Table of contents 目次

  1. About 200...003 200...003 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
    4. Related sequences 関連する数列
  2. Prime numbers of the form 200...003 200...003 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 200...003 200...003 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 200...003 200...003 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

20w3 = { 23, 203, 2003, 20003, 200003, 2000003, 20000003, 200000003, 2000000003, 20000000003, … }

1.3. General term 一般項

2×10n+3 (1≤n)

1.4. Related sequences 関連する数列

2. Prime numbers of the form 200...003 200...003 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. 2×101+3 = 23 is prime. は素数です。
  2. 2×103+3 = 2003 is prime. は素数です。
  3. 2×105+3 = 200003 is prime. は素数です。
  4. 2×106+3 = 2000003 is prime. は素数です。
  5. 2×107+3 = 20000003 is prime. は素数です。
  6. 2×1012+3 = 2(0)113<13> is prime. は素数です。
  7. 2×1016+3 = 2(0)153<17> is prime. は素数です。
  8. 2×1017+3 = 2(0)163<18> is prime. は素数です。
  9. 2×1022+3 = 2(0)213<23> is prime. は素数です。
  10. 2×1024+3 = 2(0)233<25> is prime. は素数です。
  11. 2×1035+3 = 2(0)343<36> is prime. は素数です。
  12. 2×10115+3 = 2(0)1143<116> is prime. は素数です。 (Makoto Kamada / PPSIQS / September 27, 2004 2004 年 9 月 27 日)
  13. 2×10120+3 = 2(0)1193<121> is prime. は素数です。 (Makoto Kamada / PPSIQS / September 27, 2004 2004 年 9 月 27 日)
  14. 2×10358+3 = 2(0)3573<359> is prime. は素数です。 (discovered by:発見: Makoto Kamada / September 27, 2004 2004 年 9 月 27 日) (certified by:証明: Makoto Kamada / PPSIQS / December 30, 2004 2004 年 12 月 30 日)
  15. 2×101488+3 = 2(0)14873<1489> is prime. は素数です。 (discovered by:発見: Makoto Kamada / September 27, 2004 2004 年 9 月 27 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / August 25, 2006 2006 年 8 月 25 日) [certificate証明]
  16. 2×101819+3 = 2(0)18183<1820> is prime. は素数です。 (discovered by:発見: Makoto Kamada / September 27, 2004 2004 年 9 月 27 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 29, 2006 2006 年 6 月 29 日) [certificate証明]
  17. 2×104679+3 = 2(0)46783<4680> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 18, 2004 2004 年 12 月 18 日)
  18. 2×109821+3 = 2(0)98203<9822> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / January 3, 2005 2005 年 1 月 3 日)
  19. 2×1027217+3 = 2(0)272163<27218> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  20. 2×1027693+3 = 2(0)276923<27694> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  21. 2×10194413+3 = 2(0)1944123<194414> is PRP. はおそらく素数です。 (Bob Price / July 17, 2015 2015 年 7 月 17 日)

2.3. Range of search 捜索範囲

  1. n≤100000 / Completed 終了 / Dmitry Domanov / March 8, 2010 2010 年 3 月 8 日
  2. n≤200000 / Completed 終了 / Bob Price / July 17, 2015 2015 年 7 月 17 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. 2×106k+2+3 = 7×(2×102+37+18×102×106-19×7×k-1Σm=0106m)
  2. 2×1013k+10+3 = 79×(2×1010+379+18×1010×1013-19×79×k-1Σm=01013m)
  3. 2×1015k+8+3 = 31×(2×108+331+18×108×1015-19×31×k-1Σm=01015m)
  4. 2×1016k+9+3 = 17×(2×109+317+18×109×1016-19×17×k-1Σm=01016m)
  5. 2×1018k+15+3 = 19×(2×1015+319+18×1015×1018-19×19×k-1Σm=01018m)
  6. 2×1022k+1+3 = 23×(2×101+323+18×10×1022-19×23×k-1Σm=01022m)
  7. 2×1028k+2+3 = 29×(2×102+329+18×102×1028-19×29×k-1Σm=01028m)
  8. 2×1030k+4+3 = 241×(2×104+3241+18×104×1030-19×241×k-1Σm=01030m)
  9. 2×1030k+9+3 = 211×(2×109+3211+18×109×1030-19×211×k-1Σm=01030m)
  10. 2×1041k+4+3 = 83×(2×104+383+18×104×1041-19×83×k-1Σm=01041m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 23.69%. 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 23.69% です。

3. Factor table of 200...003 200...003 の素因数分解表

3.1. Last updated 最終更新日

December 21, 2024 2024 年 12 月 21 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=239, 243, 244, 255, 256, 259, 260, 264, 265, 267, 277, 278, 279, 281, 283, 284, 285, 286, 288, 289, 290, 291, 294, 296, 298, 300 (26/300)

3.4. Factor table 素因数分解表

2×101+3 = 23 = definitely prime number 素数
2×102+3 = 203 = 7 × 29
2×103+3 = 2003 = definitely prime number 素数
2×104+3 = 20003 = 83 × 241
2×105+3 = 200003 = definitely prime number 素数
2×106+3 = 2000003 = definitely prime number 素数
2×107+3 = 20000003 = definitely prime number 素数
2×108+3 = 200000003 = 7 × 31 × 223 × 4133
2×109+3 = 2000000003<10> = 17 × 211 × 233 × 2393
2×1010+3 = 20000000003<11> = 79 × 253164557
2×1011+3 = 200000000003<12> = 47 × 1171 × 3633919
2×1012+3 = 2000000000003<13> = definitely prime number 素数
2×1013+3 = 20000000000003<14> = 617 × 64879 × 499621
2×1014+3 = 200000000000003<15> = 7 × 8431 × 3388854059<10>
2×1015+3 = 2000000000000003<16> = 19 × 105263157894737<15>
2×1016+3 = 20000000000000003<17> = definitely prime number 素数
2×1017+3 = 200000000000000003<18> = definitely prime number 素数
2×1018+3 = 2000000000000000003<19> = 107 × 1279 × 14614221098551<14>
2×1019+3 = 20000000000000000003<20> = 21977 × 910042316967739<15>
2×1020+3 = 200000000000000000003<21> = 7 × 173 × 2339 × 81971 × 861381217
2×1021+3 = 2000000000000000000003<22> = 11850947 × 168762884518849<15>
2×1022+3 = 20000000000000000000003<23> = definitely prime number 素数
2×1023+3 = 200000000000000000000003<24> = 232 × 31 × 79 × 174456743 × 884907301
2×1024+3 = 2000000000000000000000003<25> = definitely prime number 素数
2×1025+3 = 20000000000000000000000003<26> = 17 × 61 × 181 × 106554713181350794099<21>
2×1026+3 = 200000000000000000000000003<27> = 7 × 3793020318169<13> × 7532632618541<13>
2×1027+3 = 2000000000000000000000000003<28> = 1433 × 6053 × 335676199 × 686898522953<12>
2×1028+3 = 20000000000000000000000000003<29> = 944220544009<12> × 21181492106794667<17>
2×1029+3 = 200000000000000000000000000003<30> = 541 × 2659 × 139031879314767479609237<24>
2×1030+3 = 2000000000000000000000000000003<31> = 29 × 199 × 8837 × 1632417869<10> × 24023856568681<14>
2×1031+3 = 20000000000000000000000000000003<32> = 8898053 × 723962431 × 3104695253724121<16>
2×1032+3 = 200000000000000000000000000000003<33> = 72 × 227 × 13326490787<11> × 1349249466612248603<19>
2×1033+3 = 2000000000000000000000000000000003<34> = 19 × 376757 × 279392706425459492737396141<27>
2×1034+3 = 20000000000000000000000000000000003<35> = 241 × 3229088693532413<16> × 25699991466148591<17>
2×1035+3 = 200000000000000000000000000000000003<36> = definitely prime number 素数
2×1036+3 = 2000000000000000000000000000000000003<37> = 59 × 79 × 120943 × 3547890075714688351659371161<28>
2×1037+3 = 20000000000000000000000000000000000003<38> = 5049497107807891<16> × 3960790465465279655633<22>
2×1038+3 = 200000000000000000000000000000000000003<39> = 7 × 31 × 348331826708401<15> × 2645922409342926726059<22>
2×1039+3 = 2000000000000000000000000000000000000003<40> = 211 × 2341 × 88033849 × 45993497522560350084477797<26>
2×1040+3 = 20000000000000000000000000000000000000003<41> = 6770723 × 2359303200251<13> × 1252019786340070350611<22>
2×1041+3 = 200000000000000000000000000000000000000003<42> = 17 × 11764705882352941176470588235294117647059<41>
2×1042+3 = 2000000000000000000000000000000000000000003<43> = 473476023375163705877<21> × 4224078731047546560439<22>
2×1043+3 = 20000000000000000000000000000000000000000003<44> = 6263 × 2187467868975357653<19> × 1459842158613772062977<22>
2×1044+3 = 200000000000000000000000000000000000000000003<45> = 7 × 419 × 1091 × 1115911 × 22068793 × 2537961573918528140906387<25>
2×1045+3 = 2000000000000000000000000000000000000000000003<46> = 23 × 83 × 5281 × 1137872495299<13> × 174346928210271221879232893<27>
2×1046+3 = 20000000000000000000000000000000000000000000003<47> = 601 × 10825259 × 734482643 × 4185387670524992598018391019<28>
2×1047+3 = 200000000000000000000000000000000000000000000003<48> = 176905403 × 1130547719902031482893713540224658938201<40>
2×1048+3 = 2000000000000000000000000000000000000000000000003<49> = 6871 × 10949 × 26584934299123232854555060648941702283057<41>
2×1049+3 = 20000000000000000000000000000000000000000000000003<50> = 79 × 253164556962025316455696202531645569620253164557<48>
2×1050+3 = 200000000000000000000000000000000000000000000000003<51> = 7 × 6491 × 237151 × 1153609 × 8988086730774101<16> × 1790067864550241141<19>
2×1051+3 = 2(0)503<52> = 19 × 197 × 159239027032849<15> × 3355526347347494765062846183242829<34>
2×1052+3 = 2(0)513<53> = 409 × 4335631 × 10342885269851<14> × 1090467352009655798670870606607<31>
2×1053+3 = 2(0)523<54> = 31 × 829 × 14753 × 527513318280406704433683764738692440130410049<45>
2×1054+3 = 2(0)533<55> = 1129 × 5536417031655899<16> × 319968523864926281807959061371083793<36>
2×1055+3 = 2(0)543<56> = 947 × 630641640613593647<18> × 33488629391928160215301711261193567<35>
2×1056+3 = 2(0)553<57> = 7 × 87796968481<11> × 9368987878212461<16> × 34734396543207627172561909369<29>
2×1057+3 = 2(0)563<58> = 172 × 47 × 47161 × 381357863 × 1982502477023<13> × 4129570129161813841531043869<28>
2×1058+3 = 2(0)573<59> = 29 × 133373771 × 830083951270177<15> × 8577012162065861<16> × 726279061919048761<18>
2×1059+3 = 2(0)583<60> = 36382287863<11> × 1715548838023451276899<22> × 3204327551100096307916697319<28>
2×1060+3 = 2(0)593<61> = 97 × 3347 × 89627 × 13472671 × 195022804897<12> × 26159207707463133368869943944733<32>
2×1061+3 = 2(0)603<62> = 197689 × 493060093873981<15> × 2608655530952645899<19> × 78655827078856343401733<23>
2×1062+3 = 2(0)613<63> = 7 × 79 × 67187 × 5382940938022136860142931615845020393406317220316048073<55>
2×1063+3 = 2(0)623<64> = 173 × 709 × 123805374165243868085316016373<30> × 131703755921620208014649133623<30>
2×1064+3 = 2(0)633<65> = 241 × 82987551867219917012448132780082987551867219917012448132780083<62>
2×1065+3 = 2(0)643<66> = 250214207989<12> × 799315121261189397901309758464692809702923108613928727<54>
2×1066+3 = 2(0)653<67> = 5045396267<10> × 269952174593306396039669287<27> × 1468411861087106185253786003407<31>
2×1067+3 = 2(0)663<68> = 23 × 3083 × 474717736202574865914293<24> × 594145999077637914442282147060469278819<39>
2×1068+3 = 2(0)673<69> = 7 × 31 × 179 × 289067 × 12221768408569<14> × 1457419800611451039734374629295231356806366627<46>
2×1069+3 = 2(0)683<70> = 19 × 211 × 58676451232029416603<20> × 2067397236615734055061<22> × 4112502436486078502075149<25>
2×1070+3 = 2(0)693<71> = 193 × 1009 × 9015029 × 318197099659911533<18> × 35802897529245969120774911383627717355267<41>
2×1071+3 = 2(0)703<72> = 107 × 155731 × 110242819 × 108873161835557496912230201617128500051561735049298977361<57>
2×1072+3 = 2(0)713<73> = 149 × 13422818791946308724832214765100671140939597315436241610738255033557047<71>
