Factorization of 22...2252

Table of contents 目次

About 22...2252 22...2252 について
Prime numbers of the form 22...2252 22...2252 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
Factor table of 22...2252 22...2252 の素因数分解表

1. About 22...2252 22...2252 について

1.1. Classification 分類

Near-repdigit of the form AA...AABA AA...AABA の形のニアレプディジット (Near-repdigit)

1.2. Sequence 数列

2w52 = { 52, 252, 2252, 22252, 222252, 2222252, 22222252, 222222252, 2222222252, 22222222252, … }

2. Prime numbers of the form 22...2252 22...2252 の形の素数

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

No prime number of the form 22...2252 exists. 22...2252 の形の素数は存在しません。

3. Factor table of 22...2252 22...2252 の素因数分解表

3.2. Range of factorization 分解範囲

n≤100 / Completed 終了 / December 21, 2021 2021 年 12 月 21 日
n≤150 / Completed 終了 / December 29, 2021 2021 年 12 月 29 日
n≤200 / Completed 終了 / February 11, 2022 2022 年 2 月 11 日
n≤300 / Remaining 53 残り 53

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

n=211, 213, 216, 224, 225, 226, 227, 230, 235, 236, 239, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 264, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 283, 284, 285, 286, 287, 288, 289, 290, 292, 293, 294, 297, 299, 300 (53/300)

3.4. Factor table 素因数分解表

2×10²+1349 = 52 = 2² × 13

2×10³+1349 = 252 = 2² × 3² × 7

2×10⁴+1349 = 2252 = 2² × 563

2×10⁵+1349 = 22252 = 2² × 5563

2×10⁶+1349 = 222252 = 2² × 3 × 18521

2×10⁷+1349 = 2222252 = 2² × 211 × 2633

2×10⁸+1349 = 22222252 = 2² × 13 × 427351

2×10⁹+1349 = 222222252 = 2² × 3 × 7² × 19 × 19891

2×10¹⁰+1349 = 2222222252_<10> = 2² × 17 × 197 × 165887

2×10¹¹+1349 = 22222222252_<11> = 2² × 5555555563_<10>

2×10¹²+1349 = 222222222252_<12> = 2² × 3³ × 7243 × 284083

2×10¹³+1349 = 2222222222252_<13> = 2² × 43 × 59 × 218981299

2×10¹⁴+1349 = 22222222222252_<14> = 2² × 13 × 427350427351_<12>

2×10¹⁵+1349 = 222222222222252_<15> = 2² × 3 × 7 × 1315463 × 2011081

2×10¹⁶+1349 = 2222222222222252_<16> = 2² × 23 × 103 × 14951 × 15685277

2×10¹⁷+1349 = 22222222222222252_<17> = 2² × 71 × 78247261345853_<14>

2×10¹⁸+1349 = 222222222222222252_<18> = 2² × 3 × 85463461 × 216683461

2×10¹⁹+1349 = 2222222222222222252_<19> = 2² × 571 × 3299 × 337283 × 874409

2×10²⁰+1349 = 22222222222222222252_<20> = 2² × 13 × 1153 × 68711 × 5394218897_<10>

2×10²¹+1349 = 222222222222222222252_<21> = 2² × 3² × 7 × 881834215167548501_<18>

2×10²²+1349 = 2222222222222222222252_<22> = 2² × 1697 × 327375106396909579_<18>

2×10²³+1349 = 22222222222222222222252_<23> = 2² × 29 × 15581 × 24934003 × 493108129

2×10²⁴+1349 = 222222222222222222222252_<24> = 2² × 3 × 200597 × 46401283 × 1989536071_<10>

2×10²⁵+1349 = 2222222222222222222222252_<25> = 2² × 337681 × 861083 × 1910626752481_<13>

2×10²⁶+1349 = 22222222222222222222222252_<26> = 2² × 13 × 17 × 2329699 × 10790346921373997_<17>

2×10²⁷+1349 = 222222222222222222222222252_<27> = 2² × 3 × 7 × 19 × 1613 × 11657 × 7405142757763057_<16>

2×10²⁸+1349 = 2222222222222222222222222252_<28> = 2² × 121266323 × 4581284744285975881_<19>

2×10²⁹+1349 = 22222222222222222222222222252_<29> = 2² × 958367 × 5796897801735197012789_<22>

2×10³⁰+1349 = 222222222222222222222222222252_<30> = 2² × 3² × 89 × 69357747260368983215425163_<26>

2×10³¹+1349 = 2222222222222222222222222222252_<31> = 2² × 413795050880801_<15> × 1342586273985163_<16>

2×10³²+1349 = 22222222222222222222222222222252_<32> = 2² × 13 × 179 × 373 × 757943 × 8444729315965915471_<19>

2×10³³+1349 = 222222222222222222222222222222252_<33> = 2² × 3 × 7 × 8527 × 310250105019660549155095889_<27>

2×10³⁴+1349 = 2222222222222222222222222222222252_<34> = 2² × 43 × 92893 × 196127807 × 709147993261652491_<18>

2×10³⁵+1349 = 22222222222222222222222222222222252_<35> = 2² × 5555555555555555555555555555555563_<34>

2×10³⁶+1349 = 222222222222222222222222222222222252_<36> = 2² × 3 × 18518518518518518518518518518518521_<35>

2×10³⁷+1349 = 2222222222222222222222222222222222252_<37> = 2² × 211 × 2632964718272775144813059505002633_<34>

2×10³⁸+1349 = 22222222222222222222222222222222222252_<38> = 2² × 13 × 23 × 47 × 229 × 1726326615540468151466378080099_<31>

2×10³⁹+1349 = 222222222222222222222222222222222222252_<39> = 2² × 3⁵ × 7 × 11731 × 25667386949_<11> × 108469212872816280977_<21>

2×10⁴⁰+1349 = 2222222222222222222222222222222222222252_<40> = 2² × 4732073 × 5940571911341_<13> × 19762769336175852191_<20>

2×10⁴¹+1349 = 22222222222222222222222222222222222222252_<41> = 2² × 5413 × 12436012754939_<14> × 82529328027978090638909_<23>

2×10⁴²+1349 = 222222222222222222222222222222222222222252_<42> = 2² × 3 × 17 × 19249501 × 93099953 × 1448334169_<10> × 419681286490709_<15>

2×10⁴³+1349 = 2222222222222222222222222222222222222222252_<43> = 2² × 891487 × 427039410558727_<15> × 1459299801503944042787_<22>

