Table of contents 目次

  1. About 811...117 811...117 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 811...117 811...117 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 811...117 811...117 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 811...117 811...117 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

81w7 = { 87, 817, 8117, 81117, 811117, 8111117, 81111117, 811111117, 8111111117, 81111111117, … }

1.3. General term 一般項

73×10n+539 (1≤n)

2. Prime numbers of the form 811...117 811...117 の形の素数

2.1. Last updated 最終更新日

October 15, 2015 2015 年 10 月 15 日

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

  1. 73×103+539 = 8117 is prime. は素数です。
  2. 73×109+539 = 8111111117<10> is prime. は素数です。
  3. 73×1017+539 = 8(1)167<18> is prime. は素数です。
  4. 73×10153+539 = 8(1)1527<154> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 7, 2005 2005 年 1 月 7 日)
  5. 73×10194+539 = 8(1)1937<195> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 7, 2005 2005 年 1 月 7 日)
  6. 73×10641+539 = 8(1)6407<642> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 1, 2006 2006 年 6 月 1 日)
  7. 73×10675+539 = 8(1)6747<676> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 1, 2006 2006 年 6 月 1 日)
  8. 73×101461+539 = 8(1)14607<1462> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / August 23, 2006 2006 年 8 月 23 日)
  9. 73×1026429+539 = 8(1)264287<26430> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 15, 2010 2010 年 9 月 15 日)
  10. 73×1048461+539 = 8(1)484607<48462> is PRP. はおそらく素数です。 (Erik Branger / srsieve and PFGW / May 1, 2013 2013 年 5 月 1 日)
  11. 73×1072735+539 = 8(1)727347<72736> is PRP. はおそらく素数です。 (Bob Price / October 15, 2015 2015 年 10 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 / October 15, 2015 2015 年 10 月 15 日

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

  1. 73×103k+1+539 = 3×(73×101+539×3+73×10×103-19×3×k-1Σm=0103m)
  2. 73×106k+539 = 7×(73×100+539×7+73×106-19×7×k-1Σm=0106m)
  3. 73×1013k+7+539 = 79×(73×107+539×79+73×107×1013-19×79×k-1Σm=01013m)
  4. 73×1016k+11+539 = 17×(73×1011+539×17+73×1011×1016-19×17×k-1Σm=01016m)
  5. 73×1018k+2+539 = 19×(73×102+539×19+73×102×1018-19×19×k-1Σm=01018m)
  6. 73×1021k+2+539 = 43×(73×102+539×43+73×102×1021-19×43×k-1Σm=01021m)
  7. 73×1022k+16+539 = 23×(73×1016+539×23+73×1016×1022-19×23×k-1Σm=01022m)
  8. 73×1027k+8+539 = 757×(73×108+539×757+73×108×1027-19×757×k-1Σm=01027m)
  9. 73×1028k+1+539 = 29×(73×101+539×29+73×10×1028-19×29×k-1Σm=01028m)
  10. 73×1033k+32+539 = 67×(73×1032+539×67+73×1032×1033-19×67×k-1Σm=01033m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 12.02%. 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 12.02% です。

3. Factor table of 811...117 811...117 の素因数分解表

3.1. Last updated 最終更新日

September 30, 2017 2017 年 9 月 30 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=190, 192, 195, 199, 202, 203, 204, 206, 209, 216, 218, 220, 223, 225, 228, 229, 230, 233, 234, 235, 237, 241, 242, 243, 244, 246, 248 (27/250)

