<34> = 17 × 727079 × 476434099675784797306101367<27>
53×1034-719 = 58888888888888888888888888888888881<35> = 32 × 151 × 8923 × 10309561429<11> × 471045457166534777<18>
53×1035-719 = 588888888888888888888888888888888881<36> = 249779 × 2666281 × 884242774508149421827219<24>
53×1036-719 = 5888888888888888888888888888888888881<37> = 10141 × 40129 × 100577513 × 143877653899682891933<21>
53×1037-719 = 58888888888888888888888888888888888881<38> = 3 × 661981800841<12> × 29652823694989204993466147<26>
53×1038-719 = 588888888888888888888888888888888888881<39> = 7 × 257 × 487 × 28168661 × 52981991617<11> × 450379643446301<15>
53×1039-719 = 5888888888888888888888888888888888888881<40> = 73 × 22531 × 29031681353<11> × 123326908229227740619979<24>
53×1040-719 = 58888888888888888888888888888888888888881<41> = 3 × 19 × 6364698105533<13> × 162323237399322949583843501<27>
53×1041-719 = 588888888888888888888888888888888888888881<42> = 383 × 29788255769355667<17> × 51616614023938225547221<23>
53×1042-719 = 5888888888888888888888888888888888888888881<43> = 389 × 28863400884919<14> × 524488846910387211753173291<27>
53×1043-719 = 58888888888888888888888888888888888888888881<44> = 32 × 83 × 78833853934255540681243492488472408151123<41>
53×1044-719 = 588888888888888888888888888888888888888888881<45> = 7 × 11527 × 5248098173<10> × 18064170661673<14> × 76983747590692301<17>
53×1045-719 = 5888888888888888888888888888888888888888888881<46> = 8316036677323<13> × 23890111037137<14> × 29641405714917392131<20>
53×1046-719 = 58888888888888888888888888888888888888888888881<47> = 3 × 1057019 × 1439273765063<13> × 12902857543795728614844555191<29>
53×1047-719 = 588888888888888888888888888888888888888888888881<48> = 73 × 4373 × 630901 × 2475779 × 62278991 × 18963406916939064856501<23>
53×1048-719 = 5888888888888888888888888888888888888888888888881<49> = 8123 × 19403329703<11> × 37362905684305402197576029039534149<35>
53×1049-719 = 58888888888888888888888888888888888888888888888881<50> = 3 × 17 × 19901131630841<14> × 65653305833119<14> × 883748750693136097789<21>
53×1050-719 = 588888888888888888888888888888888888888888888888881<51> = 7 × 1020431 × 83576701427<11> × 986430404304479046285922004045459<33>
53×1051-719 = 5(8)501<52> = 1277 × 5219363 × 270069505663<12> × 105104482081139<15> × 31126348409390483<17>
53×1052-719 = 5(8)511<53> = 33 × 89 × 31586237 × 775857030136164707942794544452471768839671<42>
53×1053-719 = 5(8)521<54> = 23 × 109 × 523 × 1103 × 90832571 × 4482912043331268641870927013961628917<37>
53×1054-719 = 5(8)531<55> = 29 × 59 × 2447 × 135999900809<12> × 10342148982373708347801189384190257577<38>
53×1055-719 = 5(8)541<56> = 3 × 73 × 324049601 × 829808261428236393837035673125349789656718499<45>
53×1056-719 = 5(8)551<57> = 72 × 103 × 2339 × 3607 × 196331 × 94832058049<11> × 742813241475451784330375535329<30>
53×1057-719 = 5(8)561<58> = 9433 × 13772342817761197393<20> × 45328954386675800692352806994309449<35>
53×1058-719 = 5(8)571<59> = 3 × 19 × 5693 × 928699 × 195408001355075689093084587602280319205325220919<48>
53×1059-719 = 5(8)581<60> = 1439 × 3041 × 6079 × 22137266975879997584492865758562678360431746851761<50>
53×1060-719 = 5(8)591<61> = 47 × 163451145079199928449<21> × 766562438051565733856576133742869405727<39>
53×1061-719 = 5(8)601<62> = 32 × 173 × 227 × 335576792461<12> × 496508824638364333888450621457281750844384939<45>
53×1062-719 = 5(8)611<63> = 7 × 14831 × 6036631328398351551723133<25> × 939658900966640069286878670397021<33>
53×1063-719 = 5(8)621<64> = 73 × 171731111 × 1859895683663<13> × 160979708619372611<18> × 1568923604310336361825739<25>
53×1064-719 = 5(8)631<65> = 3 × 431059762717327820590592963<27> × 45538069955515600072496823745066709929<38>
53×1065-719 = 5(8)641<66> = 17 × 5279 × 10079 × 10710374819<11> × 60786993230888927604330673214722109188883285867<47>
53×1066-719 = 5(8)651<67> = 547809605884906381<18> × 10749882487687030023021378185909490274022078632501<50>
53×1067-719 = 5(8)661<68> = 3 × 131 × 293 × 466331 × 1096677422571488573157642767070124807067895827091213178799<58>
53×1068-719 = 5(8)671<69> = 7 × 84126984126984126984126984126984126984126984126984126984126984126983<68>
53×1069-719 = 5(8)681<70> = 23131 × 254588599234312778906614019665768401231632393276939556823694993251<66>
53×1070-719 = 5(8)691<71> = 32 × 61 × 877 × 218744934291839<15> × 1497871847355353<16> × 373292066202795930160185719879978791<36>
53×1071-719 = 5(8)701<72> = 73 × 113 × 6364765061<10> × 194707126518016727<18> × 57606014795866199553396322501488149293027<41>
53×1072-719 = 5(8)711<73> = 19001638949978093411483292353<29> × 309914787055549124861366649484252317708420977<45>
53×1073-719 = 5(8)721<74> = 3 × 467 × 971 × 130469 × 18942967 × 20460813561661003<17> × 856047297349113315460909978111401345019<39>
53×1074-719 = 5(8)731<75> = 7 × 991 × 84891003155382570115163455224000128137363253407653004020309772075665113<71>
53×1075-719 = 5(8)741<76> = 23 × 24799 × 12320448234531581377<20> × 1935414601243321605500959<25> × 432982988896796484956780471<27>
53×1076-719 = 5(8)751<77> = 3 × 19 × 191297 × 5400703626086421590684320201359426394732475687331501231243241669024889<70>
53×1077-719 = 5(8)761<78> = 1811 × 11217617 × 640033828396636394021746364327<30> × 45290944032109792251013954122507637069<38>
53×1078-719 = 5(8)771<79> = 1723 × 249433 × 1810739385797299987<19> × 7567252481558441531474173718208851119511917081763257<52>
53×1079-719 = 5(8)781<80> = 33 × 73 × 18913 × 19023881 × 83039971735286605303083574612839591473231739353808478739716533587<65>
53×1080-719 = 5(8)791<81> = 7 × 263 × 1377425118623<13> × 2140234132645573623178530253<28> × 108505133899209751853390153523354379739<39>
53×1081-719 = 5(8)801<82> = 17 × 313 × 127107968483092153063368594434293<33> × 8706975523887808671037951737209736665513544677<46> (Makoto Kamada / GGNFS-0.70.1 / 0.14 hours)
53×1082-719 = 5(8)811<83> = 3 × 29 × 6211 × 41597 × 226643 × 15497719 × 745899774432181616569046041284707022402873013761676948313917<60>
53×1083-719 = 5(8)821<84> = 95111 × 114571 × 27803521223963<14> × 362177277718577<15> × 11515990247800079<17> × 466021140831431727043581445169<30>
53×1084-719 = 5(8)831<85> = 83 × 1471 × 48232813420006788996002136804639814640387973830513533854429728886085925392028117<80>
53×1085-719 = 5(8)841<86> = 3 × 258858156034976966128582043589426419<36> × 75831605734598797514321239433181893407284362046233<50> (Makoto Kamada / GGNFS-0.70.3 / 0.16 hours)
53×1086-719 = 5(8)851<87> = 7 × 216660013 × 9273643199<10> × 41870309655332305070117723204095084730629672490821257008703279042109<68>
53×1087-719 = 5(8)861<88> = 73 × 12611 × 362504857789<12> × 17646035296551866236141897788241545229657766805015381372793198528203743<71>