2×10⁴⁴+1349 = 22222222222222222222222222222222222222222252_<44> = 2² × 13 × 151 × 3273369204303882367_<19> × 864593971479078970303_<21>

2×10⁴⁵+1349 = 222222222222222222222222222222222222222222252_<45> = 2² × 3 × 7 × 19 × 201859291 × 689772468002201098285027570726207_<33>

2×10⁴⁶+1349 = 2222222222222222222222222222222222222222222252_<46> = 2² × 61 × 471617 × 260029156381_<12> × 74265337923068442153262579_<26>

2×10⁴⁷+1349 = 22222222222222222222222222222222222222222222252_<47> = 2² × 4191427 × 1325456832614657384121339953088901597369_<40>

2×10⁴⁸+1349 = 222222222222222222222222222222222222222222222252_<48> = 2² × 3² × 6029 × 1023857937663433323299525544231686764997983_<43>

2×10⁴⁹+1349 = 2222222222222222222222222222222222222222222222252_<49> = 2² × 555555555555555555555555555555555555555555555563_<48>

2×10⁵⁰+1349 = 22222222222222222222222222222222222222222222222252_<50> = 2² × 13 × 103 × 2292001 × 1092436488873045583_<19> × 1657051161067064849599_<22>

2×10⁵¹+1349 = 222222222222222222222222222222222222222222222222252_<51> = 2² × 3 × 7² × 29 × 10825361 × 801631705531_<12> × 1501740483617714980120351511_<28>

2×10⁵²+1349 = (2)₅₀52_<52> = 2² × 71 × 15213805351604459_<17> × 514317486897522860324808022126967_<33>

2×10⁵³+1349 = (2)₅₁52_<53> = 2² × 330540341 × 1413125297862161666423_<22> × 11893847146426454889241_<23>

2×10⁵⁴+1349 = (2)₅₂52_<54> = 2² × 3 × 5449 × 5783 × 45827 × 14861028366491_<14> × 862910888534705735893596359_<27>

2×10⁵⁵+1349 = (2)₅₃52_<55> = 2² × 43 × 719 × 18515821 × 33859160837_<11> × 230292930510821_<15> × 124460166788157667_<18>

2×10⁵⁶+1349 = (2)₅₄52_<56> = 2² × 13 × 28570387176000616487159_<23> × 14957810152093618555499021977889_<32>

2×10⁵⁷+1349 = (2)₅₅52_<57> = 2² × 3² × 7 × 367 × 182803 × 2116721325613_<13> × 6209746583562902737114866770385277_<34>

2×10⁵⁸+1349 = (2)₅₆52_<58> = 2² × 17 × 601 × 1237 × 25516532907937_<14> × 453473581702847_<15> × 3798925239491093446073_<22>

2×10⁵⁹+1349 = (2)₅₇52_<59> = 2² × 1885717202289331_<16> × 2946123389451453245618839688851399176842473_<43>

2×10⁶⁰+1349 = (2)₅₈52_<60> = 2² × 3 × 23 × 2351 × 499439 × 33001027 × 1383749045066147_<16> × 15016147757758857358965047_<26>

2×10⁶¹+1349 = (2)₅₉52_<61> = 2² × 131 × 2693 × 20921 × 75272684761950276028252289289121344265709901596941_<50>

2×10⁶²+1349 = (2)₆₀52_<62> = 2² × 13 × 73116132008544837427_<20> × 5844817219002836986787552304415462910413_<40>

2×10⁶³+1349 = (2)₆₁52_<63> = 2² × 3 × 7 × 19 × 479 × 27917 × 28973011699468864051_<20> × 359382311302855545127586165206909_<33>

2×10⁶⁴+1349 = (2)₆₂52_<64> = 2² × 743 × 2707 × 4889 × 56497650550778163999411889243327769683014182722924967_<53>

2×10⁶⁵+1349 = (2)₆₃52_<65> = 2² × 32839 × 1281586627_<10> × 85455710567_<11> × 361950193868076661_<18> × 4267757172534709660133_<22>

2×10⁶⁶+1349 = (2)₆₄52_<66> = 2² × 3³ × 787 × 17249059 × 1427651591_<10> × 106169887468706081678374972802792767705353823_<45>

2×10⁶⁷+1349 = (2)₆₅52_<67> = 2² × 199 × 211 × 983 × 2371298939477112264769783_<25> × 5676127448414292575814307113286303_<34>

2×10⁶⁸+1349 = (2)₆₆52_<68> = 2² × 13 × 3187 × 68399 × 1686130801_<10> × 1162682310365148334662606679855370566541342207027_<49>

2×10⁶⁹+1349 = (2)₆₇52_<69> = 2² × 3 × 7 × 1478179 × 84015408155593_<14> × 21302090748365574939726719690721456594648463949_<47>

2×10⁷⁰+1349 = (2)₆₈52_<70> = 2² × 10729 × 6647653807_<10> × 12654973411_<11> × 615514967552177193599182831561223359660194911_<45>

2×10⁷¹+1349 = (2)₆₉52_<71> = 2² × 59 × 9569957779_<10> × 11357534971_<11> × 543716563661_<12> × 143407745895593_<15> × 11110566568526858118701_<23>

2×10⁷²+1349 = (2)₇₀52_<72> = 2² × 3 × 131635967 × 53459116963562642203021_<23> × 2631539487786342827985284038674877272803_<40>

2×10⁷³+1349 = (2)₇₁52_<73> = 2² × 47744201 × 11636084465117670637226823746732206400428725481353338713439890963_<65>

2×10⁷⁴+1349 = (2)₇₂52_<74> = 2² × 13² × 17 × 89 × 982505870796992453_<18> × 22113969595819294519804415378892471340410636663743_<50>

2×10⁷⁵+1349 = (2)₇₃52_<75> = 2² × 3² × 7 × 1289 × 5487043 × 120987103 × 202540847 × 1436957537_<10> × 3540788859979464828992218882008431839_<37>

2×10⁷⁶+1349 = (2)₇₄52_<76> = 2² × 43 × 43049 × 300120714553807832586422911023271780375502634669716853512819926430809_<69>

2×10⁷⁷+1349 = (2)₇₅52_<77> = 2² × 2377 × 3797 × 9349369045777_<13> × 9791698446251611_<16> × 6723840194244287110474785990387260527541_<40>

2×10⁷⁸+1349 = (2)₇₆52_<78> = 2² × 3 × 3319 × 10557571 × 2262387346987_<13> × 233597404919878634489389627079768362078624931726433167_<54>

2×10⁷⁹+1349 = (2)₇₇52_<79> = 2² × 29 × 286453 × 420303679433290091_<18> × 16048455572019132163397_<23> × 9914702465979516516962751292237_<31>