3.4. Factor table 素因数分解表

73×101+539 = 87 = 3 × 29
73×102+539 = 817 = 19 × 43
73×103+539 = 8117 = definitely prime number 素数
73×104+539 = 81117 = 32 × 9013
73×105+539 = 811117 = 61 × 13297
73×106+539 = 8111117 = 72 × 165533
73×107+539 = 81111117 = 3 × 79 × 342241
73×108+539 = 811111117 = 661 × 757 × 1621
73×109+539 = 8111111117<10> = definitely prime number 素数
73×1010+539 = 81111111117<11> = 3 × 157 × 172210427
73×1011+539 = 811111111117<12> = 17 × 181 × 8329 × 31649
73×1012+539 = 8111111111117<13> = 7 × 1158730158731<13>
73×1013+539 = 81111111111117<14> = 32 × 9012345679013<13>
73×1014+539 = 811111111111117<15> = 479 × 2213 × 16453 × 46507
73×1015+539 = 8111111111111117<16> = 18013 × 109883 × 4097923
73×1016+539 = 81111111111111117<17> = 3 × 23 × 87299 × 13465484707<11>
73×1017+539 = 811111111111111117<18> = definitely prime number 素数
73×1018+539 = 8111111111111111117<19> = 7 × 71 × 91334443 × 178685527
73×1019+539 = 81111111111111111117<20> = 3 × 63127 × 468107 × 914953051
73×1020+539 = 811111111111111111117<21> = 19 × 79 × 6151273 × 87848561929<11>
73×1021+539 = 8111111111111111111117<22> = 9619 × 4650869 × 181307729347<12>
73×1022+539 = 81111111111111111111117<23> = 33 × 11126657 × 269992615602103<15>
73×1023+539 = 811111111111111111111117<24> = 43 × 4733 × 6211 × 641673141458513<15>
73×1024+539 = 8111111111111111111111117<25> = 7 × 6163 × 26203 × 20075261 × 357419239
73×1025+539 = 81111111111111111111111117<26> = 3 × 2823999173<10> × 9574024417406243<16>
73×1026+539 = 811111111111111111111111117<27> = 18149 × 165089 × 270713250268657897<18>
73×1027+539 = 8111111111111111111111111117<28> = 17 × 33623 × 14190410820168811459787<23>
73×1028+539 = 81111111111111111111111111117<29> = 3 × 1289 × 64579 × 324799134193359350269<21>
73×1029+539 = 811111111111111111111111111117<30> = 29 × 65539 × 426758855933166990915707<24>
73×1030+539 = 8111111111111111111111111111117<31> = 7 × 837665513 × 1383285023374429800787<22>
73×1031+539 = 81111111111111111111111111111117<32> = 32 × 8861 × 1017079977317723245571870633<28>
73×1032+539 = 811111111111111111111111111111117<33> = 67 × 12106135986733001658374792703151<32>
73×1033+539 = 8111111111111111111111111111111117<34> = 79 × 153689 × 8072842163<10> × 82753050722431289<17>
73×1034+539 = 81111111111111111111111111111111117<35> = 3 × 7351 × 957889 × 3839701709861228758605001<25>
73×1035+539 = 811111111111111111111111111111111117<36> = 757 × 1071480992220754440041097901071481<34>
73×1036+539 = 8111111111111111111111111111111111117<37> = 7 × 149 × 7776712474699051880259933951209119<34>
73×1037+539 = 81111111111111111111111111111111111117<38> = 3 × 89 × 96179 × 51076741786261<14> × 61839454006188329<17>
73×1038+539 = 811111111111111111111111111111111111117<39> = 19 × 23 × 47 × 107 × 1697 × 43577 × 10328803 × 483201321093828047<18>
73×1039+539 = 8111111111111111111111111111111111111117<40> = 236449 × 582574403 × 58883209032354241539916111<26>
73×1040+539 = 81111111111111111111111111111111111111117<41> = 32 × 107070252433<12> × 84172265164424520667202018261<29>
73×1041+539 = 811111111111111111111111111111111111111117<42> = 47497 × 4057488313<10> × 4208786477808385318657070797<28>
73×1042+539 = 8111111111111111111111111111111111111111117<43> = 7 × 97 × 38731734341<11> × 308420780601113451075635051503<30>
73×1043+539 = 81111111111111111111111111111111111111111117<44> = 3 × 17 × 167 × 9523436786557603746754856300470953517801<40>
73×1044+539 = 811111111111111111111111111111111111111111117<45> = 43 × 291029873621<12> × 64814820763630788678192301172939<32>
73×1045+539 = 8111111111111111111111111111111111111111111117<46> = 33149 × 244686449398507077471752122571151802802833<42>
73×1046+539 = 81111111111111111111111111111111111111111111117<47> = 3 × 59 × 79 × 163 × 127733 × 278605237377484192473082505661427181<36>
73×1047+539 = 811111111111111111111111111111111111111111111117<48> = 20159617 × 498248249834233<15> × 80751814893747285298833397<26>
73×1048+539 = 8111111111111111111111111111111111111111111111117<49> = 72 × 18143 × 9123787676712456832298408348990627870321731<43>
73×1049+539 = 81111111111111111111111111111111111111111111111117<50> = 34 × 2393 × 20923491095111275487<20> × 19999469907229284331856027<26>
73×1050+539 = 811111111111111111111111111111111111111111111111117<51> = 991 × 9067 × 13863548509<11> × 63035696123564719<17> × 103295670932783491<18>
73×1051+539 = 8(1)507<52> = 259781 × 837659 × 37273974814305366333854138757174077560523<41>
73×1052+539 = 8(1)517<53> = 3 × 131 × 787 × 1360171 × 2570351741<10> × 1855709813627563<16> × 40421919587421259<17>
73×1053+539 = 8(1)527<54> = 71 × 2770579631<10> × 4123361057256875029594047534286370819796517<43>
73×1054+539 = 8(1)537<55> = 7 × 69457057 × 492751058925218546939<21> × 33856212099517587002574097<26>
73×1055+539 = 8(1)547<56> = 3 × 63199 × 116295083 × 3678642097483988050564179371292035352397267<43>
73×1056+539 = 8(1)557<57> = 19 × 383 × 419 × 4843083926221<13> × 105187520135657<15> × 522189026697027555766847<24>
73×1057+539 = 8(1)567<58> = 29 × 248498209 × 10536297931217<14> × 106824543911752766831952180623482241<36>
73×1058+539 = 8(1)577<59> = 32 × 643 × 5101 × 1111703 × 241360817 × 47647204153370377<17> × 214920863977039137133<21>
73×1059+539 = 8(1)587<60> = 17 × 79 × 1373 × 5987 × 28813546661<11> × 2549927447497932863293804023914050513729<40>
73×1060+539 = 8(1)597<61> = 7 × 23 × 499 × 29819 × 157742591 × 21464060508532919811239294060479425419820307<44>
73×1061+539 = 8(1)607<62> = 3 × 1069 × 29399039 × 163647173 × 682005071029725559<18> × 7708185281751266170255447<25>
73×1062+539 = 8(1)617<63> = 757 × 2950834712926929655402379<25> × 363111152084134743283781070771635339<36>
73×1063+539 = 8(1)627<64> = 6563 × 1582673 × 434539396153<12> × 1141688232709<13> × 10650295744531<14> × 147791141619848009<18>
73×1064+539 = 8(1)637<65> = 3 × 31699956683850695773051237<26> × 852904542005600025391576396530086999747<39>
73×1065+539 = 8(1)647<66> = 43 × 61 × 67 × 619 × 1199703252932436829<19> × 6215023454642971176352971395070571948687<40>
73×1066+539 = 8(1)657<67> = 7 × 394221991 × 2939283411843350794092890060844319387952992603931521238141<58>
73×1067+539 = 8(1)667<68> = 32 × 229 × 39355221305730767157259151436735133969486225672542994231494959297<65>
73×1068+539 = 8(1)677<69> = 6133 × 473211911 × 517805789 × 770996821039<12> × 791068709296694893<18> × 884948552590667353<18>
73×1069+539 = 8(1)687<70> = 39209143 × 327624614897<12> × 36457050386622013<17> × 17319483993732088350384883792080679<35>
73×1070+539 = 8(1)697<71> = 3 × 481619 × 46521274183<11> × 1206712699015021582248220679168485644471897385630654307<55>
73×1071+539 = 8(1)707<72> = 109 × 895957 × 305022703537<12> × 27229177297041201604118780548130232685544958542456557<53>
73×1072+539 = 8(1)717<73> = 7 × 79 × 413464996673<12> × 5237319212449<13> × 6773410955658354258348873393171122044393057957<46>
73×1073+539 = 8(1)727<74> = 3 × 367 × 2120093 × 57814926268503143<17> × 601032758750357110206992760781476244333473908483<48>
73×1074+539 = 8(1)737<75> = 192 × 283 × 467 × 5791 × 10818506224857381816507827<26> × 271361960642571669488758836900059307961<39>
73×1075+539 = 8(1)747<76> = 17 × 457 × 1481 × 2758462981<10> × 13421870537499240703757720819<29> × 19040570872818537676250754959827<32>
73×1076+539 = 8(1)757<77> = 33 × 98473 × 18384062672325071804611577936347<32> × 1659426134824735910015498559718802987341<40> (Makoto Kamada / msieve 0.83)
73×1077+539 = 8(1)767<78> = 239906027293440064447350689<27> × 3380953451907249967879943684302628440621174347041453<52>
73×1078+539 = 8(1)777<79> = 7 × 313 × 937 × 75805465751<11> × 115901055490201<15> × 449687142963999117889089884101472411122308388501<48>
73×1079+539 = 8(1)787<80> = 3 × 371069 × 1310087 × 194229202620311<15> × 286345101280826956838603139331538334075110676511468283<54>
73×1080+539 = 8(1)797<81> = 1049 × 3299 × 13250819 × 17688044622312686266160721586673575602422669302832802314739906095693<68>