2×1073+3 = 2(0)723<74> = 17 × 151 × 7759 × 28481543869<11> × 35256146990949820675155255501335850511972129326274272679<56>
2×1074+3 = 2(0)733<75> = 72 × 23909542862637059743<20> × 170711446743697725633505677829515883121491856455923629<54>
2×1075+3 = 2(0)743<76> = 79 × 331 × 10206815431870182840270817231<29> × 7493498919620788902689385842385931447646537<43>
2×1076+3 = 2(0)753<77> = 103035186006031<15> × 1934982246763493955490755927821<31> × 100315363558355014647859823017153<33>
2×1077+3 = 2(0)763<78> = 7159 × 6478104454016753760887<22> × 4312505747417765608582777589439413779944095761779091<52>
2×1078+3 = 2(0)773<79> = 5693 × 1237661 × 2486863 × 114139310551026338652399651844405362963557000608503422372020997<63>
2×1079+3 = 2(0)783<80> = 4561 × 685978596651857<15> × 6392332516138127241768447324856462524373231004706954463263139<61>
2×1080+3 = 2(0)793<81> = 7 × 6299 × 414473453 × 19966584998152201<17> × 548100043780603304955338234337098221979945589533507<51>
2×1081+3 = 2(0)803<82> = 1277 × 1523 × 2530899979<10> × 133940570111507996479098559<27> × 3033556371527318787524930840338672101713<40>
2×1082+3 = 2(0)813<83> = 825611 × 8812588523511893<16> × 2748849941029302910494614920725892417409755520329614893557061<61>
2×1083+3 = 2(0)823<84> = 31 × 113 × 229 × 24979 × 5278397362612613211007287739<28> × 1890937814311875696421686100672206606653923849<46>
2×1084+3 = 2(0)833<85> = 10689751 × 30870029 × 174101240977<12> × 27501614868292675787<20> × 1265800626727778453024504210132287247243<40>
2×1085+3 = 2(0)843<86> = 61 × 263 × 784009 × 730869849769<12> × 188791641851297<15> × 92965737425275667<17> × 123958877689262908298519237788099<33>
2×1086+3 = 2(0)853<87> = 7 × 29 × 83 × 6271 × 3708068388463<13> × 803341897652669<15> × 606376773754238324363<21> × 1047920541237702507248025832637<31>
2×1087+3 = 2(0)863<88> = 19 × 2633 × 13351343 × 9391183921538689<16> × 60685815889202975701<20> × 5254035963287563578959421946859218396907<40>
2×1088+3 = 2(0)873<89> = 79 × 9712441 × 98836273 × 160330424167<12> × 259333214069<12> × 636360516185020985689<21> × 9967375987265890256911580767<28>
2×1089+3 = 2(0)883<90> = 17 × 23 × 293 × 31220972566629346037<20> × 55916398361587507836687691938105593431350598515146351210658005213<65>
2×1090+3 = 2(0)893<91> = 1153 × 1612351060219207303<19> × 1075823634240573613236619945236180905716293882720442899436436921102117<70>
2×1091+3 = 2(0)903<92> = 14341 × 225859 × 751763 × 45186538905301<14> × 181770388080836974514656491761082559023131975054065757127548899<63>
2×1092+3 = 2(0)913<93> = 7 × 9241 × 162557 × 90668547845459<14> × 188080429537884826493<21> × 6577596128333935936571<22> × 169566414790523540512576421<27>
2×1093+3 = 2(0)923<94> = 7321913 × 159129109 × 4211620326587<13> × 175746623295851659<18> × 2319100651175680426597602137387367174469580704823<49>
2×1094+3 = 2(0)933<95> = 59 × 241 × 94427 × 3614470427<10> × 19340062151882758570550401967047<32> × 213089577421509928559482959036656417177388199<45>
2×1095+3 = 2(0)943<96> = 1097 × 2777 × 323537 × 3184710803<10> × 63716737888419215547415929687932010189450906872448170069806562750426211617<74>
2×1096+3 = 2(0)953<97> = 13387084763939<14> × 6888003416488249330043<22> × 21689554339683136588679658930304369012462798870108076460065939<62>
2×1097+3 = 2(0)963<98> = 109 × 347 × 787429 × 784377317 × 145923420596482481004347<24> × 5866952744783258583080885755055224630524999042809897791<55>
2×1098+3 = 2(0)973<99> = 7 × 31 × 26891720626840241453<20> × 34272964492098008972146833105500148126083732893462398747862634497615158084103<77>
2×1099+3 = 2(0)983<100> = 211 × 79382035150980920346405340690307261392830949801<47> × 119405769425714490171006230771951087269574666783273<51> (Makoto Kamada / GGNFS-0.54.5b for P47 x P51)
2×10100+3 = 2(0)993<101> = 170547889 × 2351903621<10> × 49861360773942694081325021246938997255965585182246410257045279125241288931457688087<83>
2×10101+3 = 2(0)1003<102> = 79 × 383 × 617 × 774799 × 1690313 × 216954797 × 18484717176979<14> × 176407766384435368999<21> × 11562800031772242924518824714175876232173<41>
2×10102+3 = 2(0)1013<103> = 439 × 701 × 5551873 × 322353810266010223<18> × 3631408672796406702085696216743007169009354928263686873187008923205595863<73>
2×10103+3 = 2(0)1023<104> = 47 × 2068430377411<13> × 71811408358293195292411<23> × 77125858976287579050890129854699<32> × 37144778449564313154341134715055031<35> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1191110923 for P32 x P35 / May 15, 2007 2007 年 5 月 15 日)
2×10104+3 = 2(0)1033<105> = 7 × 1499 × 72924583 × 32500127761170009153191422527529<32> × 8042133907689848374500596451675451989411649913723669050575553<61> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1905153368 for P32 x P61 / May 15, 2007 2007 年 5 月 15 日)
2×10105+3 = 2(0)1043<106> = 17 × 19 × 467 × 3961175617793<13> × 3347237247165798725331239871160802804281762325288903139153487422487976442557810503419931<88>
2×10106+3 = 2(0)1053<107> = 173 × 5594493493318388089<19> × 20909268680821569816065383<26> × 988289716009437275446318931091762783722563293522184539500353<60>
2×10107+3 = 2(0)1063<108> = 34159 × 135257 × 8581253024316133683871<22> × 70366470719053751070081322438416837323<38> × 71688355828884849285727325871272978657<38> (Makoto Kamada / Msieve 1.21 for P38(7036...) x P38(7168...) / 7.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 17, 2007 2007 年 5 月 17 日)
2×10108+3 = 2(0)1073<109> = 131 × 971 × 1663 × 211153 × 785013631 × 10956056139051043916590023409<29> × 5206172069618515898494220381496970287426897628124942838563<58>
2×10109+3 = 2(0)1083<110> = 2719 × 8543 × 430741 × 1991149621<10> × 17549207512483876748254230582091<32> × 57204838642635824463463028377398262905391805414776179409<56> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=785503868 for P32 x P56 / May 15, 2007 2007 年 5 月 15 日)
2×10110+3 = 2(0)1093<111> = 7 × 26184862097599361168293556342151923<35> × 1091142984253028074855253881145711454222019861072878061773867745555021996423<76> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P35 x P76 / 0.48 hours on Core 2 Quad Q6600 / May 17, 2007 2007 年 5 月 17 日)
2×10111+3 = 2(0)1103<112> = 23 × 86956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261<110>
2×10112+3 = 2(0)1113<113> = 677 × 54670303 × 1130429630033873669<19> × 478020270900772726633696605954219944463744295928749633602720299644323342149372542277<84>
2×10113+3 = 2(0)1123<114> = 31 × 6451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451613<112>
2×10114+3 = 2(0)1133<115> = 29 × 79 × 269 × 46091 × 141642068744903728734080380860557<33> × 497100539534504959831516767690043182490203130774494939527873200330969211<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P33 x P72 / 0.64 hours on Core 2 Quad Q6600 / May 17, 2007 2007 年 5 月 17 日)
2×10115+3 = 2(0)1143<116> = definitely prime number 素数
2×10116+3 = 2(0)1153<117> = 72 × 15031 × 6544399742820969529407841<25> × 41493132409708849993961614871982844651028070979055904408757610584660729478322747116357<86>
2×10117+3 = 2(0)1163<118> = 252481430303<12> × 14233541343533<14> × 79171895467787<14> × 7029372274658901576417661765722869204475035431907927006123940343512211180833331<79>
2×10118+3 = 2(0)1173<119> = 714997972759321<15> × 991811671612623385550841555017839892819<39> × 28203043059484251487882072762043305121719614244673667495654922297<65> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P39 x P65 / 0.96 hours on Core 2 Quad Q6600 / May 17, 2007 2007 年 5 月 17 日)
2×10119+3 = 2(0)1183<120> = 5228659514109126391498531522208323958331928046131<49> × 38250721711810786837816564744277352704880578237524903785562032046531313<71> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P49 x P71 / 1.03 hours on Core 2 Quad Q6600 / May 17, 2007 2007 年 5 月 17 日)
2×10120+3 = 2(0)1193<121> = definitely prime number 素数
2×10121+3 = 2(0)1203<122> = 17 × 14488801 × 65881399 × 2194247719<10> × 45230755231<11> × 39243438138434903<17> × 82493772245610301788337353942271<32> × 3835995654100008613560231526090607813<37> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3804634123 for P32 x P37 / May 15, 2007 2007 年 5 月 15 日)
2×10122+3 = 2(0)1213<123> = 7 × 1255591 × 1846821995548619239<19> × 873192647167017533911<21> × 2445409000264004985346080302093575163<37> × 5770283446250729246099452389095675049097<40> (Makoto Kamada / Msieve 1.21 for P37 x P40 / 7.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 17, 2007 2007 年 5 月 17 日)
2×10123+3 = 2(0)1223<124> = 19 × 252444851578307<15> × 416974864952176659286921762537731373167739280498222726745880301034569498329218744986251818415970890775078491<108>
2×10124+3 = 2(0)1233<125> = 107 × 241 × 807932595751<12> × 15473661967469980997<20> × 62038450235564933442218840576529640620666357432793040061287595166043436265300664996855027<89>
2×10125+3 = 2(0)1243<126> = 41765060149<11> × 323601526579<12> × 9993023712544651881405293<25> × 397869046237867494121907980309<30> × 3721939007586273114581978136315755902636906895389<49> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3873787057 for P30 x P49 / May 15, 2007 2007 年 5 月 15 日)
2×10126+3 = 2(0)1253<127> = 9496596035573<13> × 72990180616825855013<20> × 1363935016086710284190348118562849<34> × 2115455595883918282267614450587132366299796154935856176143403<61> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P34 x P61 / 2.12 hours on Core 2 Quad Q6600 / May 19, 2007 2007 年 5 月 19 日)
2×10127+3 = 2(0)1263<128> = 79 × 83 × 32843 × 3835231 × 1195589420583881466001<22> × 8927757006598681262632931194240133629<37> × 2268642375519091333458799446695979155571481664083795247<55> (Jo Yeong Uk / Msieve v. 1.21 for P37 x P55 / 01:31:38 on Core 2 Quad Q6600 / May 19, 2007 2007 年 5 月 19 日)
2×10128+3 = 2(0)1273<129> = 7 × 31 × 2963 × 193441 × 1608014948402127570106586247594522610290635832095644274448651737684348026668594835032873733512861038079830762256699673<118>
2×10129+3 = 2(0)1283<130> = 199 × 211 × 108307883 × 439778908259318879132175124451656910736124888008620424152716208102430896908420952389976088353089547098694511271471669<117>
2×10130+3 = 2(0)1293<131> = 12197 × 103423915189057<15> × 15854625846360807465839312919222637107991076910585397853870551265862533057270279414491351892335733031540359985607<113>
2×10131+3 = 2(0)1303<132> = 8093 × 4567358173159<13> × 540506822274149821<18> × 20250623254125963298303817<26> × 494328683079133106401078242337242213766572794591865006865231436633400917<72>