2×10⁸⁰+1349 = (2)₇₈52_<80> = 2² × 13 × 42557 × 88800658279_<11> × 82610648897563_<14> × 1368865943054677136364212541357689331383894060159_<49>

2×10⁸¹+1349 = (2)₇₉52_<81> = 2² × 3 × 7 × 19 × 2772713 × 656711437871_<12> × 76467184549141399934668400619408583802219975046520436133619_<59>

2×10⁸²+1349 = (2)₈₀52_<82> = 2² × 23 × 263 × 811² × 50363 × 81799 × 1672337 × 3409699 × 1786381598479_<13> × 1251459714420029333_<19> × 2658959145345807391_<19>

2×10⁸³+1349 = (2)₈₁52_<83> = 2² × 4437900461431716184333_<22> × 40759605039343455937739_<23> × 30712839536793782226839183106568918949_<38>

2×10⁸⁴+1349 = (2)₈₂52_<84> = 2² × 3² × 47 × 103 × 751 × 1697891623720280830867069344756558013861526091953918773088842916096128389077_<76>

2×10⁸⁵+1349 = (2)₈₃52_<85> = 2² × 149814619705320180720632801_<27> × 3708286658860882856591492331597362440886197891912237209163_<58>

2×10⁸⁶+1349 = (2)₈₄52_<86> = 2² × 13 × 109 × 608431 × 353022726143_<12> × 758843151827_<12> × 24054239319454216377852365015542060799420948900791729_<53>

2×10⁸⁷+1349 = (2)₈₅52_<87> = 2² × 3 × 7 × 71 × 10181 × 14251 × 256811267258208015325224437599654036112496231502535286361213035536764276703_<75>

2×10⁸⁸+1349 = (2)₈₆52_<88> = 2² × 167 × 232153 × 2138429 × 113701774106387_<15> × 58935184441039971347922311936674912917147512454675632058931_<59>

2×10⁸⁹+1349 = (2)₈₇52_<89> = 2² × 97 × 4868660914334321126863443176414021_<34> × 11763762073745833544644696709764233155937267066478799_<53> (Eric Jeancolas / ECM for P34 x P53 / December 21, 2021 2021 年 12 月 21 日)

2×10⁹⁰+1349 = (2)₈₈52_<90> = 2² × 3 × 17 × 130555781 × 527750711627137_<15> × 15810018717641395078623012854956491616431896002761866320602827029_<65>

2×10⁹¹+1349 = (2)₈₉52_<91> = 2² × 463 × 3095008120336058403691900896211418353_<37> × 387690100001772897776539251764111392804140805836917_<51> (Eric Jeancolas / ECM for P37 x P51 / December 21, 2021 2021 年 12 月 21 日)

2×10⁹²+1349 = (2)₉₀52_<92> = 2² × 13 × 193 × 505907 × 6897431258579_<13> × 634554260105709540726571851889045927008635003593923206909197609826719_<69>

2×10⁹³+1349 = (2)₉₁52_<93> = 2² × 3³ × 7⁴ × 59107 × 4517683633693_<13> × 3209348201544608970615858964586060354593115359802647834651668783641719_<70>

2×10⁹⁴+1349 = (2)₉₂52_<94> = 2² × 36493 × 15223619750515319528554943566041584839710507646824200683844999193148153222688064986587991_<89>

2×10⁹⁵+1349 = (2)₉₃52_<95> = 2² × 113 × 538386637 × 1965533827951_<13> × 2993547953842345639403149_<25> × 15519868503177110897990636243760866043011116877_<47>

2×10⁹⁶+1349 = (2)₉₄52_<96> = 2² × 3 × 39029704199_<11> × 265454513671_<12> × 2020781870309_<13> × 3705271396633_<13> × 238715932181910260438849058575410106673864285917_<48>

2×10⁹⁷+1349 = (2)₉₅52_<97> = 2² × 43 × 211 × 96289 × 635916227546766346759177134387982921741712334294219668528150027271273777505350248430779_<87>

2×10⁹⁸+1349 = (2)₉₆52_<98> = 2² × 13 × 4880516705090504747500374847281936875319752221_<46> × 87562537569985128259915839619956991528906745638531_<50> (Eric Jeancolas / ECM for P46 x P50 / December 21, 2021 2021 年 12 月 21 日)

2×10⁹⁹+1349 = (2)₉₇52_<99> = 2² × 3 × 7 × 19 × 43997 × 296441 × 731500309009759_<15> × 53188851777664005902960290172879_<32> × 274383591322871496649263001150008941921_<39> (Eric Jeancolas / ECM for P32 x P39 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁰⁰+1349 = (2)₉₈52_<100> = 2² × 445385992115321728858837_<24> × 1247357495275038045416142238534739780731311873622687391386417761361865131199_<76>

2×10¹⁰¹+1349 = (2)₉₉52_<101> = 2² × 1477499 × 9435823 × 300110176188629_<15> × 563780323851181_<15> × 2877824957848271_<16> × 818399777021209629629318416024830985089761_<42>

2×10¹⁰²+1349 = (2)₁₀₀52_<102> = 2² × 3² × 63949 × 96527537665527834777288769271964213766796032872646007070835189075244953105956926709922586845343_<95>

2×10¹⁰³+1349 = (2)₁₀₁52_<103> = 2² × 17851 × 38180981 × 815113079890866915079943349575197303273085055099195973437288805317450472995324564426684973_<90>

2×10¹⁰⁴+1349 = (2)₁₀₂52_<104> = 2² × 13 × 23 × 431 × 7703 × 287191 × 9650504777_<10> × 2019288084861640532902323572427513323109433121961249857282538959385276780912487_<79>

2×10¹⁰⁵+1349 = (2)₁₀₃52_<105> = 2² × 3 × 7 × 181397 × 4362557279745923_<16> × 3343004472702525649427007225714120739126940325448372291864078447492943260793230913_<82>

2×10¹⁰⁶+1349 = (2)₁₀₄52_<106> = 2² × 17 × 61 × 1348937 × 61108461501381977587_<20> × 6499137444549437668159532159148833270378453783385101373896036690259679715621_<76>

2×10¹⁰⁷+1349 = (2)₁₀₅52_<107> = 2² × 29 × 12073 × 15109987 × 6704605426859_<13> × 89510003483759_<14> × 191741205051968857_<18> × 9126199429094204594284680287899035323674185412841_<49>