73×1081+539 = 8(1)807<82> = 89 × 13334197 × 32473044621604819<17> × 244124018199946043706982639<27> × 862164145252398756702261844789<30>
73×1082+539 = 8(1)817<83> = 3 × 23 × 19823197880599540701727129951602161<35> × 59300389196379243211302448630881749268520360313<47> (Makoto Kamada / GGNFS-0.70.1 / 0.17 hours)
73×1083+539 = 8(1)827<84> = 113 × 50958639115113071<17> × 6591248122916390143502653<25> × 21370585710913087897514626888666294589743<41>
73×1084+539 = 8(1)837<85> = 7 × 47 × 143574753821<12> × 171714263882411496792496174226710104534329806735852471523702529067054313<72>
73×1085+539 = 8(1)847<86> = 32 × 29 × 79 × 293 × 607 × 1301 × 98808433221534084690661<23> × 719745279518215376810093<24> × 239059664670097957364815441<27>
73×1086+539 = 8(1)857<87> = 43 × 55639 × 377484546738627213158583133<27> × 898118002704853070994459990176868059679727093511932837<54>
73×1087+539 = 8(1)867<88> = 674790229 × 362938165717<12> × 33119130418020162699052618936321986703662278505881763037760873567669<68>
73×1088+539 = 8(1)877<89> = 3 × 71 × 157 × 247296619 × 9808055530491858624836883864672702926936166298095699031491777399326779748423<76>
73×1089+539 = 8(1)887<90> = 757 × 734030845788124691<18> × 23517685298856895871<20> × 62069119724059523814886634629490013955648844319421<50>
73×1090+539 = 8(1)897<91> = 74 × 431 × 57667 × 184846912730318249093495753<27> × 735311503341241138770426099924679602914725179511148057<54>
73×1091+539 = 8(1)907<92> = 3 × 17 × 107 × 53825353813633733<17> × 276146474857622643261695231996669724376975275640782643602281717226479257<72>
73×1092+539 = 8(1)917<93> = 19 × 5821 × 69163 × 640019 × 8677604867<10> × 1087712520145506680879387033053<31> × 17552883177220524482226257802659392189<38> (Makoto Kamada / msieve 0.81 / 2.4 minutes)
73×1093+539 = 8(1)927<94> = 26237 × 311194159 × 993424207450052422265394391015786236638857438447919692336793977350186269010497599<81>
73×1094+539 = 8(1)937<95> = 32 × 1627 × 46978571 × 24559128299<11> × 290830902819030502363119679248825419<36> × 16508096035503964309212568615774559269<38> (Makoto Kamada / msieve 0.83)
73×1095+539 = 8(1)947<96> = 19387 × 4511123 × 22382567665543<14> × 414357463226583956611147396188856225156020267497201145781630028392970219<72>
73×1096+539 = 8(1)957<97> = 7 × 5623 × 206069741904705447298369226165776050179393590384164810627552935929247506697266611902927037197<93>
73×1097+539 = 8(1)967<98> = 3 × 199 × 5381 × 414180121839053<15> × 692228753942359<15> × 193074797436874732331<21> × 456119409027522325978714656511670623981613<42>
73×1098+539 = 8(1)977<99> = 67 × 79 × 4894459 × 7416247 × 4221721460584878947600614334808959993408166392695055981531005328979438877759269253<82>
73×1099+539 = 8(1)987<100> = 449272333 × 51223937288068349621801208863557468330570063<44> × 352450165453982208101356410195982733128975901423<48> (Makoto Kamada / GGNFS-0.71.4 / 0.57 hours)
73×10100+539 = 8(1)997<101> = 3 × 1811 × 13399 × 115764387895421315406884185827946408195287133<45> × 9624834682658174276920764764174786414413908641647<49> (Makoto Kamada / GGNFS-0.71.4 / 0.56 hours)
73×10101+539 = 8(1)1007<102> = 2858447 × 622316203 × 38522561947455443997902763106112987<35> × 11836517257669882662882071389433418987260311357562251<53> (juno1369 / Msieve v1.43 for P35 x P53 / 0.82 hours / December 28, 2009 2009 年 12 月 28 日)
73×10102+539 = 8(1)1017<103> = 7 × 27367 × 194069 × 598067731625433489234865144990900388471467<42> × 364794750005354827030833798025213605939117294859291<51> (juno1369 / Msieve 1.43 for P42 x P51 / 2.61 hours / December 29, 2009 2009 年 12 月 29 日)
73×10103+539 = 8(1)1027<104> = 33 × 389 × 4441 × 6163 × 17471 × 21391 × 754996942466671173686066285616320998975955388623352341861435886152450255833686024353<84>
73×10104+539 = 8(1)1037<105> = 23 × 59 × 52067 × 22430044781<11> × 511808868767460994136916715309669197558835299375765464600643174880486025272138111086103<87>
73×10105+539 = 8(1)1047<106> = 179 × 359 × 21269 × 19330551521<11> × 71937765014437013<17> × 12423821342435636608474230894375569<35> × 343502115760281757618883387533358849<36> (Makoto Kamada / Msieve 1.44 for P35 x P36 / December 26, 2009 2009 年 12 月 26 日)
73×10106+539 = 8(1)1057<107> = 3 × 2297 × 587201 × 28081202431<11> × 325737999979459<15> × 2299463498480296050373<22> × 953017045679287177788463523373962268288151893178711<51>
73×10107+539 = 8(1)1067<108> = 17 × 43 × 562103 × 811724867 × 18300429221<11> × 132885300861268548101525690361415314379827576753799458229809435513937231864289167<81>
73×10108+539 = 8(1)1077<109> = 7 × 10287310004221<14> × 68324641514054998106753<23> × 91502955867934170045472465270787<32> × 18016399278343733149949156388392256834701<41> (Makoto Kamada / Msieve 1.44 for P32 x P41 / December 26, 2009 2009 年 12 月 26 日)
73×10109+539 = 8(1)1087<110> = 3 × 3891446453<10> × 6947811659130913149182432560388885566155068210837600605945440986140439907278106657539310881284028563<100>
73×10110+539 = 8(1)1097<111> = 19 × 827 × 223423 × 12460578526577563698511278863556250895773871<44> × 18541939288512124877673221403825333737766481760055168374173<59> (juno1369 / Msieve 1.43 snfs / 1.61 hours / December 30, 2009 2009 年 12 月 30 日)
73×10111+539 = 8(1)1107<112> = 79 × 769 × 15217 × 1350977 × 9211482283715729<16> × 705050788234569272539352873743461920761291988615855757027233967580651907259976547<81>
73×10112+539 = 8(1)1117<113> = 32 × 659 × 2052875074741870417695478817<28> × 118322201993232308204168823427867<33> × 56301979147689985638131287295813264828707053223813<50> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2545526799 for P33 / December 25, 2009 2009 年 12 月 25 日)
73×10113+539 = 8(1)1127<114> = 29 × 7937 × 27551 × 5013428217715612657<19> × 6942089510134059210994937<25> × 130055231524355047359402761497<30> × 28257632258466700855152699800623<32> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=490118306 for P30 / December 25, 2009 2009 年 12 月 25 日)
73×10114+539 = 8(1)1137<115> = 7 × 112672914076753<15> × 4367574102413326936556721115646557<34> × 2354629071840639615590099160972319066050594197607217430722515473111<67> (juno1369 / Msieve 1.43 snfs / 2.04 hours / December 30, 2009 2009 年 12 月 30 日)
73×10115+539 = 8(1)1147<116> = 3 × 696827 × 1256429 × 17446015073<11> × 340852541580186998234413939<27> × 5193180217282978509530012403309619225396650183603760655542062719339<67> (juno1369 / GMP-ECM 6.2.3 B1=250000, sigma=2866700313 for P27 / December 29, 2009 2009 年 12 月 29 日)
73×10116+539 = 8(1)1157<117> = 757 × 1528789 × 105338475634607<15> × 112104638388651784000199383548597161<36> × 59350763544652311415152679228980494654029220277455271927427<59> (juno1369 / Msieve 1.43 for P36 x P59 / 4.29 hours / December 29, 2009 2009 年 12 月 29 日)
73×10117+539 = 8(1)1167<118> = 247225487 × 57711841507680491<17> × 55057257348622991229962119895720041<35> × 10325417092886776856446656385902665296693188953177972498561<59> (juno1369 / Msieve 1.43 for P35 x P59 / 2.66 hours / December 28, 2009 2009 年 12 月 28 日)
73×10118+539 = 8(1)1177<119> = 3 × 1038178937631371<16> × 26042752416768014626855985688394241133568554202226822293759255894635783661236952711417030960893935745709<104>
73×10119+539 = 8(1)1187<120> = 76500007 × 6613321108897125481<19> × 51806319745671817972603<23> × 103474186258853362396467881478649499<36> × 299078025018669606363187180763945483<36> (Makoto Kamada / Msieve 1.44 for P36 x P36 / December 26, 2009 2009 年 12 月 26 日)
73×10120+539 = 8(1)1197<121> = 7 × 269 × 1289 × 3849790554791<13> × 4928798917649505399689975306668513<34> × 176116039402804889481273305561348806375555227861413919486835737280777<69> (juno1369 / Msieve 1.43 snfs / 2.27 hours / December 30, 2009 2009 年 12 月 30 日)
73×10121+539 = 8(1)1207<122> = 32 × 1877 × 194706513771573413<18> × 24660000884464391139179625923543356937999202943516326560347436589761158611292327056702242992106748413<101>
73×10122+539 = 8(1)1217<123> = 2687 × 598556539472972048127695960257<30> × 504321524439073152777443986824990395821411863393094533961909982910365554159390023571810163<90> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3779937203 for P30 / December 25, 2009 2009 年 12 月 25 日)