53×1088-719 = 5(8)871<89> = 32 × 307 × 10867 × 24509 × 4790117 × 22888234738212157<17> × 61431256064071256744393<23> × 11881448800631545245681966651037<32>
53×1089-719 = 5(8)881<90> = 2477 × 2549 × 173617 × 3144457 × 24319157 × 15751326793<11> × 445999068794380552343439707090512553984992327365615613<54>
53×1090-719 = 5(8)891<91> = 103 × 15530717964718934354255993<26> × 3681328748792105755986721998852761638866417150499267372708235039<64>
53×1091-719 = 5(8)901<92> = 3 × 191 × 14433366476376882121<20> × 7120509977091590839924585451198628198749604746526788747649789653995357<70>
53×1092-719 = 5(8)911<93> = 7 × 67537 × 6659333 × 29334098039133288295361<23> × 6376613339626367516413377119408574820099517297915040673643<58>
53×1093-719 = 5(8)921<94> = 20149 × 21881 × 340467921179<12> × 174742186484123448271<21> × 224511572927862778526862044082485723569405656200033761<54>
53×1094-719 = 5(8)931<95> = 3 × 19 × 17883277 × 142455251 × 1242204541<10> × 90511908665806157449139637089<29> × 3606900009848750786607741807322282673371<40>
53×1095-719 = 5(8)941<96> = 73 × 52706587557947686850779175264478158779867<41> × 153054323082490719429614998253590499790578055440076491<54> (Makoto Kamada / GGNFS-0.70.7 / 0.44 hours)
53×1096-719 = 5(8)951<97> = 89 × 57405809 × 1152623611425666172347046019212682518266112592571823330003416551017616613178220869811881<88>
53×1097-719 = 5(8)961<98> = 32 × 17 × 23 × 1039 × 62889962241303172759934053<26> × 21569403285854316220119761407429<32> × 11873508875196513574288164122867593<35>
53×1098-719 = 5(8)971<99> = 72 × 163 × 787 × 93686053192360217005888840154464615051696759599165812311729700676065074756786144843835159849<92>
53×1099-719 = 5(8)981<100> = 1667 × 2239103 × 4435949902561517<16> × 355661663721729300119539646258820180495556944741674143728501212491786046393<75>
53×10100-719 = 5(8)991<101> = 3 × 324491 × 3787247 × 619416855855512342314957<24> × 22002089602448522330195231<26> × 1172030385078651080530939940727621590053<40>
53×10101-719 = 5(8)1001<102> = 1093 × 899589341557183037<18> × 4094063572893842408371090892240081082571<40> × 146289890507830428192767618596204419086371<42> (Makoto Kamada / Msieve 1.41 for P40 x P42 / April 16, 2009 2009 年 4 月 16 日)
53×10102-719 = 5(8)1011<103> = 179 × 4094934691079161<16> × 129498844361738502967<21> × 62039381095487231560436730366456924422756702873859877437408068597<65>
53×10103-719 = 5(8)1021<104> = 3 × 73 × 617 × 1613 × 8081 × 642079 × 1901177 × 316102187 × 12594200321983278331<20> × 157570442389731402339029<24> × 43663720436575394648925187381<29>
53×10104-719 = 5(8)1031<105> = 7 × 173 × 6221 × 78168002771689891486441118351680469734831569118382475713090923737688889844603337871059637628772751<98>
53×10105-719 = 5(8)1041<106> = 10857465529<11> × 35522304553<11> × 15268759957603035625296940698463366000562188721225646929396136230574543101931783341713<86>
53×10106-719 = 5(8)1051<107> = 34 × 47 × 115589 × 11101133 × 2835711100471259861<19> × 4251132953866624156072208625201612298587591539301152486681441123670362419<73>
53×10107-719 = 5(8)1061<108> = 97 × 269 × 461 × 1384979565662153197387040503504412975669<40> × 35348016964029802824250185131245245092377627875980924329954213<62> (Ignacio Santos / GNFS, Msieve for P40 x P62 / 0.76 hours / April 17, 2009 2009 年 4 月 17 日)
53×10108-719 = 5(8)1071<109> = 421 × 29297501 × 430615281038629<15> × 319181918660889098930037073298941<33> × 3473705275298972895412113439373104122491255140892849<52> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=534822391 for P33 / April 10, 2009 2009 年 4 月 10 日)
53×10109-719 = 5(8)1081<110> = 3 × 149 × 151 × 306151033404305107<18> × 80828735637788743799<20> × 913816114880227934763160998136931<33> × 38582339849728197044686962075943831<35> (Makoto Kamada / Msieve 1.41 for P33 x P35 / April 16, 2009 2009 年 4 月 16 日)
53×10110-719 = 5(8)1091<111> = 7 × 29 × 2617 × 593491 × 658012843 × 2838475120437573349667574349717310451478963981064381036128795055601206087548972054997692987<91>
53×10111-719 = 5(8)1101<112> = 73 × 73751 × 106363 × 14493900658606329765271121197487209608426062754421<50> × 709523408350170592136127179652066112526467686866489<51> (Ignacio Santos / GNFS, Msieve for P50 x P51 / 0.96 hours / April 17, 2009 2009 年 4 月 17 日)
53×10112-719 = 5(8)1111<113> = 3 × 19 × 59 × 670785656039321<15> × 26104941582692408387080867553243408576812896413999854445492803836930051639516616911852068440147<95>
53×10113-719 = 5(8)1121<114> = 17 × 3073637843<10> × 26030474118504845162784711103<29> × 21345774804552219173791307932777<32> × 20283259285534416690786936552147311459023421<44> (Makoto Kamada / Msieve 1.41 for P32 x P44 / April 16, 2009 2009 年 4 月 16 日)
53×10114-719 = 5(8)1131<115> = 347 × 1098821 × 12422477353909752603224071<26> × 9200036238141958862016780487<28> × 135138527632857965281947845888266035181084871056851319<54>
53×10115-719 = 5(8)1141<116> = 32 × 223 × 5273 × 258714152872988458408233821774037897987784234433911<51> × 21508396256747219765998592929869798919896339768469661174761<59> (Ignacio Santos / GNFS, Msieve for P51 x P59 / 1.34 hours / April 17, 2009 2009 年 4 月 17 日)
53×10116-719 = 5(8)1151<117> = 7 × 181 × 41051 × 197395949587579<15> × 411598764225558521<18> × 139354406204265262380917778504260890327793818179835316727054908460471213759227<78>
53×10117-719 = 5(8)1161<118> = 23291 × 8244941 × 2020992133164073<16> × 15173754371698899854501201542634460820931476529584690374746231860621347841247740198848786487<92>
53×10118-719 = 5(8)1171<119> = 3 × 38449 × 149749 × 1275805291<10> × 143413164431<12> × 18633297070769158516079458790673540997390269049164903204969912716208946135788203888035987<89>
53×10119-719 = 5(8)1181<120> = 23 × 73 × 3137 × 247302525192062034320407341931514849<36> × 452105295957014023819909058843366067525219824276276508453661905503232282583903<78> (Ignacio Santos / GGNFS, Msieve snfs / 1.79 hours / April 17, 2009 2009 年 4 月 17 日)
53×10120-719 = 5(8)1191<121> = 331 × 43613 × 3706627 × 26786575570913598534091002158361449653541557924127<50> × 4108594908349800945919523446359933990845020074836239443163<58> (Ignacio Santos / GGNFS, Msieve snfs / 1.36 hours / April 17, 2009 2009 年 4 月 17 日)
53×10121-719 = 5(8)1201<122> = 3 × 194659 × 384621067 × 207102242897777867<18> × 1133539780530774666049337268862213<34> × 1116819481169900334059112170711297777323250963240946700829<58> (Max Dettweiler / YAFU v1.10, Msieve 1.38 for P34 x P58 / April 17, 2009 2009 年 4 月 17 日)
53×10122-719 = 5(8)1211<123> = 7 × 1179004951<10> × 7480215383<10> × 177347056604174454511<21> × 630717286820354075676054389814809387<36> × 85279936633148638422763035773378265185304157643<47> (Makoto Kamada / Msieve 1.41 for P36 x P47 / April 16, 2009 2009 年 4 月 16 日)