2×10¹⁰⁸+1349 = (2)₁₀₆52_<108> = 2² × 3 × 197 × 20747 × 172831739659941608229499_<24> × 35140377054873509787301961_<26> × 746027417229729373487864745700989247079460438972821_<51>

2×10¹⁰⁹+1349 = (2)₁₀₇52_<109> = 2² × 181 × 19927 × 670249409 × 1134166313741_<13> × 9131262112158916975513_<22> × 110243077203027119245733_<24> × 201285123774475053965006128738506049_<36>

2×10¹¹⁰+1349 = (2)₁₀₈52_<110> = 2² × 13 × 23392909519322089_<17> × 18268374312201062295465543342648242431209490696359133674570376571904469494976559810600096959_<92>

2×10¹¹¹+1349 = (2)₁₀₉52_<111> = 2² × 3² × 7 × 4908498814857116866225808144096827463_<37> × 179654564140547339218023662039588245377858384381737618850422402043089027_<72> (Eric Jeancolas / ECM for P37 x P72 / December 21, 2021 2021 年 12 月 21 日)

2×10¹¹²+1349 = (2)₁₁₀52_<112> = 2² × 37489 × 562813 × 110443591 × 321053641 × 7485888203_<10> × 200752886230231220048270414755633_<33> × 494124360509959367029994676083144711319211_<42> (Eric Jeancolas / ECM for P33 x P42 / December 21, 2021 2021 年 12 月 21 日)

2×10¹¹³+1349 = (2)₁₁₁52_<113> = 2² × 45413422259_<11> × 22124891312929_<14> × 3246996271650754577417572331248548548681_<40> × 1702865427822268042238442157552541232408267288193_<49> (Eric Jeancolas / ECM for P40 x P49 / December 21, 2021 2021 年 12 月 21 日)

2×10¹¹⁴+1349 = (2)₁₁₂52_<114> = 2² × 3 × 1231231 × 2147731067_<10> × 63754920942007331_<17> × 8027777245579059060924567097_<28> × 13682888076194788063403268903321744885516417950705039_<53>

2×10¹¹⁵+1349 = (2)₁₁₃52_<115> = 2² × 19319233 × 28756605169343708187356897427323101054558198845448758527605912489152936638610629912458509898170157974468011_<107>

2×10¹¹⁶+1349 = (2)₁₁₄52_<116> = 2² × 13 × 1597289 × 583780703048830691_<18> × 873859029080073780247337033_<27> × 524456567982062074132275058072026898153156894320655168980005453_<63>

2×10¹¹⁷+1349 = (2)₁₁₅52_<117> = 2² × 3 × 7 × 19 × 78623 × 1130807 × 197212500879463_<15> × 44621597687861406376711_<23> × 64595947889009333559210399473957_<32> × 2755063846003229625682347690065417_<34> (Eric Jeancolas / ECM for P32 x P34 / December 21, 2021 2021 年 12 月 21 日)

2×10¹¹⁸+1349 = (2)₁₁₆52_<118> = 2² × 43 × 89 × 103 × 6961 × 72531247 × 1471156943402963378319005658316024629197_<40> × 1897474832169106246787138829242907983353622371826985875790677_<61> (Eric Jeancolas / ECM for P40 x P61 / December 21, 2021 2021 年 12 月 21 日)

2×10¹¹⁹+1349 = (2)₁₁₇52_<119> = 2² × 151 × 104270281350049_<15> × 1262382582798182017_<19> × 1753611975995671152859_<22> × 159391627664769125443013529761595254229283716921185783688112279_<63>

2×10¹²⁰+1349 = (2)₁₁₈52_<120> = 2² × 3⁴ × 1819193942991441256997395058312153_<34> × 14647344741336650027843096193155951_<35> × 25739764634476407500099447158936648967761111271741_<50> (Eric Jeancolas / ECM for P34 x P35 x P50 / December 21, 2021 2021 年 12 月 21 日)

2×10¹²¹+1349 = (2)₁₁₉52_<121> = 2² × 1257079 × 167885483 × 2632399375148511215902529260878624102827362867230258955229869247086936989472901586716030994207545119757959_<106>

2×10¹²²+1349 = (2)₁₂₀52_<122> = 2² × 13 × 17 × 71 × 4391 × 4651 × 7589 × 564685808339187503_<18> × 4045532270819290164706092208931591353180131550675728180356331987217589304665168191008719_<88>

2×10¹²³+1349 = (2)₁₂₁52_<123> = 2² × 3 × 7 × 8540089 × 562519203137_<12> × 204107186762315537_<18> × 2698050994519785417065812260624555479769701328118713876898610990971842780317254797383_<85>

2×10¹²⁴+1349 = (2)₁₂₂52_<124> = 2² × 1873 × 18133 × 22943 × 495175961573943676289_<21> × 1439826946769573977018296136753902354884125554931863975953273147102412111575825650944301841_<91>

2×10¹²⁵+1349 = (2)₁₂₃52_<125> = 2² × 5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555563_<124>

2×10¹²⁶+1349 = (2)₁₂₄52_<126> = 2² × 3 × 23 × 169633 × 394489 × 30298921673_<11> × 5027383160468909_<16> × 2889613644451764680543_<22> × 27335323995418322834319704900859972737285453689059250156634701621_<65>

2×10¹²⁷+1349 = (2)₁₂₅52_<127> = 2² × 211 × 3251 × 317846279 × 11718315809_<11> × 54207638673558413_<17> × 4011300992537121958345839153821319098818575320066445237304853350360752968958122084681_<85>

2×10¹²⁸+1349 = (2)₁₂₆52_<128> = 2² × 13 × 223 × 50017632132685709_<17> × 38313881478643554147278026518967664533108597421653778390368020470552176316649959339264914284551157344541293_<107>

2×10¹²⁹+1349 = (2)₁₂₇52_<129> = 2² × 3² × 7 × 59 × 347 × 149971 × 288551 × 995349466337259212433908116531071421862200879941766019619587342160006537617914693303874154276087033089709591097_<111>

2×10¹³⁰+1349 = (2)₁₂₈52_<130> = 2² × 47² × 21661 × 202551907 × 286383537760261_<15> × 25180350349571249029_<20> × 12627650616302102919011430161_<29> × 629483810211273677925790392737024160540329105442949_<51>

2×10¹³¹+1349 = (2)₁₂₉52_<131> = 2² × 383 × 14505366985784740353930954453147664635915288656803017116333043225993617638526254714244270380040615027560197272991006672468813461_<128>