73×10123+539 = 8(1)1227<124> = 17 × 71 × 307 × 3748614659<10> × 1526008893358585225920732351717574027017596455084078703<55> × 3826545143889515680557900251242310375250503214483528029<55> (juno1369 / GGNFS + Msieve snfs / 3.39 hours / January 3, 2010 2010 年 1 月 3 日)
73×10124+539 = 8(1)1237<125> = 3 × 79 × 5717 × 22689642679855193929950368309374331716894969383124955851<56> × 2638372768669009683409049140907966882808615447780456466294015223<64> (Erik Branger / GGNFS, Msieve snfs / 3.08 hours / January 18, 2010 2010 年 1 月 18 日)
73×10125+539 = 8(1)1247<126> = 61 × 89 × 7109 × 12659 × 6788143 × 244569115150043293921406096542019616838278899203040495509466377753968522179224469157133631132034531889784681<108>
73×10126+539 = 8(1)1257<127> = 7 × 23 × 113179708608149<15> × 791441482756084185191<21> × 562428207119963407789017305716496068269561968579766636456588544698881335963671728683695583<90>
73×10127+539 = 8(1)1267<128> = 3 × 163 × 185936207 × 535280533 × 1066147427<10> × 48688251203161<14> × 108882123268925579479827719<27> × 294868278807496764886296914960586419893677204426896613475291<60>
73×10128+539 = 8(1)1277<129> = 19 × 43 × 6203 × 4659197 × 39226182707257723<17> × 7425902027878376094326259710821<31> × 117928880912626379267008270559953435624686342191265121954275887053717<69> (juno1369 / Msieve 1.43 snfs / 5.52 hours / December 29, 2009 2009 年 12 月 29 日)
73×10129+539 = 8(1)1287<130> = 3018783563<10> × 107316288629929<15> × 12687877515185948221<20> × 13430061128768322366284708997667<32> × 146931787596280269457343840160423556435481599219451165353<57> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=712045089 for P32 / December 25, 2009 2009 年 12 月 25 日)
73×10130+539 = 8(1)1297<131> = 36 × 47 × 169097 × 7875971647<10> × 2704495892893<13> × 12098578459878403788252736605458503<35> × 54324313419155534317429552139816910647691666236365831565862532919<65> (juno1369 / Msieve 1.43 snfs / 4.84 hours / December 31, 2009 2009 年 12 月 31 日)
73×10131+539 = 8(1)1307<132> = 67 × 45121 × 73859 × 158930413670669<15> × 5220906549801139<16> × 4377946751102471097053030853445155851039972424935844716856175584878252568028823327425451299<91>
73×10132+539 = 8(1)1317<133> = 72 × 564269 × 478157752014427<15> × 144037713956554289472387353971510618069<39> × 4259421885991397832179548105297689347884949786481183807202527744210463639<73> (juno1369 / ggnfs + msieve snfs / 5.99 hours / January 17, 2010 2010 年 1 月 17 日)
73×10133+539 = 8(1)1327<134> = 3 × 25951 × 1161929 × 325650293341<12> × 121629518631371350446248499949<30> × 22637837881032126712358380960656100977789151792603131418488320176883199796461623249<83> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3810152174 for P30 / December 25, 2009 2009 年 12 月 25 日)
73×10134+539 = 8(1)1337<135> = 193 × 11207069886113763490122332244943588751260774535448653785897<59> × 374999735596041595200728140830981771273259795543228584103186291650760119877<75> (Dmitry Domanov / GGNFS/msieve snfs / 7.15 hours / December 28, 2009 2009 年 12 月 28 日)
73×10135+539 = 8(1)1347<136> = 13211588753733908805466621755851252552475926032614891662130817<62> × 613939115295177382999456500545990952152261251933687481845615901208005485901<75> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 3.96 hours / December 28, 2009 2009 年 12 月 28 日)
73×10136+539 = 8(1)1357<137> = 3 × 92639 × 6168096013<10> × 3352711271557<13> × 1016814619635084444969726624056432822055534417281<49> × 13879575252546127967101570987951708454334345831164746868271281<62> (juno1369 / GGNFS + Msieve snfs / 7.25 hours / January 4, 2010 2010 年 1 月 4 日)
73×10137+539 = 8(1)1367<138> = 79 × 70612088903<11> × 13030877406858185094614153<26> × 11158364424218821373118074954319795136240556201378703672527184264004371588753753809072655299277848797<101>
73×10138+539 = 8(1)1377<139> = 7 × 97 × 60816289767547294249914611663<29> × 1881006318752934742776078262372181233<37> × 104424018135397027538521421180052004430196899844849794609078881837909237<72> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2708498472 for P37 / December 25, 2009 2009 年 12 月 25 日)
73×10139+539 = 8(1)1387<140> = 32 × 17 × 143906933053623178779377272709<30> × 4897133031784022852847743355915750444918480439<46> × 752255376458486865885684529070279241924326272598795765285726839<63> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2206053082 for P30 / December 25, 2009 2009 年 12 月 25 日) (juno1369 / GGNFS + Msieve snfs / 16.82 hours / January 3, 2010 2010 年 1 月 3 日)
73×10140+539 = 8(1)1397<141> = 3631 × 191195831 × 39136809523967<14> × 893380385284771<15> × 33415953031266296622177432426562727241805056886659386156211786353774503911170001803974236657141650521<101>
73×10141+539 = 8(1)1407<142> = 29 × 747829 × 181709887 × 100133242747<12> × 14886732204042677624540518223596561<35> × 1380777924913989606529128904503409218613441212005716736609459206887797769628888153<82> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=4115183934 for P35 / December 25, 2009 2009 年 12 月 25 日)
73×10142+539 = 8(1)1417<143> = 3 × 3803 × 7585504322398796604207592379<28> × 25892790994585220860757993393055600042426463811514203273<56> × 36196738864588306864977801297128252842044488227320821039<56> (juno1369 / GGNFS + Msieve snfs / 15.08 hours / January 16, 2010 2010 年 1 月 16 日)
73×10143+539 = 8(1)1427<144> = 757 × 3634877307129738186019022041540048291079066655062659111654408962991<67> × 294777760481506813103960828075281842473043461985574147443471434987112162391<75> (Dmitry Domanov / GGNFS/msieve snfs / 13.30 hours / December 29, 2009 2009 年 12 月 29 日)
73×10144+539 = 8(1)1437<145> = 7 × 107 × 411233 × 31477848859092359<17> × 555698873242014709<18> × 1505448880374143714855423543016367303545134345088533993116932250064021438992270154924302172903393074171<103>
73×10145+539 = 8(1)1447<146> = 3 × 941447609 × 30326569657<11> × 70034825700269<14> × 4244442795445363325855330606221<31> × 3185700280396892094798185622811767648069997040852289903844037471942822609128846247<82> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3891058682 for P31 / December 25, 2009 2009 年 12 月 25 日)
73×10146+539 = 8(1)1457<147> = 19 × 82883 × 34275341 × 210265526492861449<18> × 1489304615474189828274945366705643096212760968899<49> × 47987474339909728739490792928098002913092390501317080666389331546731<68> (Sinkiti Sibata / Msieve 1.40 snfs / 14.93 hours / January 19, 2010 2010 年 1 月 19 日)
73×10147+539 = 8(1)1467<148> = 112786151573<12> × 120749490302990783799959605193<30> × 1708120723570426969324310756809683355264139184123883<52> × 348674915690754508376606199270902128728059796219884200691<57> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=4162488653 for P30 / December 25, 2009 2009 年 12 月 25 日) (juno1369 / GGNFS + Msieve snfs / 23.04 hours / January 3, 2010 2010 年 1 月 3 日)
73×10148+539 = 8(1)1477<149> = 32 × 23 × 463 × 7877 × 2578057 × 909150727 × 6229032591539294759<19> × 13950024020880353946851104237<29> × 527526407039542433662271113975710732364989081006596008769512669528711478939413<78>
73×10149+539 = 8(1)1487<150> = 43 × 97363793 × 138244759 × 77733748223<11> × 1675550863969141<16> × 12503509555421827534907857508627<32> × 860531117258789094707169113672374160889437471268403046267541475151041200017<75> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1927834895 for P32 / December 26, 2009 2009 年 12 月 26 日)
73×10150+539 = 8(1)1497<151> = 7 × 79 × 67619 × 67427671717901952324044891039484660300650380692362737<53> × 3216979636700310025255182693910930838935247585191381929974026726672301117544807085238420263<91> (Dmitry Domanov / Msieve 1.40 snfs / 13.31 hours / December 28, 2009 2009 年 12 月 28 日)
73×10151+539 = 8(1)1507<152> = 3 × 134089 × 4839473063<10> × 17400971249<11> × 92286772420981<14> × 71948727693984473<17> × 348204921824170517<18> × 68918451209054645998111188626911451<35> × 15026622878899816860633741788073042417282563<44> (Makoto Kamada / Msieve 1.45 for P35 x P44 / March 4, 2010 2010 年 3 月 4 日)