53×10123-719 = 5(8)1221<124> = 90943231 × 77869883783146913142335509<26> × 202264546609434854254852740781297727<36> × 4111248127642512233539893307565579092523923938001118957<55> (Max Dettweiler / YAFU v1.10, Msieve 1.38 for P36 x P55 / April 17, 2009 2009 年 4 月 17 日)
53×10124-719 = 5(8)1231<125> = 32 × 103 × 10391 × 313517 × 1925993 × 645449533165367934958837365343863903897071<42> × 15686216002025477513604797878670354464346679288472277430682098283<65> (Ignacio Santos / GGNFS, Msieve snfs / 2.33 hours / April 17, 2009 2009 年 4 月 17 日)
53×10125-719 = 5(8)1241<126> = 83 × 683 × 10388062743898973149797824778861664324452519693218947042440136338423484077843830176734267474975548852315067983010617384129<122>
53×10126-719 = 5(8)1251<127> = 565317637 × 264989449909797421<18> × 5758013663635117081<19> × 5684611944651483322232939<25> × 1200988163561190672640607017828603374763803692154195687467<58>
53×10127-719 = 5(8)1261<128> = 3 × 73 × 25493217427762241207<20> × 277735248679448990653<21> × 1260584242686275877442020368630191<34> × 30127404576352572895081225631427014656063055033555959<53> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=2686745453 for P34 / April 11, 2009 2009 年 4 月 11 日)
53×10128-719 = 5(8)1271<129> = 7 × 167 × 24969206764244227895770332415233048905828749459976209<53> × 20175026012093362314000182915103646299439827080940433333601709650431305361<74> (Ignacio Santos / GGNFS, Msieve snfs / 3.22 hours / April 17, 2009 2009 年 4 月 17 日)
53×10129-719 = 5(8)1281<130> = 17 × 21589 × 25322624759976549455734598285790216107772481213399224703<56> × 633640886576731402778133093433220256786188375338961718270777059934179<69> (Ignacio Santos / GGNFS, Msieve snfs / 3.29 hours / April 17, 2009 2009 年 4 月 17 日)
53×10130-719 = 5(8)1291<131> = 3 × 19 × 61 × 577 × 2927 × 7382416109<10> × 1369886219328469<16> × 37956724012464402598129885947865441919<38> × 26125126047863880080771368057462882723263924827439187557293<59> (Sinkiti Sibata / Msieve 1.41 for P38 x P59 / 4.66 hours / April 17, 2009 2009 年 4 月 17 日)
53×10131-719 = 5(8)1301<132> = 53789159 × 124430651 × 176402014232377<15> × 2912459122147804891<19> × 183524087459434712877168183306541<33> × 933157135244103113116304207054813375684064955578707<51> (Makoto Kamada / Msieve 1.41 for P33 x P51 / April 16, 2009 2009 年 4 月 16 日)
53×10132-719 = 5(8)1311<133> = 1281391928383407443715643<25> × 70717068655533892290512518379<29> × 64987095316455214114952282532491980060259719423095323680698090107372690517136073<80>
53×10133-719 = 5(8)1321<134> = 33 × 1736132214682934259760138027279169156218659023617<49> × 1256281025374591242622665628469340154953343169071606736108858272346763080946503313059<85> (Serge Batalov / Msieve-1.41 snfs / 2.32 hours on AMD Phenom(tm) II X4 940; openSUSE/64 / April 18, 2009 2009 年 4 月 18 日)
53×10134-719 = 5(8)1331<135> = 7 × 457 × 1361 × 1362262079<10> × 22366955165587<14> × 35115408031471<14> × 126414165203461110064362711192189231991309341210068958968228239455269842368262871632869692213<93>
53×10135-719 = 5(8)1341<136> = 73 × 17971 × 208950478073359106691735508553258069951<39> × 238220374772566897555570835368515940408729<42> × 90181194435531348598364513854322550480408866621333<50> (Ignacio Santos / GGNFS, Msieve snfs / 3.61 hours / April 17, 2009 2009 年 4 月 17 日)
53×10136-719 = 5(8)1351<137> = 3 × 2377 × 4890889 × 4871047287539<13> × 12947051357240201<17> × 26773299780154646615513200737025890199377072197990198239460992442527588961461775229495821231409281<98>
53×10137-719 = 5(8)1361<138> = 2529341 × 57317234083<11> × 10120347009555997<17> × 401370405761969480403280851842171287309279815934113212166050550483348660671964018196627310102106061806691<105>
53×10138-719 = 5(8)1371<139> = 29 × 647951 × 358891536869<12> × 207918343886153<15> × 6192700806701161<16> × 343285591799040843138102857725593336454477<42> × 1975611290293895905492495874305707347552169153691<49> (Serge Batalov / Msieve v. 1.41 for P42 x P49 / 0.88 hours / April 18, 2009 2009 年 4 月 18 日)
53×10139-719 = 5(8)1381<140> = 3 × 751 × 2415546311873706757<19> × 19628836388346054508128484997147281<35> × 1950538446329560608415371227959497329<37> × 282623148366498362008930795950925297690193155889<48> (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=2883563787 for P37, msieve qs for P35 x P48 / 0.21 hours / April 17, 2009 2009 年 4 月 17 日)
53×10140-719 = 5(8)1391<141> = 73 × 89 × 193 × 2111 × 133606127 × 354386619852558168198691820530336269705230519945387067338071404390448204591693233562244445080668640527252266400272265830943<123>
53×10141-719 = 5(8)1401<142> = 23 × 5099 × 71573920589<11> × 1321406721497617037<19> × 530920131741653693412291687168997399151011423667852391848746436217311464869344283796886360418826622773597021<108>
53×10142-719 = 5(8)1411<143> = 32 × 1709 × 278909 × 76152539500821414403933627<26> × 71133922634174006030717975784795514715709640159273987<53> × 2534107945612965006523312677086987427729240908255143361<55> (Ignacio Santos / GGNFS, Msieve snfs / 9.02 hours / April 17, 2009 2009 年 4 月 17 日)
53×10143-719 = 5(8)1421<144> = 73 × 7177 × 418279 × 38724030013<11> × 1584189593401<13> × 43804001850021173196114182337801108544800058741301859862693095118456303640113580433096013870864511349020345243<110>
53×10144-719 = 5(8)1431<145> = 401 × 1483 × 1659757226539637575580313637<28> × 5966275015328736844715661106934015056266694175298361486440382337846547463462651726656547793591422844190610439111<112>
53×10145-719 = 5(8)1441<146> = 3 × 17 × 929 × 485499853 × 850230413 × 1274328443<10> × 4221790879<10> × 3316688302115642889056012400773516430032419<43> × 168748133784761883638959898979058638917739521572854314854336157<63> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 gnfs for P43 x P63 / 5.68 hours, 0.63 hours / April 18, 2009 2009 年 4 月 18 日)
53×10146-719 = 5(8)1451<147> = 7 × 369361 × 15600681731<11> × 748067904629<12> × 331395687727519512413<21> × 58891529127516333749395895703020966043451594445976907153820401933956244542556350797391578157645469<98>
53×10147-719 = 5(8)1461<148> = 173 × 911 × 1864678338609841<16> × 8841650303160994912744847210119857502267<40> × 2266374213407869403317452567641879525824318358979772631723729317593675170965387268563441<88> (Ignacio Santos / GGNFS, Msieve snfs / 13.69 hours / April 18, 2009 2009 年 4 月 18 日)
53×10148-719 = 5(8)1471<149> = 3 × 19 × 2381 × 5711 × 13834209197<11> × 82385359894943408004943162699533169281913<41> × 66662648941747010745791795419173523195324651729972252459647715337503778584049915638822583<89> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 9.99 hours on Core 2 Quad Q6700 / April 19, 2009 2009 年 4 月 19 日)