2×10¹³²+1349 = (2)₁₃₀52_<132> = 2² × 3 × 1667401 × 1239434360076611_<16> × 29151459586250279741_<20> × 2119153971913083523883_<22> × 3902957913975322581132599_<25> × 37164300737297754018095326400860106404571363_<44>

2×10¹³³+1349 = (2)₁₃₁52_<133> = 2² × 55475790797997525853_<20> × 745801016832684032887_<21> × 15621794754686955909731557_<26> × 69504573229060618618202745289_<29> × 12366782234328463376164668605820392021_<38>

2×10¹³⁴+1349 = (2)₁₃₂52_<134> = 2² × 13 × 359 × 41248873 × 302143027 × 9510030426383_<13> × 47025557634577_<14> × 213574387873907654328383288502502341221370244710756388883428758882123848696896815265549_<87>

2×10¹³⁵+1349 = (2)₁₃₃52_<135> = 2² × 3 × 7² × 19 × 29 × 310663 × 825919 × 2042273 × 899535487027_<12> × 1967232676855691158297_<22> × 1767693552779148753386705243_<28> × 418443444063947151722262812197933052507188943519327_<51>

2×10¹³⁶+1349 = (2)₁₃₄52_<136> = 2² × 11491 × 224149 × 215691417488950627252752585075216379804197066225292901698796824410512915454309048241879820093933507921791933516470160468005557_<126>

2×10¹³⁷+1349 = (2)₁₃₅52_<137> = 2² × 33931 × 24682363 × 30624031 × 276628146795599026081_<21> × 783042578127746052699742033516524521492730526202631105285861193592041858641758416439078910193261_<96>

2×10¹³⁸+1349 = (2)₁₃₆52_<138> = 2² × 3² × 17 × 1279 × 15797 × 1004820882632276527830270183518898992416504143114237890399_<58> × 17885547922355746416686929289310612032014336893263405732569845071746583_<71> (Ignacio Santos / GNFS, Msieve for P58 x P71 / December 29, 2021 2021 年 12 月 29 日)

2×10¹³⁹+1349 = (2)₁₃₇52_<139> = 2² × 43 × 769026983 × 25178840755141589_<17> × 99927558568541121154456121421646281662101_<41> × 6677231801164980569116091277619205400154299260602537339449214302571343_<70> (Eric Jeancolas / ECM for P41 x P70 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁴⁰+1349 = (2)₁₃₈52_<140> = 2² × 13 × 402089240219_<12> × 10101538077157_<14> × 1127574276544581562393623101792579507593613313378463_<52> × 93310179736235264097581209157726119164602259611437638724603919_<62> (Eric Jeancolas / ECM for P52 x P62 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁴¹+1349 = (2)₁₃₉52_<141> = 2² × 3 × 7 × 165755453 × 300814583359_<12> × 3021996761405953_<16> × 934844874894400744454732116071273468387991_<42> × 18780534256341423750042724477517544855911489209768040510157043_<62> (Eric Jeancolas / ECM for P42 x P62 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁴²+1349 = (2)₁₄₀52_<142> = 2² × 439 × 823 × 1537669993261930089526222347696093672395717527561965794223465889712772471278631030857038822784455878558514340156590161433821912596992379_<136>

2×10¹⁴³+1349 = (2)₁₄₁52_<143> = 2² × 29548733 × 341906417 × 2331293290158227117_<19> × 6980884412467241131_<19> × 348542150650663259244197_<24> × 306881353682210652569687963_<27> × 315898970493283773828195446085046962239_<39>

2×10¹⁴⁴+1349 = (2)₁₄₂52_<144> = 2² × 3 × 573409 × 5556329 × 547336703063707749190503031229_<30> × 10619381180360877047075854888536408950254108342494662740330961178995826018627392853625990565080440709_<101> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3340064214 for P30 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P101 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁴⁵+1349 = (2)₁₄₃52_<145> = 2² × 419 × 5953 × 1748749 × 20765702384747_<14> × 2717961431019811173951426011_<28> × 2256629157126089762369871535442817035916701843917503748014037735877010141722642428424335573_<91>

2×10¹⁴⁶+1349 = (2)₁₄₄52_<146> = 2² × 13 × 15383 × 2261863397_<10> × 9095376320430904134494890823_<28> × 96564772507387206918133175097168632308028476703_<47> × 13984190630988529967173830539052021174611500728464898229_<56> (Ignacio Santos / GNFS, Msieve for P47 x P56 / December 29, 2021 2021 年 12 月 29 日)

2×10¹⁴⁷+1349 = (2)₁₄₅52_<147> = 2² × 3³ × 7 × 149 × 7027931 × 37866234336102805055678832067449899_<35> × 284792877910684896944994461419455007_<36> × 26029791587815265796309501043131437668545215964125161398387439501_<65> (Ignacio Santos / GNFS, Msieve for P35 x P36 x P65 / December 29, 2021 2021 年 12 月 29 日)

2×10¹⁴⁸+1349 = (2)₁₄₆52_<148> = 2² × 23 × 107157999526072568444407_<24> × 7280050270824059242315832150384932583_<37> × 30962832489517971707564283936975840238852099935211468009400256073742304390892707102701_<86> (Ignacio Santos / GNFS, Msieve for P37 x P86 / December 29, 2021 2021 年 12 月 29 日)

2×10¹⁴⁹+1349 = (2)₁₄₇52_<149> = 2² × 2207 × 867401 × 29743883311_<11> × 55943794617316152763849397_<26> × 1017662225820668482595376902274658447121_<40> × 1713767881801828465880219051707582828321936474547863224787901287_<64> (Ignacio Santos / Yafu for P40 x P64 / December 29, 2021 2021 年 12 月 29 日)

2×10¹⁵⁰+1349 = (2)₁₄₈52_<150> = 2² × 3 × 1907 × 59655443 × 162781659640025698941506100518668361668722161872889778166082610333339322175097315367693890063218331675344213812988264870667301095192532721_<138>

2×10¹⁵¹+1349 = (2)₁₄₉52_<151> = 2² × 10733 × 51761441866724639481557398262886010952721098998933714297545472426679917595784548174373945360621965485470563268010393697526838307607896725571187511_<146>

2×10¹⁵²+1349 = (2)₁₅₀52_<152> = 2² × 13² × 103 × 5760060543059_<13> × 117777207242017691560214758027471810975178287681_<48> × 470451941666858458638372321341586521392973604227922453106761121921254594438104313366071_<87> (Ignacio Santos / GNFS, Msieve for P48 x P87 / December 30, 2021 2021 年 12 月 30 日)