2×10132+3 = 2(0)1313<133> = 463 × 275297805609606581<18> × 81483035220514238963<20> × 192565755118774612646331983883006930030794800546537948994802291846665356618143697402920173027<93>
2×10133+3 = 2(0)1323<134> = 23 × 2739490804091120297<19> × 202774642894094696157617<24> × 1565375987184300132253742064897937509211101557738800048039377218390189814067798915031396989<91>
2×10134+3 = 2(0)1333<135> = 7 × 157756740409116882389<21> × 245627325886145161242134796623575019<36> × 737339247296593171731659164098751163305183427019906464474193591876106604044019<78> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P36 x P78 / 3.54 hours on Cygwin on AMD 64 3400+ / May 19, 2007 2007 年 5 月 19 日)
2×10135+3 = 2(0)1343<136> = 257 × 1039 × 99257 × 7020006299581572894488170104402102406297674139<46> × 10749361742827382298904906120880763303050229911440763032084434365062835850279407<80> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P46 x P80 / 3.55 hours on Core 2 Quad Q6600 / May 20, 2007 2007 年 5 月 20 日)
2×10136+3 = 2(0)1353<137> = 23719 × 7835404340941139<16> × 107614850749561407878824124427790571175221117550451406518629318663620901554531941180527256812039819026153650029950983<117>
2×10137+3 = 2(0)1363<138> = 17 × 1328613771450100770246781828785320550322299965818189662049<58> × 8854872751704570530521108482218419399537655969341394293738394189902236177869491<79> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P58 x P79 / 6.22 hours on Core 2 Quad Q6600 / May 20, 2007 2007 年 5 月 20 日)
2×10138+3 = 2(0)1373<139> = 22082396421516652591<20> × 90569880271293352518303498238803858248630888025984330258335249566554794436493185827628586008360528546509702442784359533<119>
2×10139+3 = 2(0)1383<140> = 20663 × 967913662101340560422010356676184484343996515510816435173982480762715965735856361612544161060833373663069254222523350917098194841020181<135>
2×10140+3 = 2(0)1393<141> = 7 × 79 × 7873 × 754242675153051504745993<24> × 60905079120205992651499182035774058280731042907790381089516679191263999393874607733267630012429589633047391859<110>
2×10141+3 = 2(0)1403<142> = 19 × 167 × 511171 × 31993217 × 416824282517<12> × 40464415611439<14> × 40059260051938443901187811141767299<35> × 57043556884754993123007599776067037686087494765852279033731828829<65> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P35 x P65 / 3.69 hours on Core 2 Quad Q6600 / May 20, 2007 2007 年 5 月 20 日)
2×10142+3 = 2(0)1413<143> = 29 × 18121 × 10062555889<11> × 5499130730309<13> × 142203315288161311512583<24> × 1628892178337141932454034590460430447783<40> × 2969240859409506695099012352547967144102089819518203<52> (Jo Yeong Uk / Msieve v. 1.21 for P40 x P52 / 01:28:26 on Core 2 Quad Q6600 / May 18, 2007 2007 年 5 月 18 日)
2×10143+3 = 2(0)1423<144> = 31 × 79869969541<11> × 213191226127907995641964733297<30> × 228969479001528543632608227557<30> × 1654770841768982551074895703714451566312262310294250115213002864298336917<73> (Makoto Kamada / GMP-ECM 6.1.2 B1=50000, sigma=3963908166 for P30(2289...) / May 12, 2007 2007 年 5 月 12 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P30(2131...) x P73 / 5.26 hours on Core 2 Quad Q6600 / May 21, 2007 2007 年 5 月 21 日)
2×10144+3 = 2(0)1433<145> = 1201 × 1168960033824751568738318599288806794044795142960334049<55> × 1424581581949223240674405227318668880791852510435284297667922774714016704281163739428947<88> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp for P55 x P88 / 9.47 hours on Cygwin on AMD 64 3200+ / May 18, 2007 2007 年 5 月 18 日)
2×10145+3 = 2(0)1443<146> = 61 × 227 × 7911360529<10> × 185405024863733<15> × 1698566896904071<16> × 511073459929064433496515670727<30> × 1134320138268801249042282616951572493682856422065040483699499756236497921<73> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1063430585 for P30 x P73 / May 15, 2007 2007 年 5 月 15 日)
2×10146+3 = 2(0)1453<147> = 7 × 14243 × 106441 × 1088196679<10> × 11297303071<11> × 1532990132749980953389945553120218010491917071949279249377201842143209739521102656071536651055954979955117249500808887<118>
2×10147+3 = 2(0)1463<148> = 1689189684351792543788723<25> × 37217298101001103011342694765763<32> × 31813154456124267948681707302764451170058560372489661494512147777300060017072412206709935547<92> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P25 x P32 x P92 / 16.66 hours on Core 2 Quad Q6600 / May 22, 2007 2007 年 5 月 22 日)
2×10148+3 = 2(0)1473<149> = 151 × 54917 × 79496880961<11> × 360248308916767<15> × 22142194087798266515774322687941954125664442651683<50> × 3803413556430766247732445539023188610808389140958333384583058412229<67> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp for P50 x P67 / 12.42 hours on Cygwin on AMD 64 3200+ / May 19, 2007 2007 年 5 月 19 日)
2×10149+3 = 2(0)1483<150> = 47 × 173 × 197 × 3634354939784511165317<22> × 228523786955320896343849<24> × 150335330555761799982346599520277823222294967921805913894675204804052376237077781705390405123139713<99>
2×10150+3 = 2(0)1493<151> = 487 × 1824453361909318934020125483109157972584403451163125882265065433<64> × 2250962543871412830161298255938234659251521136933600855735504876723568950774217694093<85> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp for P64 x P85 / 16.18 hours on Cygwin on AMD 64 3200+ / May 19, 2007 2007 年 5 月 19 日)
2×10151+3 = 2(0)1503<152> = 206127409853<12> × 97027367754065425165181173621119251060810058720182234045762222524054645187828405948586729316796098149047845834331461971247418816223279407551<140>
2×10152+3 = 2(0)1513<153> = 7 × 59 × 9437 × 1077079 × 3473719 × 764892666772199274490037661811796227973<39> × 17930947920257063532703516829435538148362253000748922501535367754063948223945638948206096726431<95> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P39 x P95 / 17.03 hours on Core 2 Quad Q6600 / May 23, 2007 2007 年 5 月 23 日)
2×10153+3 = 2(0)1523<154> = 17 × 79 × 3677 × 294240857 × 1376440289607705711643874895620590896694660344209270221136185143972927196557968203597288965288158512426106493567881141417634298421288841289<139>
2×10154+3 = 2(0)1533<155> = 241 × 141906841 × 32826981394635607932036482961957538515492937504121287<53> × 17814706504328977485410892424619338104938573843248529336228689546358190125162267028033028349<92> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P53 x P92 / 20.71 hours on Cygwin on AMD 64 3400+ / May 19, 2007 2007 年 5 月 19 日)
2×10155+3 = 2(0)1543<156> = 23 × 1111621257288759311574554337362336029819886569891919818320899807496833211589<76> × 7822495402005635711932598925376137473625943127630073484216479297850123896513649<79> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P76 x P79 / 18.69 hours on Cygwin on AMD 64 3400+ / May 18, 2007 2007 年 5 月 18 日)
2×10156+3 = 2(0)1553<157> = 97 × 125353 × 97436968800347339<17> × 43135946585687043827750397163601212657<38> × 39134557867852232577558454632800142255822036800416522850859882961102818904957125240913476934321<95> (Robert Backstrom / GMP-ECM 5.0 B1=1358500, sigma=3378444485 for P38 x P95 / May 23, 2007 2007 年 5 月 23 日)
2×10157+3 = 2(0)1563<158> = 8678368395079<13> × 59573402681404398007654718102866364909302643<44> × 38684724398115424654512004896712075071304442379362845270019006771965113736013768988351468162809875399<101> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp for P44 x P101 / 44.23 hours on Cygwin on AMD 64 3200+ / May 21, 2007 2007 年 5 月 21 日)
2×10158+3 = 2(0)1573<159> = 73 × 31 × 176891153250092117<18> × 25560955073898763070557830367<29> × 4159977593448370364304706171478541066565887961579230858181342138794851799577442531362916884055114039300431969<109>
2×10159+3 = 2(0)1583<160> = 19 × 211 × 1895315654240578217<19> × 27027959896545436523<20> × 9738658207678451324435719062537714360497552822646565456174754048863655310132922791044018520009793860700775434306628537<118>
2×10160+3 = 2(0)1593<161> = 269741 × 300244161062830630302818080353294695395582491459143920704439<60> × 246949676822489123478546797860086337445136656832298441810501694114885422418729064737492466489097<96> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp for P60 x P96 / 32.43 hours on Cygwin on AMD 64 3200+ / May 26, 2007 2007 年 5 月 26 日)
2×10161+3 = 2(0)1603<162> = 1645747984609139286241<22> × 23143371269685496536153160328427093498540901<44> × 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383<97> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.26 for P44 x P97 / October 6, 2007 2007 年 10 月 6 日)
2×10162+3 = 2(0)1613<163> = 179397930216237714296595927956723<33> × 11148400639791637102996387547716707811007020632209029670143600424942142750952687051685685837339502521886454403702834010533758301361<131> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3516208220 for P33 x P131 / May 15, 2007 2007 年 5 月 15 日)
2×10163+3 = 2(0)1623<164> = 166140237444137244767<21> × 190635692847477990579123632346869310511<39> × 631467424737264651495425260061946168071504561817690296672097889180937084893277408137330615731353547645619<105> (Robert Backstrom / GMP-ECM 6.1.3 B1=4880000, sigma=2651749020 for P39 x P105 / December 29, 2007 2007 年 12 月 29 日)
2×10164+3 = 2(0)1633<165> = 7 × 10370741 × 97689419 × 205274357 × 139874026753<12> × 69298219423145010197<20> × 2153254071713608720591373<25> × 6582418788086270165044449804136959083935788871362889026363451583633652174166909560151<85>
2×10165+3 = 2(0)1643<166> = 94136405394950299<17> × 838305023383274289860418539450587157<36> × 25343717347214324824522098723663613215893017202640604427624247481323908812513490062007103784101162836271292998421<113> (Robert Backstrom / GMP-ECM 6.0.1 B1=1495500, sigma=1080719165 for P36 x P113 / November 12, 2007 2007 年 11 月 12 日)
2×10166+3 = 2(0)1653<167> = 79 × 729941 × 1137496712761<13> × 3151934443985899535720514258097<31> × 29139773847805639821445881025078673003<38> × 245334893549794309989767836564265608087<39> × 13531387192579406360450949532177073435621<41> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2603024962 for P31 / May 16, 2007 2007 年 5 月 16 日) (honeycrack7 / GGNFS-0.77.1-20060513-pentium4 for P38 x P39 x P41 / 149.93 hours on DualCore Intel Core 2 Duo E6400, 1600 MHz, Windows XP and Cygwin / June 12, 2007 2007 年 6 月 12 日)
2×10167+3 = 2(0)1663<168> = 337473788641314954387395638036113417304047480856561<51> × 4690700023174550771994364525354487199388452766958125990189<58> × 126343321023855007144178242728859599541361819987460022346207<60> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P51 x P58 x P60 / 86.06 hours on Core 2 Quad Q6600 / May 21, 2007 2007 年 5 月 21 日)