53×10149-719 = 5(8)1481<150> = 65563 × 1815347719<10> × 321073852383149036798633<24> × 106800209355250487145003373704765155010615558207705547567<57> × 144290479211011391034524051927928805222760474712705729043<57> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 15.47 hours, 0.42 hours / April 19, 2009 2009 年 4 月 19 日)
53×10150-719 = 5(8)1491<151> = 248747801 × 11462866529<11> × 1006667291845049530667097296308918344203566521580425950778739<61> × 2051610515873675499019042734361944316125748570732769002787444070163735651<73> (Ignacio Santos / GGNFS, Msieve snfs / 13.07 hours / April 19, 2009 2009 年 4 月 19 日)
53×10151-719 = 5(8)1501<152> = 32 × 73 × 601 × 3067 × 8360509 × 50792883547972719649<20> × 542501417551026748883<21> × 42936148687473484273728024786408390015437208617<47> × 4916094149477628730365878389162042910302106837749<49> (Sinkiti Sibata / Msieve 1.41 for P47 x P49 / 4.54 hours / April 18, 2009 2009 年 4 月 18 日)
53×10152-719 = 5(8)1511<153> = 7 × 47 × 132859 × 358120980514725128858958545331653679533<39> × 37619820414914044458839692273435650922151956137997093517622555060481625863874724410536072161511382815906487<107> (Markus Tervooren / Lattice siever (64bit/asm), msieve 1.40, factMsieve.pl snfs / 11.66 hours on Q6700@2.9Ghz, Linux / April 19, 2009 2009 年 4 月 19 日)
53×10153-719 = 5(8)1521<154> = 381407753 × 7056171646723<13> × 19433417519321671<17> × 112596664420471871059307212092454804829241838216575569612455737263662910805277122144746589154569959004700988029558469<117>
53×10154-719 = 5(8)1531<155> = 3 × 229 × 784913 × 58432003235623530165281017016867956379005573<44> × 1909904305005828208979377889723705736501215261699<49> × 978571848436525753147014195992938337808040799827522913<54> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m snfs / 24.35 hours / April 21, 2009 2009 年 4 月 21 日)
53×10155-719 = 5(8)1541<156> = 2803 × 253507 × 828743827029871116938956541522625692604886267130584263683459966773949322020069414366418630628830790059336445874045059148071620327370358407322921561<147>
53×10156-719 = 5(8)1551<157> = 21893 × 414036871 × 5097582013<10> × 458737405579699161469808051148151<33> × 277818197649398752305269669956120329087419350051266481378494174971171347683342879820983467197939102529<102> (Robert Backstrom / GMP-ECM 6.2.1 B1=2072000, sigma=272239408 for P33 / April 19, 2009 2009 年 4 月 19 日)
53×10157-719 = 5(8)1561<158> = 3 × 6610125409<10> × 119064466187<12> × 5521637296501<13> × 84491086696477194314717306030587<32> × 53461540124184596743923706059997123664492579792419166939716147777994870977570398168015036887<92> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=3671331176 for P32 / April 12, 2009 2009 年 4 月 12 日)
53×10158-719 = 5(8)1571<159> = 7 × 1032 × 36843969518977<14> × 590800533267749425396799989726967304158855580389298407<54> × 364295308035138105843948238320786618697318570121178416315717666433432812884446432322033<87> (Ignacio Santos / GGNFS, Msieve snfs / 36.12 hours / April 17, 2009 2009 年 4 月 17 日)
53×10159-719 = 5(8)1581<160> = 73 × 5966567237<10> × 4981932222649<13> × 26273193042133<14> × 2062452635612297<16> × 6078143242188653953677512610851837554339876404942979<52> × 8239870283677649983233243756347853355656983261837612011<55> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m gnfs for P52 x P55 / 8.87 hours / April 19, 2009 2009 年 4 月 19 日)
53×10160-719 = 5(8)1591<161> = 33 × 51427 × 554843 × 177844836628177373012417<24> × 2436291729293249338174146577<28> × 176415907300469890403335336000402462853700817492156675694865055254956107096206611579751850489229347<99>
53×10161-719 = 5(8)1601<162> = 17 × 109 × 94530201856501<14> × 3361919851243846832858222414340123257026579573306840501250233237011261574638521885448448424857009453375932822321715006879426893388912260958784977<145>
53×10162-719 = 5(8)1611<163> = 70679701 × 44026722517<11> × 1236279080219216121922252206884753<34> × 443544821402465146063268358238856200246841<42> × 3451185210796963823875477889316547070862232437023870711320410226459441<70> (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=3167953602 for P34 / April 19, 2009 2009 年 4 月 19 日) (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m gnfs for P42 x P70 / 15.86 hours / April 22, 2009 2009 年 4 月 22 日)
53×10163-719 = 5(8)1621<164> = 3 × 23 × 2389 × 96513550638754153673<20> × 377498624063625239463952264309281335010127635110927025061<57> × 9805380550742964674231939389316251929069674579746840643746394494793350010716857197<82> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 34.87 hours on Core 2 Quad Q6700 / April 20, 2009 2009 年 4 月 20 日)
53×10164-719 = 5(8)1631<165> = 7 × 409 × 6546181 × 87139389079<11> × 228311433299<12> × 394196473114547<15> × 4006536441729777547137177824637505314096461411055752610061051347773975842295115688775884028749697891079548448957996221<118>
53×10165-719 = 5(8)1641<166> = 367 × 1942027 × 1371144007102407524796878911<28> × 7456075032830949289097809630839141133<37> × 808199714463033799839895000646180717663570250954579698107795831316200571506223546388577376143<93> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 24.84 hours on Core 2 Quad Q6700 / April 24, 2009 2009 年 4 月 24 日)
53×10166-719 = 5(8)1651<167> = 3 × 19 × 29 × 83 × 240857467 × 11060457607<11> × 20894699998037<14> × 5424508418994216438894842882597473125698917<43> × 1421519024674072529801317548921990745200160059101495179565493543560830040916204609073619<88> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 38.60 hours on Core 2 Quad Q6700 / May 14, 2009 2009 年 5 月 14 日)
53×10167-719 = 5(8)1661<168> = 73 × 769 × 66501587107<11> × 353614322081<12> × 15289508170453564157615559715265886034189<41> × 29176204089714079058424787149185032695439825811546932354672800303249154820310505588922930701582824751<101> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 61.86 hours, 1.47 hours / April 23, 2009 2009 年 4 月 23 日)
53×10168-719 = 5(8)1671<169> = 593 × 17404799 × 2547335314631<13> × 169017775524223519035278966544358165435527479<45> × 1325229688509753839571072379572594850333978022743803818791211312741515576887190505144667080147934159967<103> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 77.13 hours, 1.64 hours / May 4, 2009 2009 年 5 月 4 日)
53×10169-719 = 5(8)1681<170> = 32 × 55619 × 268408781245025917238865818507107<33> × 23558974883254664303215516645325268137706557468101857830919331<62> × 18604352743858630351683027420410354047658125089089380509126300180803083<71> (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=504785334 for P33 / April 19, 2009 2009 年 4 月 19 日) (Erik Branger / GGNFS, Msieve snfs / 143.39 hours / September 6, 2009 2009 年 9 月 6 日)