2×10¹⁵³+1349 = (2)₁₅₁52_<153> = 2² × 3 × 7 × 19 × 91371438600013667_<17> × 36995146107345175234045401440401_<32> × 473827032967427741277655613325504947836021_<42> × 86931976714372849889890218252410331502386234942661371096491_<59> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1469805621 for P32 / December 21, 2021 2021 年 12 月 21 日) (Ignacio Santos / Yafu for P42 x P59 / December 28, 2021 2021 年 12 月 28 日)

2×10¹⁵⁴+1349 = (2)₁₅₂52_<154> = 2² × 17 × 143999 × 345507786523_<12> × 34886708003157749948471_<23> × 9660390047306735943530707_<25> × 68384004801641967463217860422627139_<35> × 28500473479572024043960658620954808301773113400164129_<53> (Ignacio Santos / Yafu for P35 x P53 / December 28, 2021 2021 年 12 月 28 日)

2×10¹⁵⁵+1349 = (2)₁₅₃52_<155> = 2² × 19501 × 10337770799_<11> × 2186001305888087_<16> × 274637641292932709149524869491_<30> × 212043070224974354480720859766951_<33> × 216475699697977692736305500894323620228349600636810023864551011_<63> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:4109549524 for P30 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2795536866 for P33 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P63 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁵⁶+1349 = (2)₁₅₄52_<156> = 2² × 3² × 4178406910841208736098843674993810257_<37> × 1477318901171859765209685335548590486283588786053403763521128397972044671608865429337091501510451911050601220405745251_<118> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2679671658 for P37 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P118 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁵⁷+1349 = (2)₁₅₅52_<157> = 2² × 71 × 211 × 11447 × 1509427 × 1030195421_<10> × 2083354997082734993813999837095855369172685085708881720141870803655526972317992762099080284011218479917387457355646257416620818666927_<133>

2×10¹⁵⁸+1349 = (2)₁₅₆52_<158> = 2² × 13 × 427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427351_<156>

2×10¹⁵⁹+1349 = (2)₁₅₇52_<159> = 2² × 3 × 7 × 269 × 1201 × 2579 × 53407 × 17503487 × 286323471861324511_<18> × 22307344455762485906385967_<26> × 531782432232178729982408649837691806282480079324563045021325046399139719285142351497673616441_<93>

2×10¹⁶⁰+1349 = (2)₁₅₈52_<160> = 2² × 43 × 18614073582874440863_<20> × 8844556712201509332345798419_<28> × 78476846284807473781921868736391140317141846332773206504195191681713336047815856383769829451581872526855690053_<110>

2×10¹⁶¹+1349 = (2)₁₅₉52_<161> = 2² × 2281767750307931858995073_<25> × 638635756416111759590926457_<27> × 3812438325337401776340506905640303302005467868841737256983001444006900663771027233216055717299429420809831683_<109>

2×10¹⁶²+1349 = (2)₁₆₀52_<162> = 2² × 3 × 89 × 63211 × 169219 × 2379032508367733_<16> × 31822767829840888982401_<23> × 55617272342149245014194821971383_<32> × 1877786954706193059421924789034940513733_<40> × 2460254971652466556677150526448855457583_<40> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:278233607 for P32 / December 21, 2021 2021 年 12 月 21 日) (Ignacio Santos / Yafu for P40 x P40 / December 28, 2021 2021 年 12 月 28 日)

2×10¹⁶³+1349 = (2)₁₆₁52_<163> = 2² × 29 × 19157088122605363984674329501915708812260536398467432950191570881226053639846743295019157088122605363984674329501915708812260536398467432950191570881226053639847_<161>

2×10¹⁶⁴+1349 = (2)₁₆₂52_<164> = 2² × 13 × 42157853 × 26548608917387754480848701_<26> × 132963579442467893295627822203587682113_<39> × 2871647903146929073775126719687623902428622979988296667719922294348903187825465749783983359_<91> (Ignacio Santos / GNFS, Msieve for P39 x P91 / January 4, 2022 2022 年 1 月 4 日)

2×10¹⁶⁵+1349 = (2)₁₆₃52_<165> = 2² × 3² × 7 × 4117571 × 861417251508092903522005017401525493444157813_<45> × 895838211910507213842954493468150713659510749469_<48> × 277525376521632801135569430882220515483261337612743174682574023_<63> (Ignacio Santos / GNFS, Msieve for P45 x P48 x P63 / January 4, 2022 2022 年 1 月 4 日)

2×10¹⁶⁶+1349 = (2)₁₆₄52_<166> = 2² × 61 × 199 × 41076020997910168176447259_<26> × 395251182226454352549478067_<27> × 2818921867738321382836987317637134311057831741713831210981547479895073668108392961314646732736806951232009889_<109>

2×10¹⁶⁷+1349 = (2)₁₆₅52_<167> = 2² × 1289 × 230819 × 18672523831078357383112692461759732726931320884002435794882518416050180875155267030555541355101182020464765698352938387278816724286023271703133547400300149393_<158>

2×10¹⁶⁸+1349 = (2)₁₆₆52_<168> = 2² × 3 × 1579 × 11279 × 469501 × 6223741 × 1662325387_<10> × 325858929086177_<15> × 656931092181430851829532129580132715877811652126019911328465528059670407043464979341504834253241158630160782926776542605559_<123>

2×10¹⁶⁹+1349 = (2)₁₆₇52_<169> = 2² × 20333 × 215689 × 3026044011046090054291520156176557487002465981802642995117757003567973024302757_<79> × 41862272189714803241651918480688926937194908764178367052043581873512668880505107_<80> (Bob Backstrom / Msieve 1.54 snfs for P79 x P80 / January 5, 2022 2022 年 1 月 5 日)

2×10¹⁷⁰+1349 = (2)₁₆₈52_<170> = 2² × 13 × 17² × 23 × 29723 × 11375876169844900997899593189134949905029391519_<47> × 190143273465388428847831091373528312534277107179565200088841283208823665109723515901902377294712667360236621025709_<114> (Bob Backstrom / Msieve 1.54 snfs for P47 x P114 / January 5, 2022 2022 年 1 月 5 日)

2×10¹⁷¹+1349 = (2)₁₆₉52_<171> = 2² × 3 × 7 × 19 × 226333337 × 94682874978137_<14> × 7358491938227108714017189_<25> × 678163554698913942614326465292288232450662449_<45> × 1302001159891330812715230697243712667933869192210623306774719546368416788193_<76> (Bob Backstrom / for P45 x P76 / December 31, 2021 2021 年 12 月 31 日)