73×10152+539 = 8(1)1517<153> = 1745815306009<13> × 7808022406911149174023<22> × 59503293284718032581799524757551327206110095896958584775594038180374930758796002796257332998908484691447086661568280131<119>
73×10153+539 = 8(1)1527<154> = definitely prime number 素数
73×10154+539 = 8(1)1537<155> = 3 × 653 × 42953 × 46764253 × 147452204335915857445739994541<30> × 139793552602618827382684497984354942835141436191042134136901854402332666593859108492679381780561090325880762827<111> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=4235551558 for P30 / March 2, 2010 2010 年 3 月 2 日)
73×10155+539 = 8(1)1547<156> = 17 × 79133 × 84317 × 599475221085078562682979979960330682641<39> × 1963100900913995135380675711855313984593<40> × 6076378157884416294070105555159258175345832674287597905950115175157<67> (Sinkiti Sibata / Msieve 1.40 snfs / March 6, 2010 2010 年 3 月 6 日)
73×10156+539 = 8(1)1557<157> = 7 × 15359 × 366994841 × 17925392154432989916583354024124347<35> × 11468080835595191865753345461774481116757139225339632148244788517722813432367358565633210419965512640595595367<110> (Sinkiti Sibata / Msieve 1.40 snfs / March 6, 2010 2010 年 3 月 6 日)
73×10157+539 = 8(1)1567<158> = 33 × 599 × 142894468259<12> × 16899191053779533<17> × 476543795873340865965033756079<30> × 2128831592037983135056857040111380449<37> × 2047219007678516092686167010521258675322425085682056550956217<61> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3074832238 for P30 / March 2, 2010 2010 年 3 月 2 日) (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3904903848 for P37 / March 2, 2010 2010 年 3 月 2 日)
73×10158+539 = 8(1)1577<159> = 71 × 1733 × 1987 × 50595934686041701823<20> × 65570719455670083652460294057920833198657316502788071689560136965403363336472565255592432588316279799424644440316750423586809839419<131>
73×10159+539 = 8(1)1587<160> = 8647 × 50221 × 104545621 × 523085323 × 1053205451<10> × 22544473813<11> × 6300715150786103<16> × 585128479347218585312440631<27> × 3901726921467421199706071228704484482678323358962569819131460590205449303<73>
73×10160+539 = 8(1)1597<161> = 3 × 32869 × 241921 × 999085593072864970429<21> × 133870803008801051710203496272893256194485349<45> × 25422044268995812704280508880344011903761008028544019465038976765785915326665903414291<86> (Sinkiti Sibata / Msieve 1.40 snfs / March 6, 2010 2010 年 3 月 6 日)
73×10161+539 = 8(1)1607<162> = 35955397 × 5495324536585396537540470189723989230042652116021927775564610982538531067163<76> × 4105092209055912051049652225481315374083335206466886484084451456080384528524747<79> (Dmitry Domanov / GGNFS/msieve snfs / March 8, 2010 2010 年 3 月 8 日)
73×10162+539 = 8(1)1617<163> = 7 × 59 × 158532804024781<15> × 20171445202441436899<20> × 19724245126089930807126500399<29> × 8453231183029379626437805957673<31> × 10523979029973651627654036858577<32> × 3500024073000809321885473328634524209<37> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=709269249 for P32 / March 2, 2010 2010 年 3 月 2 日) (Makoto Kamada / Msieve 1.45 for P31 x P37 / March 4, 2010 2010 年 3 月 4 日)
73×10163+539 = 8(1)1627<164> = 3 × 79 × 263 × 5521 × 357806838561663169804823655737984164235083986346552131832328005837<66> × 658733685326270270484301744475264396604114303780445027395322336414077093975250273310591491<90> (Dmitry Domanov / Msieve 1.40 snfs / March 8, 2010 2010 年 3 月 8 日)
73×10164+539 = 8(1)1637<165> = 19 × 67 × 512841622409617<15> × 718547535376713458738905550706787795543<39> × 1729072396006237860557913643701335115599863200015537489835627694654573181238730643846313730947428568316642659<109> (Sinkiti Sibata / Msieve 1.42 snfs / March 9, 2010 2010 年 3 月 9 日)
73×10165+539 = 8(1)1647<166> = 643 × 570373 × 121835805205544841623<21> × 547532214014996573359319054326547<33> × 3405811740779148900299187078031531<34> × 97343098654394199754060388300746336798758548389117913633003331677537573<71> (Serge Batalov / GMP-ECM B1=1500000, sigma=111487072 for P33 / March 5, 2010 2010 年 3 月 5 日) (Dmitry Domanov / GGNFS/msieve gnfs for P34 x P71 / March 6, 2010 2010 年 3 月 6 日)
73×10166+539 = 8(1)1657<167> = 32 × 157 × 233 × 71483 × 390491 × 16071389 × 36566443 × 566594514050827<15> × 8904270270944303<16> × 2976882136382019989318241884124215389682247593711453160848684422610776085653174052660401259648867841731243<106>
73×10167+539 = 8(1)1667<168> = 601 × 5501 × 342606471029609<15> × 287541311182833198054262597<27> × 449611522698403509433939597<27> × 527971565265417804380539307<27> × 285008410472230968419794930708877<33> × 36809742636755645402316898095587263<35> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2997575399 for P35 / March 2, 2010 2010 年 3 月 2 日)
73×10168+539 = 8(1)1677<169> = 7 × 764689943 × 2490976949684878788871<22> × 608313176039119351872044364904560633373367605878064202025954268214178042425140094515293979165684426857045333457046622095394725461789920427<138>
73×10169+539 = 8(1)1687<170> = 3 × 29 × 89 × 152617748567123996009431<24> × 68638225770744472591068404003753283371730597308040039476959954511214679524234081737756563711340236889087903924909659768333026064530639339258949<143>
73×10170+539 = 8(1)1697<171> = 23 × 43 × 677 × 757 × 1537223465136084283<19> × 120458465687581815235459023537135685106836164050595707917<57> × 8642217231443543059147166231865813117975343520576880809388786675261480079979243336242807<88> (Sinkiti Sibata / Msieve 1.40 snfs / March 11, 2010 2010 年 3 月 11 日)
73×10171+539 = 8(1)1707<172> = 17 × 16967823133<11> × 591655305379632746067589<24> × 5571068713079973625696269254936039922861914786570880202334935121<64> × 8530962295089731548916109784275056155975218913754234288794561580702467613<73> (Sinkiti Sibata / Msieve 1.40 snfs / May 13, 2010 2010 年 5 月 13 日)
73×10172+539 = 8(1)1717<173> = 3 × 1051 × 2113 × 38795147 × 687085243089370133761847<24> × 1072816296263454757659833<25> × 85431718385141657008914216359<29> × 42783801362035939239527237854189<32> × 116478290206682019948391965379545255745069015769099<51> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3631444413 for P32 / March 2, 2010 2010 年 3 月 2 日)
73×10173+539 = 8(1)1727<174> = 8978756348927<13> × 7610748961124802299<19> × 83177516352118148899<20> × 144799672943759271000267751614947<33> × 985514997632108992919519737077144541324461229294538693179063444828108618457614902061583393<90> (ruffenach timothee / gnffs, Msieve 1.44 snfs / April 27, 2010 2010 年 4 月 27 日)
73×10174+539 = 8(1)1737<175> = 72 × 43189 × 683957 × 3703644523<10> × 5861405182309<13> × 78881783462459<14> × 2055425809028913317<19> × 1592108850490345181785047443841575768900349050612805641746438084874766893604460228407524941787061879405572101<109>
73×10175+539 = 8(1)1747<176> = 32 × 1109 × 2600903 × 247743464702099687570146106065596843731463850498465456380793<60> × 12611882982818981569742424964730493200266281544513081170633245679063144653193990710410608293901061790172383<107> (Dmitry Domanov / Msieve 1.40 snfs / September 3, 2011 2011 年 9 月 3 日)
73×10176+539 = 8(1)1757<177> = 47 × 79 × 9714041 × 969583183 × 42282013815989719077199268721606475001945021389114500343104955857766750453<74> × 548548120368690771192885045530208149972351534770192936285082270027303943241854907951<84> (Robert Backstrom / Msieve 1.44 snfs / January 9, 2012 2012 年 1 月 9 日)
73×10177+539 = 8(1)1767<178> = 198751277 × 4724455316116802587<19> × 8104592443527747617<19> × 20997729987883811018815983791981363<35> × 50759244572754726540806879900106127244683624322649018524311800623632740586427301002784060156307873<98> (Serge Batalov / GMP-ECM B1=1500000, sigma=4147580366 for P35 / March 5, 2010 2010 年 3 月 5 日)
73×10178+539 = 8(1)1777<179> = 3 × 8441998255773834206637333967747<31> × 3202682139687162496856102754829359567790862037836391289169401054302109882766285664177734018130504781963590663964228323183235867727449383076665523237<148> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=909508406 for P31 / March 2, 2010 2010 年 3 月 2 日)