2×10168+3 = 2(0)1673<169> = 83 × 5113 × 107171503 × 57092174517726937<17> × 17170380743133123257952990693559<32> × 44858038464611919885751480065824250801088011690093127023208432690399488635724167714133938508092027766196393<107> (Robert Backstrom / GMP-ECM 6.0 B1=598000, sigma=3172473091 for P32 x P107 / February 8, 2008 2008 年 2 月 8 日)
2×10169+3 = 2(0)1683<170> = 17 × 4568033 × 43680967143031<14> × 5896028798213843137237197474833906963102993131581871751699684425911935230535986344105005014558253978688551536750366043892471178185550208899868740133<148>
2×10170+3 = 2(0)1693<171> = 7 × 29 × 1013 × 76541953053300386459<20> × 12706471680112835654690980720290430949855819667071375215198272273064756284147694488613045888308212030764851003333958296721086670252760342053743103<146>
2×10171+3 = 2(0)1703<172> = 8627 × 41713247973026961742658321646485423054431<41> × 5557713951456074967962531890753686473889384220379793822875068616831334165905093911472798378503095080109303609626110094430409519<127> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 for P41 x P127 / 206.25 hours on Core 2 Duo E6300 1.86GHz, Windows Vista and Cygwin / June 7, 2007 2007 年 6 月 7 日)
2×10172+3 = 2(0)1713<173> = 2213 × 40853 × 1531324534463359<16> × 2439195933333443<16> × 59225767811436665677404655299131091454174324294278314763315069306690006550853237485054095184846979975166325383100663147992888076712071<134>
2×10173+3 = 2(0)1723<174> = 31 × 3164590541963<13> × 1377280097548571230432695973091803101076339<43> × 10704249832674713026912742559336870309487534796404441<53> × 138284106376553420246923079942434034576006381033927871198757392949<66> (suberi / GMP-ECM 6.1.2 B1=3000000, sigma=1577510330 for P43 / May 29, 2007 2007 年 5 月 29 日) (JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs for P53 x P66 / September 18, 2007 2007 年 9 月 18 日)
2×10174+3 = 2(0)1733<175> = 797 × 6299 × 398382328716015746459924829238394574988800476783971007327645363238035632510627346596410615056501569725970723281044988718808406584224099621078648041761622754642498669901<168>
2×10175+3 = 2(0)1743<176> = 1607 × 9041761 × 65731411 × 1081691158291<13> × 76852616085817677774513791387885482895603<41> × 251898861882089203262483987189502786622824705946228241740108420753071099837412827838656218659332309040463<105> (suberi / GMP-ECM 6.2.1 B1=11000000, sigma=1680173255 for P41 x P105 / July 5, 2008 2008 年 7 月 5 日)
2×10176+3 = 2(0)1753<177> = 7 × 1307 × 17785019238356023897<20> × 3214888775730183633684484492940316319<37> × 382327974808924344375250235945475131233497457127498460037175594820337444676213458154174274593752449576287105681456329<117> (suberi / GMP-ECM 6.2.1 B1=11000000, sigma=3437713636 for P37 x P117 / July 5, 2008 2008 年 7 月 5 日)
2×10177+3 = 2(0)1763<178> = 19 × 23 × 107 × 221303620588838744540899263379<30> × 207379590086116170683595680783934802558717377003150627710449<60> × 931987848923914489652952527655347978675348054328016114007617991049256542266907254327<84> (matsuix / GMP-ECM 6.0 B1=5764801, sigma=1348195423 for P30 / November 13, 2007 2007 年 11 月 13 日) (Bart Jans / Msieve 1.44 gnfs for P60 x P84 / March 31, 2010 2010 年 3 月 31 日)
2×10178+3 = 2(0)1773<179> = 337 × 1297 × 1447 × 1787 × 29365373 × 113629080538653227<18> × 5303249027172655921940588313560365248852477668638803073380969651997775203643395415597588922210937546209863336469209756209034438146229468862433<142>
2×10179+3 = 2(0)1783<180> = 79 × 811 × 7219 × 1989079332932927<16> × 86895751811064544336849740319641090775480253420015628669829<59> × 2501810197186437126229627022814289861260018713367709797946573918927451225309193178017466201869031<97> (Bart Jans / Msieve 1.44 snfs for P59 x P97 / April 7, 2010 2010 年 4 月 7 日)
2×10180+3 = 2(0)1793<181> = 1979 × 2380977433<10> × 360880371169402630105325305389368378564231281<45> × 1176157985424367085220614176274745306343457486221056269990067414713580079192985994419522536405812661021796259633723616006609<124> (Bart Jans / Msieve 1.44 snfs for P45 x P124 / April 11, 2010 2010 年 4 月 11 日)
2×10181+3 = 2(0)1803<182> = 5511837461824511266624821670808689<34> × 1147137242371709631910079611455202628254248681165795782894651629<64> × 3163138541455391797066485435516955368132165099527456308975977784797173528030758604063<85> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=2741714901 for P34 / May 18, 2008 2008 年 5 月 18 日) (Bart Jans / Msieve 1.44 snfs for P64 x P85 / May 7, 2010 2010 年 5 月 7 日)
2×10182+3 = 2(0)1813<183> = 7 × 4567 × 5531 × 6976873 × 325612568869149323675616094472872656162481<42> × 497892182486974750287792449089666784458187470962260411347366511635973641176575824646685926038156271581256219799204240731569729<126> (Bart Jans / Msieve 1.44 snfs for P42 x P126 / May 11, 2010 2010 年 5 月 11 日)
2×10183+3 = 2(0)1823<184> = 37441 × 107770823 × 2316040002909679<16> × 147912404254559543507<21> × 8754945331971863643578588567<28> × 165263621461343967146615234240753093905509956335838533801711393326282423692813497174787331122094424554733471<108>
2×10184+3 = 2(0)1833<185> = 241 × 4253 × 41715550696982867<17> × 45046753479013599736939609<26> × 16450357456538149478222257267964459<35> × 56831071349735800699564104034197250430260949<44> × 11106952378085416134328784349105056515147150726616078638907<59> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=1916602259 for P44, Msieve 1.36 for P35 x P59 / 3.02 hours on Turion 64 X2 Mobile 1.8GHz, Gentoo Linux / June 24, 2008 2008 年 6 月 24 日)
2×10185+3 = 2(0)1843<186> = 17 × 331 × 1493783 × 23793896485348836084155362360835910425178928920797710161916857648743628889915290695980051085831247984394491270349579323987469196155415850466965348776399545418511815476929867983<176>
2×10186+3 = 2(0)1853<187> = 673 × 156033287693<12> × 309740823289<12> × 1457961196343189999407<22> × 20134967641613105163416519618269991614702019<44> × 2094605899089145833509298930888551259266468064190461646178542207742096721296987095217288855538371<97> (Bart Jans / Msieve 1.44 snfs for P44 x P97 / May 15, 2010 2010 年 5 月 15 日)
2×10187+3 = 2(0)1863<188> = 2650288267127376709<19> × 21691476478039441219<20> × 4899431565604784118723228083483<31> × 389595763391679786994327160166767<33> × 182258522814260407226204545556975019230375927589496525253684233311399812906067616297913<87> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=2035307540 for P33, B1=3000000, sigma=1333517547 for P31 x P87 / June 24, 2008 2008 年 6 月 24 日)
2×10188+3 = 2(0)1873<189> = 7 × 31 × 38749227373442623<17> × 23785222277923103118099188628420429739593966260699743933477349927854486154481670084027000572733631292076243413718690001102212460927078692317655609049585990575921572073733<170>
2×10189+3 = 2(0)1883<190> = 211 × 617 × 186762743 × 3025939986458771807<19> × 299721566142829669823<21> × 6007634365195440036739<22> × 419817276608201618522516989479656415256109781516871114787<57> × 35960856659366982010140181518614170249139085672467809368871<59> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P57 x P59 / 26.59 hours on Core 2 Quad Q6600 / July 20, 2007 2007 年 7 月 20 日)
2×10190+3 = 2(0)1893<191> = 76949 × 1032007 × 209094547936744449194474908906729<33> × 34966959780535052264850174530936020777783<41> × 34446395954434388140001513015465553314448279869307180102939860821079122131241949069764159546294081893118303<107> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=3778450102 for P33 / June 25, 2008 2008 年 6 月 25 日) (Bart Jans / Msieve 1.44 snfs for P41 x P107 / May 18, 2010 2010 年 5 月 18 日)
2×10191+3 = 2(0)1903<192> = 2221 × 283112539 × 5806007837521<13> × 2980061483271130133454822323000539259581<40> × 182806214988875869300773608643861228898368769920609146878022777<63> × 100560756952935629434227230943212354457451323996998349267619421881<66> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=134908296 for P40 / June 25, 2008 2008 年 6 月 25 日) (Ignacio Santos / GGNFS, Msieve gnfs for P63 x P66 / 93.02 hours / May 7, 2009 2009 年 5 月 7 日)
2×10192+3 = 2(0)1913<193> = 79 × 173 × 276519843869<12> × 35108586452041<14> × 10356144553255211560838847446569517<35> × 34876652767087367824771974117100355091162711256918297<53> × 41733446592368214066530327214400601607954236617362271592609176269988064074729<77> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=1047461786 for P35 / June 26, 2008 2008 年 6 月 26 日) (Bart Jans / Msieve 1.44 gnfs for P53 x P77 / April 3, 2010 2010 年 4 月 3 日)
2×10193+3 = 2(0)1923<194> = 1999 × 2393 × 3728792911<10> × 13204518309653988285253533541223281210472029154719159416351911592177934839932596309784809<89> × 84914855627628876822887170020630119458401404969220347791519669735345970257922349845596771<89> (Bart Jans / Msieve 1.44 snfs for P89(1320...) x P89(8491...) / June 9, 2010 2010 年 6 月 9 日)
2×10194+3 = 2(0)1933<195> = 7 × 443 × 27107 × 2634001 × 383403235824016344915248750822050157<36> × 95581846303913650684936313179348791612051241183194251<53> × 24649019531831500007969147622486775132580007261905157612095323460036978593433099142373379147<92> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1503835434 for P36 / May 16, 2007 2007 年 5 月 16 日) (Dmitry Domanov / Msieve 1.47 for P53 x P92 / December 16, 2010 2010 年 12 月 16 日)
2×10195+3 = 2(0)1943<196> = 19 × 47 × 113 × 11071 × 126588259468129963800476691109<30> × 14142292454874449256385710545341601030413458600321097720419472709733367544401014551310864221172502405148901436989368784462014075518851628332348975139832488253<158> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1143283122 for P30 x P158 / May 17, 2007 2007 年 5 月 17 日)
2×10196+3 = 2(0)1953<197> = 457661 × 1456329317141<13> × 34739974096182333336498956398761394712665299128822051<53> × 863767795454334095995331720940616645856427889828345455035329342862116841141043748872939590809968883391913076573287926075614753<126> (Bart Jans / Msieve 1.44 snfs for P53 x P126 / June 22, 2010 2010 年 6 月 22 日)
2×10197+3 = 2(0)1963<198> = 29836370592137497650499<23> × 16729518439454517288281783<26> × 400682673532747702599827593186249104211952228306848094072962577538564657735619425416018392875826151577920421751986920916957351046332971959489884265159<150>