53×10170-719 = 5(8)1691<171> = 7 × 59 × 1427 × 568218567627765334438930578061<30> × 2263601622974746710068103777175357428919279<43> × 129968124481852563001973196053531945137907861<45> × 5977327695821253697952452498480093874447527049209<49> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=113594766 for P30 / April 13, 2009 2009 年 4 月 13 日) (Jo Yeong Uk / GMP-ECM v6.2.3/YAFU v1.10 B1=11000000, sigma=5649517295 for P43, Msieve 1.38 for P45 x P49 / September 23, 2009 2009 年 9 月 23 日)
53×10171-719 = 5(8)1701<172> = 1129399 × 1012782147434752932667684249508918320121901242771161953907631<61> × 5148372050856343302191719932929532293542830496633217654226873938020652977210113515374231410045450654341849<106> (Ignacio Santos / GGNFS, Msieve snfs / 103.07 hours / September 8, 2009 2009 年 9 月 8 日)
53×10172-719 = 5(8)1711<173> = 3 × 8742213383<10> × 9759491317<10> × 106446437711<12> × 10601072798007631161102454630817205890692937<44> × 203883730699112554340682537696863687962527754812211444395588968498956615798570871172536737058613151<99> (Sinkiti Sibata / Msieve 1.40 snfs / September 9, 2010 2010 年 9 月 9 日)
53×10173-719 = 5(8)1721<174> = 342035173 × 2915131451<10> × 21812315423609<14> × 436720646691181<15> × 62001037182833246163037786829113100089231996298716352216446147904051416691669051500703176080636334803166892019423462844058897243<128>
53×10174-719 = 5(8)1731<175> = 227 × 571 × 406327 × 19623288819879302404741<23> × 1684402771698298205544366185060396248937<40> × 3382812834919757230081517606275227380841031584932169238707555346188691013336307085773625503489510356227<103> (Wataru Sakai / GMP-ECM 6.3 B1=11000000, sigma=1992018618 for P40 / September 21, 2011 2011 年 9 月 21 日)
53×10175-719 = 5(8)1741<176> = 3 × 73 × 1024183 × 2158548290899707807210634246105330347041<40> × 121632578456805687673146582029186126326283394657268436697370779282164748561294068326344587870149269097387136954490861643986922133<129> (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=2926320089 for P40 / April 19, 2009 2009 年 4 月 19 日)
53×10176-719 = 5(8)1751<177> = 7 × 607 × 5851 × 58997 × 60148447 × 973961250086329389674786333289700652199502176885636868584942490441<66> × 6853627644462355121635744397686678572198073275569413185596633478506316442138576298745347401<91> (Robert Backstrom / Msieve 1.44 snfs / January 12, 2012 2012 年 1 月 12 日)
53×10177-719 = 5(8)1761<178> = 17 × 84278649583<11> × 83846966942573550215335355421366466453<38> × 49020700550042523594461039571340331345624909658090604188085869487138236288231502468124541777211426910099206442117974642551726707<128> (Robert Backstrom / Msieve 1.44 snfs / February 19, 2012 2012 年 2 月 19 日)
53×10178-719 = 5(8)1771<179> = 32 × 21867644976972022514831833<26> × 299218772000076506697481087436767559110832688703189142759325693482885876756254484797364300299536544476034549717653948177700863733750518502210424230441873<153>
53×10179-719 = 5(8)1781<180> = 163 × 18628273 × 866713253195654936779138316416417782115643<42> × 223767868102340497715249431391419630304160168724277402326868315388378916065982012043885571596953803105599876369448427080060494833<129> (matsui / Msieve 1.47 snfs / August 30, 2010 2010 年 8 月 30 日)
53×10180-719 = 5(8)1791<181> = 1489 × 2112271972319<13> × 1274958669323474059<19> × 8000247039133409412409466789170274837723701287795721329334003206858697<70> × 183564764670237893771779277835991000964245420681999676385437854384908696468917<78> (Cyp / yafu v1.34.3 / January 19, 2014 2014 年 1 月 19 日)
53×10181-719 = 5(8)1801<182> = 3 × 2879 × 24081340990091404175861057053153272486112035432620191<53> × 283132532303703333726830050085836989037702953632307132314359052811450789821802506909621984361284526068569973287653670838199643<126> (Wataru Sakai / Msieve / 303.42 hours / July 12, 2009 2009 年 7 月 12 日)
53×10182-719 = 5(8)1811<183> = 72 × 91099 × 80463451769347<14> × 9797034164326174205366944565419152172096415169062759601524386591960307503<73> × 167351800281093420611703526986821738858454946149413530678912739192160215536163343456343391<90> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / May 10, 2014 2014 年 5 月 10 日)
53×10183-719 = 5(8)1821<184> = 73 × 113 × 5779 × 80273 × 543483353732909<15> × 1633503274622224469<19> × 9329922208436263697241721<25> × 1099460710064905094872964317328985126416851<43> × 168984112509748557056357145099368984533273143568828753891708684224898777<72> (Markus Tervooren / Msieve/ ggnfs/factMsieve.pl for P43 x P72 / 0.54 hours on Q6700, Linux / April 20, 2009 2009 年 4 月 20 日)
53×10184-719 = 5(8)1831<185> = 3 × 19 × 89 × 151 × 706329023 × 16666608060731198666978428169593368146276636075748852251<56> × 6530362300418088654941476095527218616589421657634046206371829150076875932254271111338049103930296678789177615836539<115> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / October 3, 2014 2014 年 10 月 3 日)
53×10185-719 = 5(8)1841<186> = 23 × 233 × 215325522097885785506678338135721202120862759<45> × 510333519255213660531524689794452061284434462061881762456420580789577174717938354675826912683331869019878654674813170859867374521644491401<138> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 125.56 hours, 3.11 hours / August 4, 2009 2009 年 8 月 4 日)
53×10186-719 = 5(8)1851<187> = 191 × 5259691725677<13> × 3099447308944650591613477138713202821707<40> × 1891278321918695664777134333464307862000581875050907573341326500308707413363978563125866066832649478491856277904323445630603178137569<133> (Rich Dickerson / GMP-ECM 6.4.4 [configured with GMP 6.0.0, --enable-asm-redc] [ECM] B1=11000000, sigma=4212705910 for P40 / April 9, 2014 2014 年 4 月 9 日)
53×10187-719 = 5(8)1861<188> = 35 × 359 × 3343 × 10417662811<11> × 26149184533<11> × 1437483587553631<16> × 426428515745133381252762803437522370327247290179<48> × 1209257198797584787595859912703484885513004961237454306684162333879536223944707805832130156178793<97> (Jo Yeong Uk / GMP-ECM 6.4.4 B1=11000000, sigma=1955507351 for P48 x P97 / May 8, 2017 2017 年 5 月 8 日)
53×10188-719 = 5(8)1871<189> = 7 × 560081 × 13681129296834545790203<23> × [10978993621490424634350629697424884281858166697298963476910768354373021255698866530489441081824582464147003842256306710929483826442990445380420086276773276605781<161>] Free to factor
53×10189-719 = 5(8)1881<190> = 46036250681<11> × 10313553303167908476634005547699068139631651503643942818358838462788115555562235849226013<89> × 12402952955683888768437065024498316965505671752164409386070508532057637458786692702033318477<92> (Robert Backstrom / Msieve 1.44 snfs / February 15, 2012 2012 年 2 月 15 日)