73×10179+539 = 8(1)1787<180> = 109 × 44464533498611281799369361039634787<35> × 11532529044360848104803913966313272799929151<44> × 14511608571463864332673932879794986415097267111934471435731219281716004568593596420298964160461732949<101> (Ignacio Santos / GMP-ECM B1=11000000, sigma=986939827 for P35 / March 4, 2010 2010 年 3 月 4 日) (Cyp / yafu v1.34.3 / January 19, 2014 2014 年 1 月 19 日)
73×10180+539 = 8(1)1797<181> = 7 × 181465621 × 123392009422763049513733941728076833937574531371463<51> × 51748875219644766022469898858926294959395334362696033184695725860485070241264469701426760651026078875478212346300483749097<122> (Robert Backstrom / Msieve 1.44 snfs / January 20, 2012 2012 年 1 月 20 日)
73×10181+539 = 8(1)1807<182> = 3 × 51803627 × 1593439381<10> × 273454175347<12> × 1197784870205536449646311436390689953645614799631085246283984588282763749603343329206428245120032230281795564891336602003063072924014726470243920216781251<154>
73×10182+539 = 8(1)1817<183> = 19 × 131 × 5407 × 6163 × 13999 × 1619256275384084594010421824099271284732933352849<49> × 431414079403494455736048920298306075778328325276439433025766529736654017160280980505568771254136391144882473769767732183<120> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / May 21, 2014 2014 年 5 月 21 日)
73×10183+539 = 8(1)1827<184> = 223 × 2693 × 328373 × 969170226247<12> × 1272545614097<13> × 33350186838071566255351683027621038285482351894672451092876103002399658701479243429203824214099279626865504878030371125439565620194367109946816504029<149>
73×10184+539 = 8(1)1837<185> = 33 × 149 × 3605150622869329<16> × 3373739474164497861951441485191<31> × 36906046711134916938186520671149<32> × 5280092307901763914162506423117264061013<40> × 8506606021274625825119162993392827032738697230383740017188602253<64> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=680531150 for P31 / March 2, 2010 2010 年 3 月 2 日) (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=138045694 for P32 / March 2, 2010 2010 年 3 月 2 日) (Dmitry Domanov / GGNFS/msieve gnfs for P40 x P64 / March 5, 2010 2010 年 3 月 5 日)
73×10185+539 = 8(1)1847<186> = 61 × 13296903460837887067395264116575591985428051001821493624772313296903460837887067395264116575591985428051001821493624772313296903460837887067395264116575591985428051001821493624772313297<185>
73×10186+539 = 8(1)1857<187> = 7 × 18466681 × 9818598073<10> × 66428351117462764179693913306081596727707912691712273987<56> × 96203419395965020706361576945441776716907486750923301010723512985963219892908614669963016663905741353374764841001<113> (Jiahao He / Msieve 1.53 snfs for P56 x P113 / July 15, 2017 2017 年 7 月 15 日)
73×10187+539 = 8(1)1867<188> = 3 × 17 × 95764337 × 200016889 × 83030891353108341907702480217309610853626300441626119925482793690465241761516419333959357604603431238721050727975437450413569038495600581626519524218554727566811454084519<170>
73×10188+539 = 8(1)1877<189> = 590921079213210541595808183938281669180770197234272207297<57> × 6095516126264280663828889925657141920706667998040538329748207<61> × 225185480048839791859793660477385346756785698320881454715964387995369923<72> (Dmitry Domanov / ggnfs/msieve for P57 x P61 x P72 / March 21, 2010 2010 年 3 月 21 日)
73×10189+539 = 8(1)1887<190> = 79 × 2777 × 163841 × 134519268787<12> × 1677529984968567264060640793588015052587451303909143998128454349660637858166411784471317523461534858018787601919550789601684797452268096194179140431022639988423185498297<169>
73×10190+539 = 8(1)1897<191> = 3 × 16804606791201059968811<23> × [1608906258442994734091702664367276123368203533862954344817876997721870572294299594821085774716192203110231266362929358078968777157332971232789427819051100013281357302349<169>] Free to factor
73×10191+539 = 8(1)1907<192> = 43 × 181 × 356497409626148009035811717922059857860225205614413<51> × 292332393015134467877912781565918378554950706681993558926970638135740187194457678578338987000300901921376540830389783592574851533316113623<138> (Robert Backstrom / Msieve 1.42 snfs / March 6, 2010 2010 年 3 月 6 日)
73×10192+539 = 8(1)1917<193> = 7 × 23 × 536100638526559551706103<24> × 3189889236329270001157252844333<31> × [29459986737875243799532313446430631894691224036718778634483848781514769077873692953443912556230744269249558723621177890358913688979967303<137>] (Serge Batalov / GMP-ECM B1=1500000, sigma=3682180613 for P31 / March 5, 2010 2010 年 3 月 5 日) Free to factor
73×10193+539 = 8(1)1927<194> = 32 × 71 × 24551 × 2952483749<10> × 89101482249607<14> × 1277792110012573<16> × 75695634409939456797914055920563<32> × 203192103463353828169867503501187033687655229886278526966431937099837521585241357554423002086963578191103390813699329<117> (Serge Batalov / GMP-ECM B1=1500000, sigma=180958772 for P32 / March 5, 2010 2010 年 3 月 5 日)
73×10194+539 = 8(1)1937<195> = definitely prime number 素数
73×10195+539 = 8(1)1947<196> = 113 × 84987054153562333<17> × 15085296440155541141333743873729726661<38> × [55988042352310604286149298179472205717375871806921287891832047902566094941448494010759744584849546295188863217405657817454097415901185404493<140>] (Ignacio Santos / GMP-ECM 6.3 B1=11000000, sigma=2168359295 for P38 / March 27, 2011 2011 年 3 月 27 日) Free to factor
73×10196+539 = 8(1)1957<197> = 3 × 199 × 857 × 158535014846912726039984268114417109098802278821394235102214907894413942741930404865852231032859965152700709129293122772773066247439279460529233313809637669309423647039380314859226336097271873<192>
73×10197+539 = 8(1)1967<198> = 29 × 67 × 107 × 757 × 37493 × 3004063137828015611286376480353160840677825583135053512856018306551219800861<76> × 45758169724153589691801149204769613764215945874623302839610683881263453455861694437491262637472860175453761997<110> (matsui / Msieve 1.48 snfs / October 31, 2010 2010 年 10 月 31 日)
73×10198+539 = 8(1)1977<199> = 7 × 1474314204582441121560966966847379159525853599903543632140282943438409<70> × 785945190739267904237801708182742885793680395063859588291133674392161518247841561952994481695367396508860527985091188551011281459<129> (Dmitry Domanov / GGNFS/msieve snfs / April 12, 2010 2010 年 4 月 12 日)
73×10199+539 = 8(1)1987<200> = 3 × 3289749075570222916020761<25> × 313915317877422142901615311141<30> × [26180854328760268978306717491342558362472315748180889032259296703748275507371427520691861348524108962920712975088930234444805432943652341196313339<146>] (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=3187340288 for P30 / March 27, 2011 2011 年 3 月 27 日) Free to factor
73×10200+539 = 8(1)1997<201> = 19 × 7103 × 8537 × 18523 × 11899001 × 50493345926575916113<20> × 63259197156806738384263340934055438243951299091730463875719627627427182669561259061163836130276950221903841279570026996263054618389704383548050909152020882323987<161>
73×10201+539 = 8(1)2007<202> = 759500265682331<15> × 10679536897625877747675503867878093342650754443814287781333248534134763344113387378158293846000151577137345284970254968208697160096846798552558159025718772994678803719546994878729753370807<188>
73×10202+539 = 8(1)2017<203> = 32 × 79 × 21859 × 11722572242001263569361<23> × [445202446325811581494381150323947491715073241353753039447511630144369865776439651924509518870025124461266864956861437285246222597358797306937271344503901289477919222611360553<174>] Free to factor
73×10203+539 = 8(1)2027<204> = 17 × 257 × 11197 × 6003761 × 55473731 × 199002247 × 1557623498069<13> × 8295217706123<13> × [19361437440069207224947850332294263769928603408502337879387006955500892115929554601926961029755993538769697395717157782387441319098307913834887069931<149>] Free to factor
73×10204+539 = 8(1)2037<205> = 7 × [1158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158731<205>] Free to factor
73×10205+539 = 8(1)2047<206> = 3 × 494580161 × 1923389933<10> × 60307024929887867<17> × 89823629760572467<17> × 1415221214605434911857418727313<31> × 659935465386671727934991067426602703744685912979<48> × 5617858058735225786897560629199444005880991058213997892484563420835455093401<76> (Serge Batalov / GMP-ECM B1=1000000, sigma=2166453898 for P31 / November 26, 2013 2013 年 11 月 26 日) (Cyp / yafu 1.34.3 / December 26, 2013 2013 年 12 月 26 日)