2×10198+3 = 2(0)1973<199> = 29 × 52157717415774943068631<23> × 1202575461497852123709722181169806824814923<43> × 22388361185594023898713964704438991440520568602692290206129907529<65> × 49111000098728410999628085323532736039706325695068709498811336069491<68> (Serge Batalov / GMP-ECM 6.2.3 B1=6000000, sigma=850451545 for P43 / October 15, 2010 2010 年 10 月 15 日) (Dmitry Domanov / Msieve 1.47 for P65 x P68 / December 9, 2010 2010 年 12 月 9 日)
2×10199+3 = 2(0)1983<200> = 23 × 6317 × 39503 × 20536689829<11> × 241585002691<12> × 2791892855273<13> × 7002385537531<13> × 21762838802020382865799787471876924157001<41> × 1650822877321040398455081458354580460326700853503002329227022520485062724197783051668669873368413008923<103> (Dmitry Domanov / Msieve 1.47 snfs for P41 x P103 / December 17, 2010 2010 年 12 月 17 日)
2×10200+3 = 2(0)1993<201> = 72 × 18873739043<11> × 1737408773621<13> × 9318870262441<13> × 288930187492555799536718659699424506652533163856455735889878594247989358356453147<81> × 46229348644433214755924438644202543849471369171438338376543760504475737398042864287<83> (matsui / Msieve 1.48 snfs for P81 x P83 / November 30, 2010 2010 年 11 月 30 日)
2×10201+3 = 2(0)2003<202> = 17 × 499 × 8297 × 27953 × 135936284483<12> × 7478174909367156756630085410748712977422468534861737613160675169747253134057445145178556471601933441936502429024529904963269336432687778258728232544744850286476330463387837842947<178>
2×10202+3 = 2(0)2013<203> = 75459871 × 1660757687861<13> × 132029726597383<15> × 9456009228465959506927<22> × 21221488856119687321569379867322835402330472661<47> × 6023545629072409264543170789653616047337589173825701217547228295524880946098290954520722849826791613<100> (Youcef Lemsafer / GMP-ECM 6.4.4 B1=43000000, sigma=4008543260 for P47 x P100 / May 23, 2013 2013 年 5 月 23 日)
2×10203+3 = 2(0)2023<204> = 31 × 98824771 × 31826521971951588907640018797426848260569<41> × 192464253228251425503197451645662761118021446373745679466517231707389<69> × 10657693467274606629576372196352389258616846699807994281991491308996833263256102006083<86> (Robert Backstrom / Msieve 1.44 snfs for P41 x P69 x P86 / February 6, 2011 2011 年 2 月 6 日)
2×10204+3 = 2(0)2033<205> = 922693552059567526219164014955711651517626553<45> × 2167566897520579402510174783317663121012032633795105207287245005273633870851781235593020963961663381430769839565223803747783161943595916201473004874971493738651<160> (Serge Batalov / Msieve v. 1.48 snfs for P45 x P160 / January 23, 2011 2011 年 1 月 23 日)
2×10205+3 = 2(0)2043<206> = 61 × 79 × 109 × 181 × 6270185253559475381466662879191156254002301361611799339<55> × 32826506479503039369336698750063291721433424023906813323290420063<65> × 1022028386387479653468938309940678095760637477538021596694668654286270417864029<79> (Alessandro Freda / GMP-ECM B1=110000000, sigma=3201252992 for P55 / September 22, 2011 2011 年 9 月 22 日) (Erik Branger / GGNFS, Msieve gnfs for P65 x P79 / September 3, 2017 2017 年 9 月 3 日)
2×10206+3 = 2(0)2053<207> = 7 × 1493 × 145681 × 167379743664560507<18> × 15567993685232505940760706614772601680121<41> × 3468236007546610073461399204071324738016996963744390772578305185411<67> × 14535335015846155083545128700750297335821188978469386272905228682577379289<74> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=499226455 for P41 / August 23, 2016 2016 年 8 月 23 日) (Erik Branger / GGNFS, Msieve gnfs for P67 x P74 / May 16, 2018 2018 年 5 月 16 日)
2×10207+3 = 2(0)2063<208> = 28463 × 270857311749049<15> × 16288571318055836231414241813607997<35> × 15926698743264002616454695209727957772508841403462184047924135159810624034384960317665828135137766364236937909347103242031365776291895400248541818446064377<155> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3075943084 for P35 x P155 / January 19, 2011 2011 年 1 月 19 日)
2×10208+3 = 2(0)2073<209> = 1109 × 71436944250506147<17> × 252450119373201597654948715446134275552730872887285725850308683488268045526638495477171048892780548376183231758379440408052665872769375794834961942805100565271952607994912789800456845359261<189>
2×10209+3 = 2(0)2083<210> = 83 × 2939971 × 153350552352975115152579315053263268996526354120806275628923786671847955100412966042975786177907<96> × 5344702203261233723032084844843090767970135101999101103065997705086649586996315570775927673608210709488953<106> (Bob Backstrom / Msieve 1.54 snfs for P96 x P106 / September 28, 2020 2020 年 9 月 28 日)
2×10210+3 = 2(0)2093<211> = 59 × 132961 × 235960541 × 123255603492262992869380731788381<33> × 1199084977466359011487493412958811038500740928248339<52> × 7310678635811017547610102448985540055887380058785678703557158308100229367942711514215410071967220954849636936363<112> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3336103212 for P33 / January 19, 2011 2011 年 1 月 19 日) (Bart Jans / YAFU-1.34.5-win64.exe for P52 x P112 / July 28, 2021 2021 年 7 月 28 日)
2×10211+3 = 2(0)2103<212> = 120129709079129747<18> × 320864695634224136102689<24> × 7706444807147547380002268715212781942618947<43> × 63141355312945909267638280376909574536930846855102300423<56> × 1066325177021885885702615421168122337725829427414224259983429724041303661<73> (Bart Jans / yafu 1.34.5 snfs for P43 x P56 x P73 / March 9, 2023 2023 年 3 月 9 日)
2×10212+3 = 2(0)2113<213> = 7 × 38496606209232151<17> × 742180451340062528227535521336169138404002826725617135772703402768721777245828258151928229695371074391441333567669377366841210502466789476289267172884323948773443939155235772244657750673727756579<195>
2×10213+3 = 2(0)2123<214> = 19 × 919 × 114540977034534104575912032529637477807685699559017238417043697382738674760895710440410056697783632094381765076456102170551514804421281713533016436630204455644006643376668002978065402897886718973712845770574423<210>
2×10214+3 = 2(0)2133<215> = 241 × 1619 × 42221 × 37262721821558861<17> × 3632556955692305706440794709<28> × 8969135440593066498734675211077118928811663535006195925575616095025581967057826520226410860467849287373698754437042850436113023253436917353753985144312715009333<160>
2×10215+3 = 2(0)2143<216> = 4673 × 39023 × 1872705139<10> × 2315119477427<13> × 220867853781191226474423398668835131939111<42> × 390906071147567986894313410737152856657319680976453783865174011214251<69> × 2929987874912251924075405443991602255950457557718600436054482092093137363129<76> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3419968382 for P42 / August 26, 2016 2016 年 8 月 26 日) (Erik Branger / GGNFS, Msieve gnfs for P69 x P76 / May 9, 2019 2019 年 5 月 9 日)
2×10216+3 = 2(0)2153<217> = 1489 × 29573 × 34577051987<11> × 26412230044931<14> × 209670129772203749853456070585956317535083191883<48> × 237197614226085491576527926883432287581048074332698060491837272168132460064785542558362013318116907798193304237528052262155827116488831149<138> (ebina / Msieve 1.53 snfs for P48 x P138 / January 28, 2023 2023 年 1 月 28 日)
2×10217+3 = 2(0)2163<218> = 17 × 16699 × 559644102114152267<18> × 125886360640615329294549164099099962516705818939230272513440333767789278951309678425967239340614738015910070466395740282195750050532416460698585576215517668174106663671701131485715926439291166523<195>
2×10218+3 = 2(0)2173<219> = 7 × 31 × 79 × 13163 × 13562222429349685645921434406744248180309030818250192516127793335092509339<74> × 65351780807764893934013313483072258103311913094521532095403372595487916237332092216596318800845741675678927384992755140004444225537054253<137> (Bob Backstrom / Msieve 1.54 snfs for P74 x P137 / February 19, 2020 2020 年 2 月 19 日)
2×10219+3 = 2(0)2183<220> = 211 × 2551 × 58733 × 3009379 × 5210336205293<13> × 39016104670831<14> × 173026861063558863211999003878761987545706054882147994572219096194342531<72> × 597660875277486126058063901126293948884112537650980710817727376575279442073706436015467874114989167237993<105> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P72 x P105 / November 10, 2020 2020 年 11 月 10 日)
2×10220+3 = 2(0)2193<221> = 149 × 389 × 292661 × 40829452320415402297185998735793803012684787441996116427169597976258098726972351<80> × 28877242459410090910650394787684608258833825056783943988625897134196387484631745302941695088821884585896508553733285197454429844993<131> (Erik Branger / GGNFs, NFS_factory, Msieve snfs for P80 x P131 / November 28, 2018 2018 年 11 月 28 日)
2×10221+3 = 2(0)2203<222> = 23 × 37517 × 25003480167225978761525393<26> × 9269868965482461920365872046686368716507671215562464587171310967501613185950741150960505854263916063747711092393970640563799117192019806575816404340831636335491844443016657182825495244786681<190>
2×10222+3 = 2(0)2213<223> = 218003 × 116380960268883306723328214228163601<36> × 9912363955474447656573757267693775408088476921958640708224310657<64> × 7952585545911381925975134891322753049222935458913535284315310985733744896502872384756133049564391016009045473030844993<118> (Serge Batalov / GMP-ECM B1=2000000, sigma=1752800746 for P36 / January 18, 2011 2011 年 1 月 18 日) (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P64 x P118 / July 14, 2020 2020 年 7 月 14 日)
2×10223+3 = 2(0)2223<224> = 151 × 1103 × 5477 × 210791936216237<15> × 104011366447992868862075514565329112745076256206226925730827402089293655265715077204489007892479858548078769076644752390302098744911576753063789415771653062525903005338124968716736285630126760008426299<201>
2×10224+3 = 2(0)2233<225> = 7 × 437061259067<12> × 41089321594798523<17> × 890223907372673457938571679703545757<36> × 386974255308341714669669536102448614215972802194983674096128774621677<69> × 4618270277759224606946901391594387036768149898258211315748163142033108554705198626659645621<91> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=233003545 for P36 / July 18, 2011 2011 年 7 月 18 日) (Bart Jans / yafu 2.11 (snfs, Using GMP-ECM 7.0.6-dev, Powered by MPIR 3.0.0) B1=457 for P69 x P91 / July 16, 2024 2024 年 7 月 16 日)
2×10225+3 = 2(0)2243<226> = 563 × 4812707 × 3069224027<10> × 24133133373107371<17> × 1111049353573404887<19> × 8969258171752867055924296849670930550442088534415101169615212244920435090453250276086265008133638483421328413031920737788219490078168364958843642998703273968107704041335477<172>
2×10226+3 = 2(0)2253<227> = 29 × 12720941 × 4966037309<10> × 34438403026587033518317081057<29> × 308191013287279902020257091518356688604839<42> × 1028584099562426569905167202906724001529859688495291993577768539171478538716639768430415552907163004966791528175694240833223495445801581361<139> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3984137105 for P42 x P139 / August 26, 2016 2016 年 8 月 26 日)