53×10190-719 = 5(8)1891<191> = 3 × 61 × 173 × 39203873 × 211360399 × 168914326803248671710673803592753171<36> × 1367636984963951639753577153207521555363953<43> × 971731430107673147043835061767876569745815441405365732504234542031134687004068231357517112959<93> (Dmitry Domanov / ECMNET / August 20, 2009 2009 年 8 月 20 日) (Robert Backstrom / Msieve 1.44 gnfs for P43 x P93 / May 10, 2012 2012 年 5 月 10 日)
53×10191-719 = 5(8)1901<192> = 73 × 617 × 719 × 18184294052990288616003020733756096211672538838401225750424729355346086898260394706022254947775719624480878290149083111353710179771269097424383109232323573551666182089540143254702009839<185>
53×10192-719 = 5(8)1911<193> = 103 × 1327 × 5861 × 23459617 × 1163563275202877<16> × 512457225422067115117031521<27> × 525514794935388469823839539467678178571927133459965254039555656752351747617228959860006542279565277370046202999911500048483367847144569<135>
53×10193-719 = 5(8)1921<194> = 3 × 17 × 2131 × 122614102349<12> × 157528172059<12> × 386318917324635401637343670457937<33> × 72616464843759242682094782381797010874803934727294295921255817042629723671550851219691527308314086340987245476998440916635306218917703<134> (Dmitry Domanov / ECMNET / August 18, 2009 2009 年 8 月 18 日)
53×10194-719 = 5(8)1931<195> = 7 × 29 × 27253 × 443577473 × 239968105889329839800818782378821416652997643853658460434843829354816357639439040919368081319335268908506284885972015898811031890697058681619463778920060231184494072847674821539783<180>
53×10195-719 = 5(8)1941<196> = 1319 × 33857 × 6522546262176896794087564739115713<34> × 20217289175101472176634624589120256959714664779605055451404756357758626997987860981678743694952263411707665143615277807384449498161455207993683372278411239<155> (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=3935644505 for P34 / April 19, 2009 2009 年 4 月 19 日)
53×10196-719 = 5(8)1951<197> = 32 × 4973 × 74797 × 122655881 × 112054989341662601618892514165224888241<39> × 1279878186755975199770625717338893764280326490898655144840134732459923961450639607812280526526379705342401644682052605125245400793894469473609<142> (Dmitry Domanov / ECMNET / August 20, 2009 2009 年 8 月 20 日)
53×10197-719 = 5(8)1961<198> = 131 × 1171 × 32333333 × 7097585846683<13> × 16728000787624434672706420429241148648586412843444468242320230169766101707633695373116355888951891699556104579851405367207507208657241805690108163449753967360123971648555279<173>
53×10198-719 = 5(8)1971<199> = 47 × 4691 × 1041730059761<13> × 502491685538339197<18> × 924006084409319617<18> × [55221876710222260402588008998816932401255149589748498226860259232933645489095553747239850670626947536473023677064529630211165055231933982906729977<146>] Free to factor
53×10199-719 = 5(8)1981<200> = 3 × 73 × 673 × 266159 × 552983 × [2714696260362570766031337190795123531048862175324846081192150312049088904859352581452966292324796370179861851827146245085427887241614536418759204398902978982143753066120155173012180379<184>] Free to factor
53×10200-719 = 5(8)1991<201> = 7 × 4159 × 3034505345452117268700680317998766514478361928655978367451115957769572858803<76> × 6665895375622611920987398511774431994286383426667359548052717579186720130290324269246467364058297937649408474006753108579<121> (Markus Tervooren / Msieve 1.44 for P76 x P121 / March 13, 2010 2010 年 3 月 13 日)
53×10201-719 = 5(8)2001<202> = 845726166293<12> × 26614080411265630091650323405683<32> × [261632763104934685678706508770395191162055898507905747696347081652713863042849725984808309953127668896691497252042853273203709573229850203050723384365743227999<159>] (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=1279820415 for P32 / April 19, 2009 2009 年 4 月 19 日) Free to factor
53×10202-719 = 5(8)2011<203> = 3 × 19 × 857 × 1259 × 1004317 × 71365367 × 779769064987480193874703347294131196204883<42> × 6591323637634753207302936999088267810917962745645943127107273<61> × 2599291561059480945565789772450143848218612000082631326002378848584710013998891<79> (Dmitry Domanov / ECMNET / August 20, 2009 2009 年 8 月 20 日) (Sinkiti Sibata / Msieve 1.42 gnfs for P61 x P79 / July 3, 2010 2010 年 7 月 3 日)
53×10203-719 = 5(8)2021<204> = 97 × 378031809054421<15> × [16059546651026268964409668584363046059215680836044311617331816381178824260303526325882771570296720082072128691536388982341201675338378757626417872870862967434248703998682944274217935072013<188>] Free to factor
53×10204-719 = 5(8)2031<205> = 1894601 × 13897365986571033101218215063619913<35> × 223657313079454078280340595149145069743916262638623599497122392196510180718091050020838810477552037958778607888933892716339481082931410115624804909510584996502701537<165> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=2014047816 for P35 / April 15, 2009 2009 年 4 月 15 日)
53×10205-719 = 5(8)2041<206> = 32 × 1747 × 677639 × 24773841302921<14> × 38890602599868190564621649574538065154223681893737437<53> × 5736691942583823449594066954210646466721732505485509130873380197100488136359317213303544868719719524663202099815154059597509844049<130> (Jamoko / GMP-ECM B1=110000000, sigma=3731845005 for P53 / October 12, 2010 2010 年 10 月 12 日)
53×10206-719 = 5(8)2051<207> = 7 × 123619 × 2180033 × 53307139 × 693021354109385569<18> × [8449967430884347989475626348947671968724318032565180599893076125554274067691741435726769202714309273644963828208614733922238445536684642611331426359590773335768558583119<169>] Free to factor
53×10207-719 = 5(8)2061<208> = 23 × 73 × 83 × 1907 × 10321 × 10487 × 78946205449<11> × 60162950045791445827271168292277<32> × 90705977533693966428569268376688123<35> × 509189635111823002172002762789805207<36> × 933265015001111635350710399242583599060595601500840677301339666502101332121449<78> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3426589799 for P32 / October 15, 2013 2013 年 10 月 15 日) (Serge Batalov / GMP-ECM B1=3000000, sigma=1008905983 for P36, B1=3000000, sigma=1311436215 for P35 / May 26, 2014 2014 年 5 月 26 日)
53×10208-719 = 5(8)2071<209> = 3 × 376801 × 28263562633162128421834460097029443<35> × 1843202941351756141750676717538014590914209160756014943721741066486468107429610790972089682564712903176768962064809701173159237915055778751489514893925259971787093129289<169> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=3180986952 for P35 / January 3, 2014 2014 年 1 月 3 日)
53×10209-719 = 5(8)2081<210> = 17 × 126093122000899602623198916245997821<36> × [274721747912386950487121041289321628965335700331942136615589864345417253493894606147963494622168586799471015871999506842142921061341303762462159167967820084961209302172850933<174>] (Serge Batalov / GMP-ECM B1=3000000, sigma=1047034051 for P36 / October 27, 2013 2013 年 10 月 27 日) Free to factor
53×10210-719 = 5(8)2091<211> = 5659 × 556253 × 1870773890256722691072274270838685632876066816713173701420693256172859013010652219746182736202513686283251492204977089291702066284124390360503996175937960211380779238766448147911528195476538883850367103<202>