73×10206+539 = 8(1)2057<207> = 10267 × 518989 × 6579171294111686771<19> × 185286319063773302036807<24> × [124871718402507395482832473446331940002733160009148358794665355433519400146737499626289138965185012196444394514715400263559001031605670597474198212078189847<156>] Free to factor
73×10207+539 = 8(1)2067<208> = 16889 × 280593794861<12> × 620979470139286279480681<24> × 71725458188308801288548157493<29> × 38427999699216481916809424730409453673360647063369735334212520172401015168467075667187265443065788513051061248909711125780203860753228612381<140> (Serge Batalov / GMP-ECM B1=1000000, sigma=692324754 for P29 / November 26, 2013 2013 年 11 月 26 日)
73×10208+539 = 8(1)2077<209> = 3 × 163 × 165871392865257895932742558509429675073846852987957282435810043172006362190411270165871392865257895932742558509429675073846852987957282435810043172006362190411270165871392865257895932742558509429675073846853<207>
73×10209+539 = 8(1)2087<210> = 167 × 24097576339939<14> × 109025317194708386119<21> × [1848686015112433825780774631023526889927792345637165003126648068092298884881080410869087634399221507430379076809756527123792715345365500664761402698802062009426796224227615711<175>] Free to factor
73×10210+539 = 8(1)2097<211> = 7 × 1449377353<10> × 1005758001611273<16> × 1556181979051114579<19> × 109681237501149011671<21> × 11974018852629202702369<23> × 117445207671949563471470936111513<33> × 3311611498256857213533591872889671316053997564857790798811619621449894405266910841887245317063<94> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3708750571 for P33 / November 12, 2013 2013 年 11 月 12 日)
73×10211+539 = 8(1)2107<212> = 34 × 821 × 194636747 × 394254657059<12> × 1329462933636268209954451344258851<34> × 11955679705044327098034826325834513246498549746523934449848028567007895311173452252308626742245969161758417219661800158360590853444775289612852705843869379<155> (Serge Batalov / GMP-ECM B1=1000000, sigma=4294177164 for P34 / November 26, 2013 2013 年 11 月 26 日)
73×10212+539 = 8(1)2117<213> = 43 × 1289 × 15699119 × 2071701953<10> × 2870749593715492707457<22> × 1092999979177826564319457<25> × 68788976635248666924942380777<29> × 55580300159713595359926717916943<32> × 37506040542679068636543437867711342352857095572191165345622338340392809196623555713527<86> (Serge Batalov / GMP-ECM B1=1000000, sigma=513610029 for P32 / November 26, 2013 2013 年 11 月 26 日)
73×10213+539 = 8(1)2127<214> = 89 × 3926729 × 108001600952189192737<21> × 214896439986943064828700736417240395977784584419810689898539542027831288053250534594783223110197588447560232595464751158564922076541398929266107711782126148951575845152760453194360538061<186>
73×10214+539 = 8(1)2137<215> = 3 × 23 × 560503936999<12> × 2097261538839985304496842819332609163773750003565703014323034421229227793578666015165264486329855832559991434774968508851833864975551473045808396999645806557855894983417063896606502570782662968254322607<202>
73×10215+539 = 8(1)2147<216> = 79 × 283 × 17179826605897432515822417114567584846293541<44> × 271688299871335820761125869206746910783450287679<48> × 30333206535446982742898736801859690160489162484121628879<56> × 256246999828833861975799183354475392163555775826022192551210283701<66> (Bob Backstrom / Msieve 1.53 snfs for P44 x P48 x P56 x P66 / September 30, 2017 2017 年 9 月 30 日)
73×10216+539 = 8(1)2157<217> = 72 × 12277 × 10780073471<11> × [1250749373561425280243701863206592132364246567367167640350084788352972785093032166475026380723795364810406388420748622947586146252254726100456595089804476664606848555019899806537037106110863975674706999<202>] Free to factor
73×10217+539 = 8(1)2167<218> = 3 × 1319 × 31735163 × 59243312411<11> × 1491895940218960933817<22> × 15035166314309288233941073377849956934887<41> × 486057295057115480685707430468933902793241554282996650028521562438033496665977931364316194355064152480154149824978898879494091576132623<135> (Cyp / GMP-ECM 6.4.4 B1=11000000, sigma=131268474 for P41 / February 18, 2014 2014 年 2 月 18 日)
73×10218+539 = 8(1)2177<219> = 19 × 67896029962421<14> × 45660021908791728276519101901367436749<38> × [13770390412343215691378353508082139071873946588562817416520165008924308503362048542458409698166411630448141983847808305566560772420875504240307846292077294242299860367<167>] (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=3995993346 for P38 / January 5, 2014 2014 年 1 月 5 日) Free to factor
73×10219+539 = 8(1)2187<220> = 17 × 190107159492038714000103521136172229<36> × 2509764410143200840228901583450541818890737210268841576611299280840581117528177871734475521975711776831046477772436400402475002105989726074488330783935097381664822944019663197574980569<184> (Serge Batalov / GMP-ECM B1=11000000, sigma=3456847792 for P36 / December 4, 2013 2013 年 12 月 4 日)
73×10220+539 = 8(1)2197<221> = 32 × 59 × 103872288784320380245387<24> × [1470571443701867783922098747593047797381563031962455713145445931252409095609534891924011564905678274143219404123796591275260107181701020086028893412357214019925142465160041630002284557238246806461<196>] Free to factor
73×10221+539 = 8(1)2207<222> = 433 × 1873235822427508339748524506030279702335129586861688478316653836284321272773928663074159609956376700025660764690787785476007185014113420579933282011803951757762381318963305106492173466769309725429817808570695406723120349<220>
73×10222+539 = 8(1)2217<223> = 7 × 47 × 259371859 × 636847273 × 149254111845605480384113374915978041620700595596598576944458757491740542685957751157369346941680174965878735205417341121077124695932892273334696355577396820372750435988873752213158077549923694291308778639<204>
73×10223+539 = 8(1)2227<224> = 3 × 704473764232253923<18> × [38379054564938135940714886172111172189892602024290544435687198707435276377949917279912979202518262296329830587660387848208803653316766904349167447242757979601651940206249322641310177645593663895510244911493<206>] Free to factor
73×10224+539 = 8(1)2237<225> = 757 × 11926657 × 134550357415725799<18> × 667699246175083183767995139673049647557859290676116758273178788083655404454087152407414957266103413468271194205805985248376856446764643879711851362426173626800021700567946411679701228974965267611167<198>
73×10225+539 = 8(1)2247<226> = 29 × 10104461 × 4129974971<10> × 39967000165009973849842501<26> × [167695044379200735853602962691264044482431356871180405949818173395894178823174966510864130036994335766302896393314575134152324041623928935761540832331941626655720103038062214980505283<183>] Free to factor
73×10226+539 = 8(1)2257<227> = 3 × 39048829 × 692390469302857635936714953399422990047589827521768630681269265130512288525656865076211044306528040496093673821487375128125789304387003180992624312422711498904026982141693340843512542643392380269253068690921231902678491<219>
73×10227+539 = 8(1)2267<228> = 457 × 1774860199367858011184050571359105275954291271577923656698273766107464138098711402868952103087770483831752978361293459761731096523219061512278142475079017748601993678580111840505713591052759542912715779236566982737661074641381<226>
73×10228+539 = 8(1)2277<229> = 7 × 71 × 79 × 661 × 1535629 × 176580781523<12> × 1471327278671<13> × 2340703046034400950179<22> × [334664821975404899785044155608048301823469305337054341478163948338478337234960447174185621442671370176018021112807207882201957181300064554493034396720109816614647572533173<171>] Free to factor
73×10229+539 = 8(1)2287<230> = 32 × 683 × 2383 × 312887 × 2802405546442373<16> × 55893272775691199<17> × [112983507264490961402940585108673308750963523567196627476799625553718971977558270499216909181689765779254837056982996908207219574631932409697976510023148305581770486324290059439121046533<186>] Free to factor
73×10230+539 = 8(1)2297<231> = 67 × 26029 × 257417507 × 8556195859<10> × 3581702043137<13> × 6766583493101<13> × [8713053236211221687190640838695822447719042718663011847697928496295786554038968853292238585852527144481251535348385645376154204362991744124512400157827318568024611268285364465290799<181>] Free to factor