2×10¹⁷²+1349 = (2)₁₇₀52_<172> = 2² × 860968847568491_<15> × 14331208788139337601079343636626473667255585181476424267_<56> × 45025364161734007626045752498758547539693975674962747355205464418853724117075907114834016536450743779_<101> (Bob Backstrom / Msieve 1.54 snfs for P56 x P101 / January 5, 2022 2022 年 1 月 5 日)

2×10¹⁷³+1349 = (2)₁₇₁52_<173> = 2² × 691 × 5309 × 3691584562695309923_<19> × 24061755804331484345142487492711_<32> × 87078175669099155315889546712844525277_<38> × 195788538372303090316391861585700331966843010582480327585149917775637951725117_<78> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1448135522 for P32 / December 21, 2021 2021 年 12 月 21 日) (Ignacio Santos / GMP-ECM B1=3000000, sigma=1:196407682 for P38 x P78 / December 29, 2021 2021 年 12 月 29 日)

2×10¹⁷⁴+1349 = (2)₁₇₂52_<174> = 2² × 3³ × 12007 × 3678993422452169_<16> × 46580077709521940145391637948452224992261854029861923849838814686943715574901103605778744077082145974125168755137700982273273206932294021144299720836143_<152>

2×10¹⁷⁵+1349 = (2)₁₇₃52_<175> = 2² × 26717193401333167_<17> × 5926366781738330180373173_<25> × 2976145593802990785433431796261_<31> × 5431259935462921569266136090312409743969320634509_<49> × 217066784450912516252426655349198253384682507017252657_<54> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3686834282 for P31 / December 21, 2021 2021 年 12 月 21 日) (Ignacio Santos / Yafu for P49 x P54 / December 29, 2021 2021 年 12 月 29 日)

2×10¹⁷⁶+1349 = (2)₁₇₄52_<176> = 2² × 13 × 47 × 983748487 × 4466115839_<10> × 1159839017877064136614314517979422613092028597_<46> × 1784327255102195843256733685464067554240984493677217663535580632234957922377808744113436547206596010385902973_<109> (Ignacio Santos / GNFS, Msieve for P46 x P109 / January 11, 2022 2022 年 1 月 11 日)

2×10¹⁷⁷+1349 = (2)₁₇₅52_<177> = 2² × 3 × 7² × 183680435986197881782573760398334995741_<39> × 56658966855423503094051390519645974637202693_<44> × 36314377796428688263212982881593070814425573639730931521955852768242927442514477963478367033_<92> (Ignacio Santos / GMP-ECM B1=3000000, sigma=1:2263940023 for P39 / January 3, 2022 2022 年 1 月 3 日) (Ignacio Santos / GNFS, Msieve for P44 x P92 / January 14, 2022 2022 年 1 月 14 日)

2×10¹⁷⁸+1349 = (2)₁₇₆52_<178> = 2² × 1358754107_<10> × 57097218970107137_<17> × 321958081661610261707278194367_<30> × 71605703246834783279463766270573_<32> × 310616644677135288210987570622575020378851397322754284021876652870502757346981418525049227_<90> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1804999252 for P30 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:4120320766 for P32 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P90 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁷⁹+1349 = (2)₁₇₇52_<179> = 2² × 233 × 10893254093959_<14> × 1088121986490353787388519_<25> × 204506899898816327915523327599591144824094401_<45> × 9836223512073161632504872953284230273907039720409007273802054657918252332450783208559678281091_<94> (Ignacio Santos / GMP-ECM B1=11000000, sigma=1:3919758709 for P45 x P94 / January 15, 2022 2022 年 1 月 15 日)

2×10¹⁸⁰+1349 = (2)₁₇₈52_<180> = 2² × 3 × 72383 × 2561362140544279190415088123711081_<34> × 99884632308501811589064226388900490098908520696277481227158530318263753806804572381202014232835207783225762690470744770585232990672170433327_<140> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3916969994 for P34 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P140 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁸¹+1349 = (2)₁₇₉52_<181> = 2² × 43 × 1035637 × 234247156503421_<15> × 328601135488357_<15> × 148133889134435290229371_<24> × 279242821298808174564844112553762128930701973344535376302357_<60> × 3918065134777849127427821671701885892849469862284674249295227_<61> (Bob Backstrom / for P60 x P61 / January 2, 2022 2022 年 1 月 2 日)

2×10¹⁸²+1349 = (2)₁₈₀52_<182> = 2² × 13 × 11299 × 454181186801_<12> × 152850376212605666879_<21> × 544814278613532491167291691434486411616777825738388106491855429728843091243909880851305902291712806814612675919333733997074859419177666591118131_<144>

2×10¹⁸³+1349 = (2)₁₈₁52_<183> = 2² × 3² × 7 × 95226731 × 18847733591_<11> × 40339799904731_<14> × 28732157769307858453440121_<26> × 423903451729942086822851526400611342121791081828198687795805413292021142798000194615040044283799464731241152788995881458931_<123>

2×10¹⁸⁴+1349 = (2)₁₈₂52_<184> = 2² × 752726983 × 648550161689_<12> × 10369002253509827484424520713_<29> × 7791230744849366586000730273081979415193263328335803_<52> × 14086509841917890167402258485125287304854472065317064587473265849727554735779099591_<83> (Ray Chandler / YAFU Version 2.07 / January 30, 2022 2022 年 1 月 30 日)

2×10¹⁸⁵+1349 = (2)₁₈₃52_<185> = 2² × 97 × 118361 × 505643 × 177378163 × 8608323727_<10> × 3852643094808247933849_<22> × 18281402522693788839943269749_<29> × 389424440108875544495796802176454577642002830323_<48> × 22850352196594093099814512350993960687197283661987243051_<56> (Eric Jeancolas / ECM for P48 x P56 / December 21, 2021 2021 年 12 月 21 日)

2×10¹⁸⁶+1349 = (2)₁₈₄52_<186> = 2² × 3 × 17 × 103 × 2749 × 15275484097_<11> × 4788880847515030439_<19> × 1514890921356216739602025039471_<31> × 53600946031584938514984623635866232627549_<41> × 647683036578507841350090624475056698151660476290843093119180357876711025280447_<78> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:518363151 for P31 / December 21, 2021 2021 年 12 月 21 日) (Ignacio Santos / GMP-ECM B1=3000000, sigma=1:2600984776 for P41 x P78 / December 29, 2021 2021 年 12 月 29 日)

2×10¹⁸⁷+1349 = (2)₁₈₅52_<187> = 2² × 59 × 211 × 16470851 × 52446629506393_<14> × 1089570560111203_<16> × 47413721661930559188817861705023351693757737477832905821495590655172379711403873048386571057986154780842806233932631218922855853936923252717832203_<146>