53×10211-719 = 5(8)2101<212> = 3 × 48649 × 1618300147<10> × 3857893687<10> × 9627212954256511421<19> × [6713179817392035199355634473378325489397705064010469300562473564409062347826621101448239735734284053757952116837209607047035855655230566406443674795610579166452530150467<169>] Free to factor
53×10212-719 = 5(8)2111<213> = 7 × 152267 × [552496497120085947606027465747562682551879160468020825156645787511306632324318362658909198868612267444581734611747680895953338439234923699712524605639988487223935482586404979306921290410818673672739228637749<207>] Free to factor
53×10213-719 = 5(8)2121<214> = 293 × 13842670239667069<17> × 5997682471234380510251527889<28> × 242081943264585582611986136338833792815863172541254024804865080880798021315412648848871814625026108369094140480278424851112842379252533193262514173845956744913446022737<168>
53×10214-719 = 5(8)2131<215> = 33 × 439 × 176179 × 49388671138327<14> × 142310292915120902745028400179286447<36> × [4012243494192290266929449619250321020974352546058802613425248682062951095194072712916122267243745399045607101332273273719572828438843626272665315747866783727<157>] (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=2356929567 for P36 / January 5, 2014 2014 年 1 月 5 日) Free to factor
53×10215-719 = 5(8)2141<216> = 73 × 17683 × 1271261195242222769288953453<28> × 358855628700916618834402368015510844058836572185265298472228585983780494175104390726755207755791024475366858844582472542061552166031478455773949572018264916559094700213701954233021503<183>
53×10216-719 = 5(8)2151<217> = 481306408883809<15> × 12235218106789247254621199770166743637490879534231574449802910801850425594201243410213400175115877313480315176562463330025713548451640443036430548768642702160374209967365983525075208131398271899770579409<203>
53×10217-719 = 5(8)2161<218> = 3 × 887 × 643619 × 50193643 × 5013080329487<13> × 8292613758239501<16> × 460381769122640408551<21> × 35792883986732310364143454034615208320088420856422014333663658627799923842372156708311771657107109289182868156824455814524607596783681732347783978174249<152>
53×10218-719 = 5(8)2171<219> = 7 × 659 × 123121 × 44805040139<11> × 16464154697132297<17> × 1405566709794605738242612498862187057149118127873762454134466880443510942773622117905130899932140748590884686751669960348553809524948824909035730156611374663427695288988677495151063759<184>
53×10219-719 = 5(8)2181<220> = 1193 × 3769 × 12781610629<11> × 22810067614541<14> × 53206522394828516559977<23> × [84428631316366647273557704037927152039913463446598699568429696242533464612432546493259832563241131726382228313050379055890011652579147378500737196547706862879891352681<167>] Free to factor
53×10220-719 = 5(8)2191<221> = 3 × 19 × 379 × 1720547576071<13> × [1584355400034748908521975211621330474007692006820542680715910581682987182220791147251601738244643911092753771820467985117959494529484482941596088067842201468214542485237300941745504739311352254139959578637<205>] Free to factor
53×10221-719 = 5(8)2201<222> = 647 × 149827 × 5739193 × 364170337 × 3148947081107<13> × 923035141962977659573240388548930407308656524886022217608308069339369832224564838854976956274166688609380740000169792708578228160923637191984328845026181762008659179894137940189686394327<186>
53×10222-719 = 5(8)2211<223> = 29 × 8290999 × 113221583 × 41203279824853<14> × [5250098954733442313390140420331319828110971711524809511930949779242356601639637818198920940692083423416769959653957641853335078229567768206515753798638278202997599713854698656487767853575478489<193>] Free to factor
53×10223-719 = 5(8)2221<224> = 32 × 73 × 1021 × 2096047 × [41883332718986234305303238097219258881236675311034192772794932275009677124029381653923991379012642095521296566991162052929915351486220723853613489937678208049407816853012146101471112024520441012542340713716191259<212>] Free to factor
53×10224-719 = 5(8)2231<225> = 72 × 19805968661393911<17> × [606793880927172199836014017786962263520983964963710655976291282702844370587410540074142989543854020836346679560273627072926315547915786520155493158713795532710864039199963317363156379614746787852318229684679<207>] Free to factor
53×10225-719 = 5(8)2241<226> = 17 × 4157 × 4306633 × 5514904676021043139247<22> × 3508557030358124197606291876279755691941234941616919679088803933330914831277961405476163186652900322626441879755186019864643105869752998894303740511153435408930935284052079670953843525284167299<193>
53×10226-719 = 5(8)2251<227> = 3 × 103 × [190578928443006112909025530384753685724559510967277957569219705142035239122617763394462423588637180870190578928443006112909025530384753685724559510967277957569219705142035239122617763394462423588637180870190578928443006112909<225>] Free to factor
53×10227-719 = 5(8)2261<228> = 536842127 × 1096949846651823747224086400523647595355140392864304572150107901068071151742696394034831191421922238395588669755957674478271502878701784312259996855442175254046128330180185149458080604186431309793407641589365971811837503<220>
53×10228-719 = 5(8)2271<229> = 59 × 89 × 42695139851805561308003597<26> × 3212989126160258441205622140401<31> × 806753529393695866592572924011151<33> × 10133576995006851845182679782625849598140988874262764668542118608907928137081502198107971005504837878880501058025814778948736372801174073<137> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=689885817 for P31 / October 15, 2013 2013 年 10 月 15 日) (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=2634922576 for P33 / January 1, 2014 2014 年 1 月 1 日)
53×10229-719 = 5(8)2281<230> = 3 × 23 × 1063 × 405827 × 56201107811<11> × 322923814670201<15> × 879476479793727957130162628396071878177431<42> × 123948389281761066221716336812850451095725162297782187592341204336609727089445555558772545930465753549232667491451946369153584560934906727727458111325789<153> (Serge Batalov / GMP-ECM B1=3000000, sigma=3161167232 for P42 / May 19, 2014 2014 年 5 月 19 日)
53×10230-719 = 5(8)2291<231> = 7 × 331 × 69830381 × 1243330390493<13> × 5793291368735417233<19> × 505301973127971487547045727498758464366263740105222638319156723210468727075624068141683455050982541126313725309963842683619611894458614298538551461708582426772522793776483043899457155765037<189>
53×10231-719 = 5(8)2301<232> = 73 × 491 × [164296763353761930889961467759085146022623354319919897578017713051052894257983117732580668160837231506539321175372845154950447476184719161032527659205113659260912560022567555419158242582621122363889431378201849423566355742791867<228>] Free to factor