73×10231+539 = 8(1)2307<232> = 293 × 49752944312647<14> × 1569057773015986833152550673<28> × 34694768379048015270796714523<29> × 10220944176707624052255490624209965239702319769498995796572461738730689349111511922170795107224219508768254281984561264977363937627079393409363933263140754420013<161>
73×10232+539 = 8(1)2317<233> = 3 × 134811412689561077472383328964046458363459<42> × 200554511651746900258791056282109508092434618400854164596292236339782524178950689521089409602940798670918966411125881717162579817071732502813347439074658655309532372454508319803722946207931621<192> (Serge Batalov / GMP-ECM B1=43000000, sigma=1786201044 for P42 / January 5, 2014 2014 年 1 月 5 日)
73×10233+539 = 8(1)2327<234> = 43 × 2393 × 2657 × 30180503976031517564477117304859813<35> × [98299465055265860284788260717705608349713582123717720091240589279545865986168804815762219872089869592267599269423950381232866468230983569374707451983781012433964100076527483005466941827403763<191>] (Serge Batalov / GMP-ECM B1=1000000, sigma=1780832869 for P35 / November 27, 2013 2013 年 11 月 27 日) Free to factor
73×10234+539 = 8(1)2337<235> = 7 × 97 × 709 × 10248028827184200292796729<26> × 164984839812834662846023538501<30> × 1753789586603174961020402857498453<34> × [5682016314209769436381598391365456971401263299630964888980859389121333496979314090637816590322280866331110964222929775801779479626262328510031<142>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1983363793 for P34 / November 12, 2013 2013 年 11 月 12 日) (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=2661142266 for P30 / January 6, 2014 2014 年 1 月 6 日) Reserved
73×10235+539 = 8(1)2347<236> = 3 × 17 × 1103 × 12133897 × [118832260352430961324528420289537301247883400794248992011170556535539416011959258805301092943275743546407210663802558645584217760142669834435816669217754156475999031503527343193449091470773210382526003578942696986172008835337<225>] Free to factor
73×10236+539 = 8(1)2357<237> = 19 × 23 × 118437804563131661485562028820339<33> × 3128490784959817161138064850490421<34> × 5009261284221455410349983325098826656180759745071698279723479569295963128988567940204541072546629279914359144336724545175824375482837379579593866883171888249887094760439<169> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2535522395 for P33 / November 12, 2013 2013 年 11 月 12 日) (Serge Batalov / GMP-ECM B1=1000000, sigma=284097015 for P34 / November 27, 2013 2013 年 11 月 27 日)
73×10237+539 = 8(1)2367<238> = 9041 × 13064511815816004022794743<26> × 124780637824559584313789142692961927559<39> × [550330387975277253431926458094017881356970203229460455224628900457276867429082334659448616325931466496737397107783256155038161700329366982054442361035084116178903494731901<171>] (Cyp / GMP-ECM 6.4.4 B1=11000000, sigma=4117902074 for P39 / February 18, 2014 2014 年 2 月 18 日) Free to factor
73×10238+539 = 8(1)2377<239> = 33 × 5927 × 11579 × 11595246893<11> × 329212208658102373<18> × 9861700342168229500942498811279<31> × 682949847681053621409921844120057<33> × 448871472738723599042315206511856076020672490716693942577573467211<66> × 3793080438711834670501799315831292635191139885423229090761641736587996351<73> (Serge Batalov / GMP-ECM B1=1000000, sigma=3716065520 for P31 / November 27, 2013 2013 年 11 月 27 日) (Serge Batalov / GMP-ECM B1=2000000, sigma=3333039120 for P33 / January 6, 2014 2014 年 1 月 6 日) (Erik Branger / GGNFS, Msieve gnfs for P66 x P73 / April 9, 2014 2014 年 4 月 9 日)
73×10239+539 = 8(1)2387<240> = 50723 × 1434011 × 340799539 × 9468994380533<13> × 37906207157209997<17> × 1734263841663547232463403313<28> × 3839051087805098221509192639931<31> × 1255340243760528069642922851172944509<37> × 10907098479106037115706562663300257791856035602551475377240091907049293331513109401048482632838913<98> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3257373556 for P34 / November 12, 2013 2013 年 11 月 12 日) (Serge Batalov / GMP-ECM B1=1000000, sigma=2722275247 for P37 / November 26, 2013 2013 年 11 月 26 日)
73×10240+539 = 8(1)2397<241> = 7 × 92347 × 973061993 × 4407158009<10> × 2925906124861213170161228193734844368674355989847333290699892892753575835264896778458490055039827603843210788535774713784618411800562582417456947505822945980564892646796159767646427474881269183385809520980318877781329<217>
73×10241+539 = 8(1)2407<242> = 3 × 79 × 376099 × 301528538979738771161<21> × [3017876078476896502622488392500202520050902948858950014153067969806608127010952143297406259592606592482993480706484888561182835018527885841004807405094870960051823616200780634077859429852516401653388595112230819619<214>] Free to factor
73×10242+539 = 8(1)2417<243> = 158130139 × 4296768643478771181497<22> × 1330442159247589557131659<25> × [897279466813143773714053257774805889747750741113589846310296519109151026586282454703375956375049324578782144388632833138443908483033553683975721531791104117330797906127207774018955571066861<189>] Free to factor
73×10243+539 = 8(1)2427<244> = 569 × 130843 × [108947580801282981038869000060283830565838677439767609855274585863642762983897713217590497901234549660391511369837438105815988553865675599477310101482537337757482664242287492180604529918328729544366009200700805164260991403912002871834351<237>] Free to factor
73×10244+539 = 8(1)2437<245> = 3 × 157 × 983 × 21187 × 19350091 × 32790569249<11> × 52542105821<11> × 37602844969804315954523<23> × [6595934165365278191445210650727455234985779506047881959420894082338759403582669406679712256962664494254934699610200750846044894437598864100725077245316222213543774310191450688182182771<184>] Free to factor
73×10245+539 = 8(1)2447<246> = 61 × 541 × 156495874420663<15> × 6865902997412666423<19> × 11948142285144276569<20> × 1692977612441978083714634201<28> × 1130839821128840077360835583866757176026059087541213634089960598804571607928008264504170018012948152175333149075382891490085275883306219722101038362941897996020357<163>
73×10246+539 = 8(1)2457<247> = 7 × 3315650936963<13> × [349472903137236737286500408836540698037201786587686023434521310587899204617172410541053920764020749449123177675547851647736343323554268171484011099047446905845229417238390139557851349867170661729949009169226321213918403683600337659737<234>] Free to factor
73×10247+539 = 8(1)2467<248> = 32 × 9623 × 45704537 × 158440603 × 27680123557<11> × 230818001449073<15> × 1672198430189820342505157953257508871<37> × 12105313550634032441145196062735029239117064758827912188711469993312228514147848910074871807347815157271851267187118788525088236605496843565728419219438206421689486491<167> (Serge Batalov / GMP-ECM B1=3000000, sigma=513639557 for P37 / January 9, 2014 2014 年 1 月 9 日)
73×10248+539 = 8(1)2477<249> = 5011 × 785219 × 1542259 × 59341727 × 2978735550844691448336335814791<31> × 135474610912118508388985350695313<33> × [5581588209727704990750082501205880378678954358633425833482963486010859458855644645453220848448274599062052742237617871300740542260998917235588954380117818548072927<163>] (Serge Batalov / GMP-ECM B1=1000000, sigma=1618039536 for P31, B1=1000000, sigma=2545671248 for P33 / November 27, 2013 2013 年 11 月 27 日) Free to factor
73×10249+539 = 8(1)2487<250> = 1701607 × 6312599 × 755114630708203955588711479311797443282277462709192542535822765371168716567573427359457218091520590176786034185018799809306159198486562427707371729783666680423268163065006723455975841459680059024209207792182069715813222262673928486563469<237>
73×10250+539 = 8(1)2497<251> = 3 × 107 × 4111 × 9772393 × 155391487 × 41840268366555479<17> × 4249966065100125217<19> × 636072418028105995243548002676133<33> × 357860041051541196008096862194663314496870170966165716318453174179223886453364451184889962141843212267420894350124224508822838378435515235078312557490554252460183<162> (Serge Batalov / GMP-ECM B1=1000000, sigma=528429691 for P33 / November 26, 2013 2013 年 11 月 26 日)
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