2×10227+3 = 2(0)2263<228> = 43487 × 307094493299567<15> × 5031198260593263891617<22> × 74886256965519871334769275700323<32> × 2101902840186131241722118415897003086697369<43> × 18910905566000687007887699558211333779414413422462577851011490134640200866850723840023041133175444944230137768633<113> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=482573774 for P32 / January 16, 2011 2011 年 1 月 16 日) (Wataru Sakai / GMP-ECM 6.3 B1=11000000, sigma=2936496433 for P43 x P113 / May 1, 2011 2011 年 5 月 1 日)
2×10228+3 = 2(0)2273<229> = 199 × 1181 × 6173 × 105084989 × 17083918279<11> × 767896302209505050003146912464602518879633928669251854961606907754707101127257051516487414995613832836219063828809988072496657112464532568896658630809131958305759599030725192301495881944030727513796599<201>
2×10229+3 = 2(0)2283<230> = 57107 × 108541 × 200971 × 1018007 × 18783727546253<14> × 139480357090048738747355796955163<33> × 6019602897740235756130241844286505519803719669335035781200606880871282490177308360796844372059325837131408698158912333639168832200933397020123068003317475286785943<163> (Serge Batalov / GMP-ECM B1=2000000, sigma=4237028320 for P33 x P163 / January 18, 2011 2011 年 1 月 18 日)
2×10230+3 = 2(0)2293<231> = 7 × 107 × 223 × 69904523675109869<17> × 17129237623550992616750351617709202709533809357071908993032797476481392213963174100140023682464905339612490610153686632309834113557467080452653861824477378381369274461653695705520666714985089643165962577594581<209>
2×10231+3 = 2(0)2303<232> = 19 × 79 × 11891717 × 38773021789<11> × 708571878670155673326184388705611847017473808511487815723<57> × 4078412757004926776546671607645512852983279323295602472062649395153810624543139617652083742092035958733113896873697338878289928642316421239002833826473997<154> (Bart Jans / GMP-ECM ... B1=110000000 for P57 x P154 / October 10, 2023 2023 年 10 月 10 日)
2×10232+3 = 2(0)2313<233> = 7757 × 1983458117<10> × 35477375981<11> × 32854650334137656373025109<26> × 1682959005764942797710492283318711234866672148274636411<55> × 662660818481625406360671526436741825484403134161651390762656946656619180722708319645996142519337253144402000258253118808187871273<129> (Thomas Kozlowski / for P55 x P129 / October 11, 2024 2024 年 10 月 11 日)
2×10233+3 = 2(0)2323<234> = 17 × 31 × 104889594944747<15> × 6160704186583644264137<22> × 587295422704655809349817396130905113438043456227891303437473279582171770052483662201661781514575828749320095609995888002571810211543553879356143372283394678232933610496139925359228388934781475951<195>
2×10234+3 = 2(0)2333<235> = 551441743 × 158143764891244446038167<24> × 22933919497913977171778558583614097888939205081185324665189950263391327271913165449056636945666180797040352470805868301231825776544777134600436817156295398518486563779353472664582135657555615616107347963<203>
2×10235+3 = 2(0)2343<236> = 173 × 293 × 1516733 × 294554881 × 1006450003978150955610622536778022241376494965006516251<55> × 8009481381449913760222747014527126488113599398476113969299<58> × 109558054209954774973007823503829435185846518156577529897141277789443056808508404845988686273187816498751<105> (Bart Jans / GMP-ECM 7.0.5 B1=110000000 for P55 / August 30, 2023 2023 年 8 月 30 日) (Bart Jans / GMP-ECM 7.0.5 for P58 x P105 / September 29, 2023 2023 年 9 月 29 日)
2×10236+3 = 2(0)2353<237> = 7 × 197848571 × 680172929372689<15> × 6984623751214589<16> × 416009117829833083931<21> × 112666061761374014547050603<27> × 273994941568772804037816247<27> × 148691185111062034661216400753058174723061987<45> × 15918896058929104333330760038031728946908584744344451554408900071070386231777447<80> (Andreas Tete / Yafu v1.22.2 via GGNFS on WinVista32bit for P45 x P80 / January 21, 2011 2011 年 1 月 21 日)
2×10237+3 = 2(0)2363<238> = 587 × 92829259 × 18877420280809<14> × 142021478699030646324860885993783768119<39> × 219869279109683917579497840127963982176287248324268568990219<60> × 62265256733594355521517071488667747095938113157077240654262952799637785654118437487632528233429732710859586014290559<116> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1464538622 for P39 / July 16, 2011 2011 年 7 月 16 日) (Bart Jans / yafu 2.11 for P60 x P116 / August 25, 2024 2024 年 8 月 25 日)
2×10238+3 = 2(0)2373<239> = 131 × 1543 × 20833460994718767148414253<26> × 4749319098808241578588785782853549672516143137789110959080051266021108694004298480837066161372210284262884736244200738150798102719444003766128819278468353043485087801017164670262032907314185556412929499602547<208> (Serge Batalov / GMP-ECM B1=2000000, sigma=821564662 for P26 / January 18, 2011 2011 年 1 月 18 日)
2×10239+3 = 2(0)2383<240> = 593 × 6579439 × 56572949627327999337675814857559<32> × [906103096831503939361731342546528364684210293919371206439035784124966108509353686804188830570103109859260183043890148370161842294031943573339314265046061597981936935053465686921478148223421848012971<198>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1522721609 for P32 / January 19, 2011 2011 年 1 月 19 日) Free to factor
2×10240+3 = 2(0)2393<241> = 8546647 × 66531131 × 3517299275323177196396323878242807957296633507054190178337309036220354881411576344233898437853877392305738457939717984652385479674563799775822117909026234210925740713862954661188386837489874709778115533632841577009120161049679<226>
2×10241+3 = 2(0)2403<242> = 47 × 233 × 6369681529<10> × 264166548527948161691233371387564085199610377736871<51> × 171613773436862237669660882738773437793072830226236246915707<60> × 6324534049590248284917609070192472173882822072762948242794194849862195587747383691209846288685570277284463688513328081<118> (Bart Jans / .\yafu2.11 "factor(286720336485927528157074630618560246464682164906916560287778508735396405547709213906203402043919871078730293858859443563398583806211514827063151439774576464197437626780420026839120378675172965216885214233401641105690900415972557)" -work 45 -pretest 50, GMP-ECM B1=43000000, sigma=1904828009 for P51 / March 25, 2024 2024 年 3 月 25 日) (Bart Jans / yafu 2.11, GMP-ECM B1=0 for P60 x P118 / December 20, 2024 2024 年 12 月 20 日)
2×10242+3 = 2(0)2413<243> = 72 × 598301600617633238291925741066574249<36> × 6822031979937394094042382427923263195497047248689958485459220266506440404563867042452394156523754522724427523385409471476713046867648435929206332216179985044859877132275189312944267098519986626078807305403<205> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2971613829 for P36 x P205 / January 21, 2011 2011 年 1 月 21 日)
2×10243+3 = 2(0)2423<244> = 23 × 14612779 × 26291210089<11> × 968296582236923032226465104845999109<36> × [233749326899097806110029159166617589598305063532831757381274243679957200416005087451099431222578019841974486267326745833842240275357267003215028562089459447719620647828761509015726182290459<189>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2876315301 for P36 / January 19, 2011 2011 年 1 月 19 日) Free to factor
2×10244+3 = 2(0)2433<245> = 79 × 241 × 23357 × 30306914117061908001539<23> × [1483976702264232854261938813281277880100327562156834705502405347634883182582526949591509599762246003499087045626689364686926224013083697359708684746078327315819050090130912952860709553024048266083848883483412767499<214>] Free to factor
2×10245+3 = 2(0)2443<246> = 6397592281888306385172750508836130410647589273710135869<55> × 15176510844417676322078085602490646507276983688902079473476701244300421692052915503455058979721<95> × 2059878003651738705074583981500086714416914728639047071846532324077474145687339476014622364979847<97> (RSALS + Greg Childers / ggnfs-lasieve4I14e on the RSALS grid + MPI msieve on Greg's local cluster for P55 x P95 x P97 / January 12, 2012 2012 年 1 月 12 日)
2×10246+3 = 2(0)2453<247> = 179 × 365531 × 30566995295999243405732433426727221310807821647818114884798573206020371465716004583765480597454542636824251805160653326119318663508871894624440828402864255840615372303939433088304732891152198281251478200788142463411574091897745636718077347<239>
2×10247+3 = 2(0)2463<248> = 197 × 8389 × 228421 × 2035604521<10> × 1471650239089<13> × 3947817424007308101721<22> × 15422695734406081196708125159<29> × 3581989853921960120548906898407049839043637359408048176681208494286388294114721<79> × 81091966621377691240046862198509221528146383892810244318568626109720151817358689211161<86> (RSALS + Dmitry Domanov / ggnfs-lasieve4I14e on the RSALS grid + msieve 1.48 for P79 x P86 / September 11, 2011 2011 年 9 月 11 日)
2×10248+3 = 2(0)2473<249> = 7 × 31 × 751139 × 470548921 × 832020595489<12> × 2175023636256101<16> × 1440944025546825142960647490142040032702715767858842028691963963263079474355335659996734514032766031645514968183756071995596126153005613326680482598728281482205019126619388376059797643533787115301964915549<205>
2×10249+3 = 2(0)2483<250> = 17 × 19 × 211 × 74405353617581747<17> × 3971025890860934787900600682943<31> × 7909666651323555630402134728237229989<37> × 12556827656486953221376911514254365828179834914555972319309764786464682771324196910728503651963646825805973789346317650824775047567969464084281316289191406502779<161> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=2396372955 for P31 / January 17, 2011 2011 年 1 月 17 日) (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=2777908596 for P37 x P161 / January 17, 2011 2011 年 1 月 17 日)
2×10250+3 = 2(0)2493<251> = 83 × 313 × 3463 × 5425951 × 64435901 × 4757674314221<13> × 50535856198897<14> × 47783392447158893860116169<26> × 2024306963840925847067681621411277602387284989904843172702101771511077754887311731<82> × 27340321354776437175235536174682028916561629122705977140438096282348866350976451165169387681323<95> (Bart Jans / yafu 2.11 for P82 x P95 / October 1, 2024 2024 年 10 月 1 日)
2×10251+3 = 2(0)2503<252> = 9767 × 20477116821951469233131975017917477219207535578990478140677792566806593631616668373093068495955769427664584826456434933961298249206511723149380567216135968055697757755707996314118972048735538036244496774854100542643595781713934677997337974813146309<248>
2×10252+3 = 2(0)2513<253> = 97 × 34796623 × 312262637 × 2670226897654362061941565517<28> × 710645441064331986474207613314272760598137924533524042705925915504929753824718031259318879153707780015446436184574316025398215596816895809085958758585775824758032173854716804486256428166426063648302672006597<207>
2×10253+3 = 2(0)2523<254> = 6851693219394996691146151<25> × 2918986498605376335012845740357795802434446836868174663775771330976080025658587478261142178923172565194424345246567295032599448739441791969581019992276885260308901333706962526755951184604226226853764141683217348943563302562154053<229>