53×10232-719 = 5(8)2311<233> = 32 × 337 × 35839 × 9763939 × 17977019 × 9348295771<10> × 11517277548943<14> × [28666855300857586749963819559620108665619005513200258209245590755765398549798605883108276286281979361028444593353573190871292576286722942615068226869218009589086615919832899171362722288731<188>] Free to factor
53×10233-719 = 5(8)2321<234> = 173 × 541 × 39841 × 216219407 × 268389420384873783938667315447273234845329<42> × [2721445847724950946062731588846489382015117054768100802652149851495239855770440565261108179628964620997589456040593534839290515925478335510888724008969545940010156881770849479<175>] (Serge Batalov / GMP-ECM B1=11000000, sigma=4226501823 for P42 / May 27, 2014 2014 年 5 月 27 日) Free to factor
53×10234-719 = 5(8)2331<235> = 5360097851<10> × 2368762400427949<16> × 339397717700284614754489893609631<33> × 1366564780473183140996202492044912197008134598522040714503430543582716865076656917383138488234621300673549013474667370386688016016955568294960270644344662178510101307525926025649<178> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=63261412 for P33 / January 6, 2014 2014 年 1 月 6 日)
53×10235-719 = 5(8)2341<236> = 3 × 8731 × [2248268197185846939597941774095708352952654865379639174164429003508146790703198903863203485239907184701595422016908673649024124341957350776500931122394872251704229713621535864119760580647077039242885079559000072114262928602637685217<232>] Free to factor
53×10236-719 = 5(8)2351<237> = 7 × 3089 × 63199 × 4242421 × 275412252873500646323664980344451<33> × 368816365457564746643000376766341972507540716772645725915820650135485048164768334371088656204661532020520201899296415868823632456129392041557115464487211197463499630351405788134888464857943<189> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=277117633 for P33 / January 5, 2014 2014 年 1 月 5 日)
53×10237-719 = 5(8)2361<238> = 11796897091962038645836986962921480389951859<44> × 3080354615618365685495471291308975489265445299<46> × 162055902248469784236533730584911606026903011946030357655554805160989881737200582566292146648594381906498104038238933443252173319086570120917738338441<150> (Serge Batalov / GMP-ECM B1=43000000, sigma=76041713 for P44 / February 23, 2014 2014 年 2 月 23 日) (Serge Batalov / GMP-ECM B1=43000000, sigma=116767916 for P46 / February 24, 2014 2014 年 2 月 24 日)
53×10238-719 = 5(8)2371<239> = 3 × 19 × 4231603 × 20796619 × 83687137926479<14> × 140282060815367821925046278900863311697487359899025868772889819765062067249734490766402222540491645873758731747083770654912784481140064981412520058883745334158262092268623895272231317037363494283639681069518311<210>
53×10239-719 = 5(8)2381<240> = 73 × 4038381703<10> × 5362374206868519290783569<25> × 372516931629552681559934100827454556566575046686118742208802648307548891873223514272143511172154377719740985141978241615493606535943768657224380766029525960417926120811040332080827806112439167927860672671<204>
53×10240-719 = 5(8)2391<241> = 34519 × 114760162933687124167<21> × 1041688051927639822176353<25> × 57514704340160273927505413<26> × 1742617105484097253524953394593462819<37> × 798659244158718217681734564349457396648355289<45> × 17828053474165083233297922135275933027392613254822771775341629387345512080317150869303<86> (Ignacio Santos / GMP-ECM 7.0 B1=11000000, sigma=1:1781124884 for P37 / October 28, 2013 2013 年 10 月 28 日) (Cyp / yafu v1.34.3 / January 27, 2014 2014 年 1 月 27 日)
53×10241-719 = 5(8)2401<242> = 33 × 17 × 307 × 15749 × 319915894236529294302271<24> × 1252596246571463787988506527<28> × 66218965642774544562042866807750303229459318032017649351460475401282510178117079445003721429434627242732644540476827617396809909742699389986677599962620649407223705084893826733498989<182>
53×10242-719 = 5(8)2411<243> = 7 × 26758464497<11> × 10767262311395672380841089666567105043<38> × 291990578395143555686199680500247994278645527385060410088833391099013909888731533881640701099267050384756741086971346367857959314337398641546167442054098932683700743102964066585549979633851992973<195> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=4005131439 for P38 / January 3, 2014 2014 年 1 月 3 日)
53×10243-719 = 5(8)2421<244> = 761 × 2626042261<10> × 2946775106897017763042065659591367061177351362688654556991833185201319668191400630057339499768797667217188187254570897516163664931543282696350452667251211219240465029471389564227716970658171285888517206204791345488830757693037071061<232>
53×10244-719 = 5(8)2431<245> = 3 × 47 × 3986243727338749692699557892767337117829<40> × [104773245896398502739983593569476851007366729696065366005310437155747309530149666399585867386927728153884338481374489928850338651937726782017235834815843700413642245505951151614536168633521448512604274929<204>] (Serge Batalov / GMP-ECM B1=3000000, sigma=3281868087 for P40 / October 27, 2013 2013 年 10 月 27 日) Free to factor
53×10245-719 = 5(8)2441<246> = 133572770563<12> × 436126065605803970723<21> × [10108887942175381151576102707168325970775552905037286835245591192587154297276880081262407554620682913434409614597312000554489186000288391605016197144852691030264908029396449354115135714101097923159215845448526402569<215>] Free to factor
53×10246-719 = 5(8)2451<247> = 13229 × 8384239 × 151915663222511629299427<24> × 349494334487711835510164795750898963197604939311965640710438902289292437968173055646684539640046652431153614511458675414384557833119448057694093534240250977460699217380466567782937010180766156692017796916068058313<213>
53×10247-719 = 5(8)2461<248> = 3 × 732 × 253309763429369390731249<24> × 14541675728535650468046825980249320709110936821760452770804310058175325117965939869506579616253837878625701792892245335854693245791410540689939908016442412557256536553999469223348801101913469523883326925978323441061534587<221>
53×10248-719 = 5(8)2471<249> = 7 × 83 × 421 × 1743914818152589833511687<25> × 3470055324237014659864405641761978249<37> × 397844597592971096937874466183565852626253517773019680354482529268559114966194094889806452731907627475477447831347576887401434233511536287650593372029409050420396703872359565564447687<183> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=3439979135 for P37 / January 3, 2014 2014 年 1 月 3 日)
53×10249-719 = 5(8)2481<250> = 1220663 × 309248077 × 681659744189993<15> × [22885632751534032193789241381507179712115014732972180897186185012178500936772404537853567981336131367440954179432732509426738988191920866575249168530910183650796029652307367704092226559191968111484111233812013433143724667<221>] Free to factor
53×10250-719 = 5(8)2491<251> = 32 × 29 × 61 × 3698818471759869913252238483065692411839010670742345888379428986174793598950373022353425594428044022918716719357382632302549393184403548074171778712950749883103378486834299911367934733301230380559568424652276169140687701079636259587267689773813761<247>
plain text versionプレーンテキスト版

4. Related links 関連リンク