2×10254+3 = 2(0)2533<255> = 7 × 29 × 874929607 × 11504717286929541313<20> × 25186651356595300393<20> × 6312260088373579878106897<25> × 2160485150910616384612863229700329402584100426321<49> × 417487140366844590288390096796497546939819052306417<51> × 682551129639259403329304549115300609823387369684932704650327739846498064784544263<81> (Bart Jans / yafu 2.11, GMP-ECM B1=525 for P49 x P51 x P81 / October 9, 2024 2024 年 10 月 9 日)
2×10255+3 = 2(0)2543<256> = 841427 × [2376914456037184449750245713531892843942492931650636359422742555206809384533655326011644503920126166619326453750592743042474272872156467524812015777958159174830377442131046424704698090268080296924153848165081462800694534404054065296217021797494019089<250>] Free to factor
2×10256+3 = 2(0)2553<257> = 409 × 577 × 2837 × [29872497861095546585465131990787901186096638686646311317601632559490806903828798528091217990324689272513132812628113341412878127328836595362054830907091795367456973420292314011972487889506398062466204029599517001141283261657834521629683187477850383<248>] Free to factor
2×10257+3 = 2(0)2563<258> = 79 × 157560332729540283522178187<27> × 5464283075452362398258387298377795719637<40> × 246769349302131207388925107714818685086451<42> × 5856297050051660586352104801396628260877827836944441370363592423153430433<73> × 2034738075720137921068598585554835141088749703530063778316653311216521306441<76> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1600077352 for P42 / January 12, 2016 2016 年 1 月 12 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1231624775 for P40 / August 26, 2016 2016 年 8 月 26 日) (anonymous / factordb, July 17, 2020 2020 年 7 月 17 日, http://factordb.com/index.php?id=1000000000024550281 for P73 x P76 / April 3, 2021 2021 年 4 月 3 日)
2×10258+3 = 2(0)2573<259> = 227 × 659 × 13997 × 294269 × 633339104263<12> × 1162233602469219947351437998067013<34> × 104906842135665595354526788405595494781<39> × 339189027633541271106000004951899141673895693<45> × 123926421046976481032896956929724975202254332647250942827525617857144356984970899324463342978550121377198642909656761<117> (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=330358097 for P34 / January 12, 2016 2016 年 1 月 12 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1659389351 for P39 / August 28, 2016 2016 年 8 月 28 日) (yoyo@Home / GMP-ECM 7.0.5-dev B1=110000000, sigma=0:17434511319835028385 for P45 x P117 / March 7, 2021 2021 年 3 月 7 日)
2×10259+3 = 2(0)2583<260> = 10459 × 288413 × 13395538583783183075332650695689358901897090589<47> × [494953980251295869018628202969587102580966990817437672924599157090359025108922211653852069797411398062266757132136858556589639550045010055980265631060481928354512850191472761379542726635589481421594940081<204>] (Bart Jans / yafu2.10 ecm, GMP-ECM B1=11000000, sigma=1346290308 for P47 / April 18, 2023 2023 年 4 月 18 日) Free to factor
2×10260+3 = 2(0)2593<261> = 7 × [28571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429<260>] Free to factor
2×10261+3 = 2(0)2603<262> = 372838591 × 67154440115507<14> × 44021920562888804050883090327890066073<38> × 994802487002707376815773093079053357264133355318728339<54> × 1824015635832801250114370353157979628952574352341848216459240129549925464086907451438666659137026309173590734156418170984405486599518141572488811677<148> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=593763633 for P38 / March 2, 2016 2016 年 3 月 2 日) (Bart Jans / yafu 2.11, GMP-ECM B1=597 for P54 x P148 / October 12, 2024 2024 年 10 月 12 日)
2×10262+3 = 2(0)2613<263> = 193 × 35809068915088039<17> × 2893874265508156213779008690894024693792796668373720499946507339677815074412991172335866419198646707661183129680295035377875839205605866095569474020557027917562793431673612412880746606514252398096345050928150976424805595191764563870134346048389<244>
2×10263+3 = 2(0)2623<264> = 31 × 3896513 × 667516455179191<15> × 932077490666316232204823973171301<33> × 726004703695084781066463892466467884695551683099876887<54> × 3665546571706149257548337890594516151290272232271381706628389889461600193876431020439722368598162380712785174493630109182411160724352704549396055558790953<154> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2787437306 for P33 / January 13, 2016 2016 年 1 月 13 日) (Bart Jans / YAFU Version 2.11 Built with Microsoft Visual Studio 1934 and Intel Compiler 2021 Using GMP-ECM 7.0.6-dev, Powered by MPIR 3.0.0 B1=402 for P54 x P154 / August 9, 2024 2024 年 8 月 9 日)
2×10264+3 = 2(0)2633<265> = 235111 × 136105139163899<15> × 7102109421004441639<19> × [8800253121271790315413721991225741907925836783393124145970778433538051711562343153453927161204521738785110063316567751600330721487244237683675532508552434211439915873066000007642783091372403544451367505989750747106391661369193<226>] Free to factor
2×10265+3 = 2(0)2643<266> = 17 × 23 × 61 × 521184241 × [1608911395694070774611244150185231473753730735771274432987969949926015925739039005676384161869676347395941610748361387651195917027366917359043715114702401971508964000173491834041181161531901446589113115787711879755025064046659353280417473080126681451033<253>] Free to factor
2×10266+3 = 2(0)2653<267> = 7 × 439883 × 544403 × 88784162878045023545363<23> × 1343812768782538866359417628304924419821756115040530131496307062903993605705689434689397589493184660895130934264595604387379945831476592800893652999405008220916861755729735634073468172227796525330324702548829605417978921655710619767<232>
2×10267+3 = 2(0)2663<268> = 192 × 19939455721<11> × 656037927920117<15> × 993284519793451<15> × 5085524851760961953941<22> × [83843827945033881911271713372038946990857009792598527992539136605729805811262989173007506311422368583180437445942572988257379709503707932742816826762674632076318171436850102984204450067011860630104796129<203>] Free to factor
2×10268+3 = 2(0)2673<269> = 59 × 683 × 6299 × 8887 × 6519088208071<13> × 81014420062824436176278451474516155065412010140105898511<56> × 16787317599972851051492925093284659950198373405982633432948142688669068485712094245807222538920243474948689352320153057656634512170635963926568653218633529936366688164237059566108808850783<188> (Bart Jans / yafu 2.11, GMP-ECM B1=660 for P56 x P188 / November 2, 2024 2024 年 11 月 2 日)
2×10269+3 = 2(0)2683<270> = 2038427 × 15509303 × 649556389 × 9739254012960174432405884401950301186549875221487251324634011101725660090368231511169860888823946160808124796623785116475990689267928852715341396844495314223457912667147752837373030800526164978198680188107174400473931717139583369946606665487660067<247>
2×10270+3 = 2(0)2693<271> = 79 × 347 × 3461 × 104619598220382624366593341609<30> × 201492452251291749485095850061512113368213000605282659116541364611430113758389794355887851327156074624814116662166747187530873679744625106847116446577115882833971842429352645869722169677849540151400638248597676514647087076707978620819<234> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3039350593 for P30 x P234 / January 13, 2016 2016 年 1 月 13 日)
2×10271+3 = 2(0)2703<272> = 1471 × 14543 × 635956667 × 282527048821<12> × 17540343457173578567<20> × 575998247306940739159<21> × 18116656502097942874778944203854163473199529<44> × 1489336715070522696214349978312134675132672244905215008264933041<64> × 19087346627929505480800220996297174262184911515965253473538090613063203900329759765924513670121229<98> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3188349533 for P44 / March 2, 2016 2016 年 3 月 2 日) (Bart Jans / yafu for P64 x P98 / August 7, 2024 2024 年 8 月 7 日)
2×10272+3 = 2(0)2713<273> = 7 × 557 × 3079 × 17504656935319<14> × 216235704933040468969<21> × 21775937841416581748801637508917330947<38> × 202119955191077614516627427405727787599706481833824118277486063912834549907942214047395464858610791784682735622219705785697418742310553859410301199887788446355732275757758324790705014474713834779<195> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1205940698 for P38 x P195 / August 26, 2016 2016 年 8 月 26 日)
2×10273+3 = 2(0)2723<274> = 3947 × 146344636689072440774032713529193<33> × 21055301667782570970742624178963293847<38> × 52053353286038150426637325575946774964569<41> × 3159190961895669359645791457898294953702752349226284728300635926125088690578776319865125771472948596793394450961253383734329436193012026734560041226380981669151<160> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1300867034 for P33 / January 13, 2016 2016 年 1 月 13 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1998646590 for P38 / August 29, 2016 2016 年 8 月 29 日) (Bart Jans / yafu2.10 ecm, GMP-ECM B1=11000000, sigma=2978372392 for P41 x P160 / April 22, 2023 2023 年 4 月 22 日)
2×10274+3 = 2(0)2733<275> = 241 × 5987 × 120278737 × 5798736081217<13> × 177984320737151824997<21> × 24078446183491256451907465731457431419<38> × 189480104875158798579391362618360560052403606999<48> × 24474153130373389444224254463798764446690478668953589684825644625602011581828829384799678940750696784747205052640429266480650023143171765613953<143> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4127209385 for P38, B1=11000000, sigma=3431327455 for P48 x P143 / August 28, 2016 2016 年 8 月 28 日)
2×10275+3 = 2(0)2743<276> = 1759 × 141107 × 394489 × 650987 × 16781217961177291<17> × 5566420776962957753<19> × 801859770891658374261617<24> × 46075253542002907288682029<26> × 36330007266882439693011254938223<32> × 128797510703025209052558458957192581040685402361<48> × 194298639552736505128931692860952322394797555172028068875018638641672051934416576920818350901<93> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1143968802 for P32 / January 13, 2016 2016 年 1 月 13 日) (Erik Branger / GGNFS, Msieve gnfs for P48 x P93 / June 8, 2016 2016 年 6 月 8 日)
2×10276+3 = 2(0)2753<277> = 827 × 33827 × 134359 × 15593986710925741595333<23> × 34122204392634562988343845434084840876595080666735233239672025812885057093447517117204320345797308916048480510961546963273626426027801811831738581794120415061503215657631911406472079605666653144211169576277188276098854192208088339970611163681<242>
2×10277+3 = 2(0)2763<278> = 617 × 631 × 5966870985409<13> × 764039600674937<15> × [11268158721212046463443818410586158096388165045355027175517721894672582810471643128073266623110403535833163324458306228440411150474901660520829861735709040322033558624576883546740119319981772568443167608363400480373532493791252918489784156447733<245>] Free to factor
2×10278+3 = 2(0)2773<279> = 7 × 31 × 173 × 4159 × 241740790091<12> × 3119853082396576061<19> × [1698443710233136100441926079912097909436160392436906442325729291607496396964883103276222775331267521047737685125842487207935657458966742472080433639819547367288287157152985230016834121598801744999880857590819483645796222887776242104260790887<241>] Free to factor
2×10279+3 = 2(0)2783<280> = 211 × 6470423 × 494331448760886596278293198104662103235151<42> × 483303511967803437500990776135623466202761321<45> × [6131640377313042154354051941181114934257591802070345410718684726196980041117114688987482454327273453430135722436063953708065945181084171122050665732091119223549965318041221895736073681<184>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3288307300 for P42, B1=11000000, sigma=3625293243 for P45 / August 29, 2016 2016 年 8 月 29 日) Free to factor
2×10280+3 = 2(0)2793<281> = 74717 × 18126886033<11> × 736662815936700510917258851023088407773<39> × 22120120699139583341586303107047453796608856789<47> × 906214744836686511410787676297543208106926331477911647422899326767705997643893239687386642864034615827838667740524661623052370835545209197211348252564005599294914177029122453975759<180> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2028156038 for P39 / March 2, 2016 2016 年 3 月 2 日) (Bart Jans / yafu 2.11, GMP-ECM B1=660 for P47 x P180 / October 2, 2024 2024 年 10 月 2 日)
2×10281+3 = 2(0)2803<282> = 17 × 15391 × 104230361493104784162139163<27> × 6693462757841054125180734563243<31> × [1095643182609945291321762531864229373769273067614923536446489557922011877832750418971078346572357927606954360077664339072280683884005572741676756395423733383215485363193237276191204017591058410053948476448864321811012261<220>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1813242056 for P31 / January 14, 2016 2016 年 1 月 14 日) Free to factor
2×10282+3 = 2(0)2813<283> = 29 × 509 × 823 × 2243 × 4273 × 3515743559017<13> × 99361006188270193<17> × 742716493585336547<18> × 19715284464414929549<20> × 2931004336288916160540727<25> × 215040092330292541612590659191<30> × 1645638673182413380172847957843510643241500347411854856743652473360771<70> × 3237595169148801752204332251216053596048073404825605710381062388678133913318379<79> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=878004919 for P30 / January 14, 2016 2016 年 1 月 14 日) (Bart Jans / yafu nfs for P70 x P79 / May 31, 2021 2021 年 5 月 31 日)
2×10283+3 = 2(0)2823<284> = 79 × 107 × 22397 × 13158465900196131511<20> × 536793859038812290331063<24> × 548813771523181687183641384743<30> × [27251566874424428237516175765592874010297710656441332454334748684278544413189878783362803196457380718243411825373751471270617760374951843062083247649004619049471781868076548697517882737865082519992688517<203>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=1737279542 for P30 / January 14, 2016 2016 年 1 月 14 日) Free to factor
2×10284+3 = 2(0)2833<285> = 72 × 705281408483365580551<21> × 3183392238558501523921519<25> × 167973158977077483570704809500341<33> × [10822844955062645870813042536806972441353242338773805967852115470296476809963244416817289784329919750031464803241081989430888256180715058530006104400674621815312901249540902288293120324283369030530025232143<206>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=366016169 for P33 / January 14, 2016 2016 年 1 月 14 日) Free to factor
2×10285+3 = 2(0)2843<286> = 19 × 1367 × 190574479 × 516303031 × 95666369093<11> × [8180487271737322573253615368088421089243260974077410891768082125780244389411164196119901116226051590203776730299752526107810405351239360386217252033075108135462429556633847041090985810719757804152234426620014586105064510891606960821379944319000754344323<253>] Free to factor
2×10286+3 = 2(0)2853<287> = 463 × 5623 × 6947 × 424238863 × [2606592684739070092038610858220056983915705599990723878190462852140779623693796573068417784450895194402183265784384853058239537415801836691321368940147166235543948029478113313309143177477644580700970260087149540658961554904911113313269970151300640716491177783905517127<268>] Free to factor
2×10287+3 = 2(0)2863<288> = 23 × 47 × 77536913 × 69562693783409119<17> × 42431777780162904945701913011443881414687786332941<50> × 808403482869616002530000712047999038001364019441621700278830270219764092763016894053977195147546614597521647696459932769127948186636785503655627172949815929390222600900333929358714687203229520183706684467445769<210> (Bart Jans / yafu 2.11, GMP-ECM B1=0 for P50 x P210 / December 6, 2024 2024 年 12 月 6 日)
2×10288+3 = 2(0)2873<289> = 5641 × [354547066123027831944690657684807658216628257401170005318205991845417479170359865272114873249423861017550079773089877681262187555397979081723098741357915263251196596348165218932813330969686225846481120368728948767948945222478283992199964545293387697216805530934231519234178337174259883<285>] Free to factor
2×10289+3 = 2(0)2883<290> = 379 × 1454701 × 78577909 × 189469037 × 13850221109543413166530858932709<32> × [175922596399424302749539913334888676989012463753563841087702532233988303420895011793871470675005310189990611706653109485382860904137683855265447143092853995759223556527012396755394766666061589183276036219445641827518291928582137364681<234>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2062882102 for P32 / January 14, 2016 2016 年 1 月 14 日) Free to factor
2×10290+3 = 2(0)2893<291> = 7 × 6579386882088443<16> × [4342567032987634207413812215948402657674311847098320895773478209704658874819229611395716416855444802580409395037123980955054448844587748747833788551017132247696544613082922508911756020364830248458142256691234949780064579392091321766454809102922254008582378803680506417572703<274>] Free to factor
2×10291+3 = 2(0)2903<292> = 83 × 98389 × 722093 × [339165931492397219906301741816037826694239395392560954336290070432724192597428817009179994231231239494154107600582985341031908380030224715924208161873613601409321306152964769429578405009278347381226474598338074598763911738554925427309967310093507438304411496122257340363742515233<279>] Free to factor
2×10292+3 = 2(0)2913<293> = 10597325507<11> × 32581874195785979<17> × 288135450717520846830991<24> × 201030042256427667962283449759197943227238492145776169862647359243856345256260903791947319333592713941396182280179180709542128116931561847549812936846356673553281884066234023522126408280891626403904809803556863325912135364470499475585326557661<243>
2×10293+3 = 2(0)2923<294> = 31 × 1549 × 54497749 × 79651067 × 712042951 × 188054504162627<15> × 41826189058900272034474403928623<32> × 74250306158492244046220065865056843276810278893<47> × 2307332830565028570153336358912198862740143119190962764188037653192367148789976687302611640720702756739348553039415581579137718753563285460061402545723336243072474148585513<172> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=344711425 for P32 / January 14, 2016 2016 年 1 月 14 日) (Bart Jans / GMP-ECM 7.0.5 for P47 x P172 / June 27, 2023 2023 年 6 月 27 日)
2×10294+3 = 2(0)2933<295> = 116670136177369806574200289113505150628303067823<48> × [17142347352363291715744365816509231076994010470995083833186516792269608788820274630824838405777597324031779259756573174606627101700347739095917352428098058023425991480227332413355966776244348840545582352471731686566179279608413199427822882636903661<248>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2032009307 for P48 / August 18, 2016 2016 年 8 月 18 日) Free to factor
2×10295+3 = 2(0)2943<296> = 331 × 222707 × 308303 × 20054734523<11> × 461032709628780464003850163193421132674179<42> × 411480390045733311291407768861231481523057367<45> × 231309028290253814232574182623891594165548609156287179017667681849489616788074765871657129610092578129150670241105090481630707788905023321079533511791488764006722449073005523547610412827<186> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1613090281 for P42 / August 29, 2016 2016 年 8 月 29 日) (Bart Jans / yafu 2.11, GMP-ECM B1=446 for P45 x P186 / October 19, 2024 2024 年 10 月 19 日)
2×10296+3 = 2(0)2953<297> = 7 × 79 × 21937 × 215156953392959603027632307<27> × 20027447636339103448037951584397<32> × [3826014733708259274282976871529332003934844276995130291212570340872104649296252181902421225203316623411480906543008187376995229369781188327551224468233923092015399395428251344140377065605184620080658215255890597693999212843300474237<232>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2241647940 for P32 / January 15, 2016 2016 年 1 月 15 日) Free to factor
2×10297+3 = 2(0)2963<298> = 17 × 26903 × 7332553831<10> × 46531874731750634631948782479<29> × 330107253547769246166324284587577672992999<42> × 38825717039348811846943481977901240854797022605767726048056303027698579821824036194532742612931791133612032239476691972284361042562167814907211321227302254924709920403779225338473969593126189210659908517129260603<212> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3578819219 for P42 x P212 / August 29, 2016 2016 年 8 月 29 日)
2×10298+3 = 2(0)2973<299> = 151 × 3269609106057023736041428298065971779<37> × [40509530904003363688975624527191943770366738965607013530674913090273237841545581415584877889069769992724479973951264699546908934532711076301121927861785107052458536009134822005730882752747298656712384346114222287113181665645108081404904639886417809744851282407<260>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2108462847 for P37 / February 28, 2016 2016 年 2 月 28 日) Free to factor
2×10299+3 = 2(0)2983<300> = 7039 × 168451 × 31378949142374237<17> × 813133191164443906144211116021<30> × 6610668094544157154202001223628179529060896817208730466881258705085865982299292780702557794729637861021865200950428603614946850786421531984084892019080719413418296152960834604857403322625975699167308020108959592432916216622019890743610325588351<244> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2224330958 for P30 x P244 / January 15, 2016 2016 年 1 月 15 日)
2×10300+3 = 2(0)2993<301> = 653 × 1496730299<10> × 3826594697851785157430647<25> × 2094863464161643755156915520197512937635764446967<49> × [255273113961491801128070532955213498782782165594098505019609037377812504203956270862670042102368903027639097557810187681650510612583554746132320092880962222192882686507940324912244719854219057069798521476086055681901<216>] (Bart Jans / GMP-ECM 7.0.5, x0=2 for P49 / July 7, 2023 2023 年 7 月 7 日) Free to factor
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