2×10¹⁸⁸+1349 = (2)₁₈₆52_<188> = 2² × 13 × 1374803797_<10> × 1365042485017_<13> × 115836980540544101_<18> × 3777167073508425441905112887_<28> × 520455769927256913115022425761547931674823220356361151292553747631162289943203296736390873882932868604774218554117867777_<120>

2×10¹⁸⁹+1349 = (2)₁₈₇52_<189> = 2² × 3 × 7 × 19 × 313 × 123564318241454830753261552588912434192416196776347_<51> × 261854250360695570393076198094024877601851159323468898352714930173_<66> × 13748570870037047875727100680409331455664544273283972141108279118979_<68> (Bob Backstrom / Msieve 1.54 snfs for P51 x P66 x P68 / January 9, 2022 2022 年 1 月 9 日)

2×10¹⁹⁰+1349 = (2)₁₈₈52_<190> = 2² × 5923 × 912467 × 1884828377_<10> × 603273365210643676825285380359507690984851153_<45> × 90402956208635589619332018154853446970060918578252247701747373391032904729703714413933776680410851354362954886187266022165803_<125> (Bob Backstrom / Msieve 1.54 snfs for P45 x P125 / January 16, 2022 2022 年 1 月 16 日)

2×10¹⁹¹+1349 = (2)₁₈₉52_<191> = 2² × 29 × 131 × 1091 × 1543 × 12437 × 16423191059099247413905721703163369_<35> × 17963369301328297977016237004508656571882431005446262031_<56> × 236759027067855860656601526421056698940576385603375334438925543248922266459036936267843_<87> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:4101639045 for P35 / December 21, 2021 2021 年 12 月 21 日) (Ray Chandler / YAFU Version 2.07 / February 1, 2022 2022 年 2 月 1 日)

2×10¹⁹²+1349 = (2)₁₉₀52_<192> = 2² × 3² × 23 × 71 × 1621 × 7211 × 17669 × 9286429 × 1290364489641173_<16> × 6237186159469055987011_<22> × 41850248221772897432965669001986115117_<38> × 19287997596162971799129139964077382710162127513_<47> × 303370457165140080102957753793587867599214721343_<48> (Ignacio Santos / GMP-ECM B1=3000000, sigma=1:3313649648 for P38 / December 30, 2021 2021 年 12 月 30 日) (Ignacio Santos / Yafu for P47 x P48 / December 30, 2021 2021 年 12 月 30 日)

2×10¹⁹³+1349 = (2)₁₉₁52_<193> = 2² × 487 × 55318825087_<11> × 20621753255079978205267559148326777980591111600259168105621209330703860734842442748548964589580233853471065857579062843438579813518812265650429254956153398973343805022886483931427_<179>

2×10¹⁹⁴+1349 = (2)₁₉₂52_<194> = 2² × 13 × 109 × 151 × 102535503857417_<15> × 253224911183891323276267794512802198659081114347803589960224951539053051038443192676406544165060068962874727321690941688821886409101133334601214413754381134840920611894259517_<174>

2×10¹⁹⁵+1349 = (2)₁₉₃52_<195> = 2² × 3 × 7 × 2645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645502645503_<193>

2×10¹⁹⁶+1349 = (2)₁₉₄52_<196> = 2² × 367049 × 56404648859240763426478054913_<29> × 2583161094889024328737814759641057531_<37> × 10388122412034472218815381477102999406906571811708194915639141018682934937257398864637265373059675322785725414592047418339529_<125> (Ignacio Santos / GMP-ECM B1=3000000, sigma=1:2796730237 for P37 x P125 / January 12, 2022 2022 年 1 月 12 日)

2×10¹⁹⁷+1349 = (2)₁₉₅52_<197> = 2² × 491 × 971 × 15074996386223_<14> × 1230348041597587987619251522609584122808091792275678749741_<58> × 628263130328801601439876543807437430289340298847432877143122535727529957918937784093179173499961341719410580405861699681_<120> (Bob Backstrom / Msieve 1.54 snfs for P58 x P120 / January 20, 2022 2022 年 1 月 20 日)

2×10¹⁹⁸+1349 = (2)₁₉₆52_<198> = 2² × 3 × 18518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518521_<197>

2×10¹⁹⁹+1349 = (2)₁₉₇52_<199> = 2² × 41363339813_<11> × 67872733153373_<14> × 88320683561693932292951535301202228685338974262732923433_<56> × 2240547406393114714098819104893094637971377542444688475593926765187108098129460366279649810708719234226473433096319139_<118> (Bob Backstrom / Msieve 1.54 snfs for P56 x P118 / January 24, 2022 2022 年 1 月 24 日)

2×10²⁰⁰+1349 = (2)₁₉₈52_<200> = 2² × 13 × 2311 × 3214219526114541877_<19> × 54940197425652897022237_<23> × 2080058239821504101292822556204988129688635540542725599_<55> × 503434473589522084035720328571888173537745069324079701147316967800617257496653719006299363554196591_<99> (Eric Jeancolas / cado-nfs-3.0.0 for P55 x P99 / February 11, 2022 2022 年 2 月 11 日)

2×10²⁰¹+1349 = (2)₁₉₉52_<201> = 2² × 3⁴ × 7 × 18211 × 1024895392205019236735577845260113457473862005494228109733952145280639252366948867751_<85> × 5249659084607047364846739098198441674189824827598528982504394599083537706757950763177251723851820084465457849_<109> (Bob Backstrom / Msieve 1.54 snfs for P85 x P109 / January 16, 2022 2022 年 1 月 16 日)

2×10²⁰²+1349 = (2)₂₀₀52_<202> = 2² × 17 × 43 × 541 × 181019 × 105302686344359686684705583_<27> × 17374006286839771770958619452394663461451_<41> × 46510899285411606402237186682211658819089_<41> × 91199935247073559578314814603838163253374763587209643388487321934016748889109643651_<83> (Ignacio Santos / GMP-ECM B1=11000000, sigma=1:3479300770 for P41(4651...) / January 22, 2022 2022 年 1 月 22 日) (Eric Jeancolas / cado-nfs-3.0.0 for P41(1737...) x P83 / January 24, 2022 2022 年 1 月 24 日)

2×10²⁰³+1349 = (2)₂₀₁52_<203> = 2² × 503 × 430293607 × 35612418218719_<14> × 3157490000813228100667627_<25> × 191237347723545867813632490620325989_<36> × 521603729391557899318337311952110804204316741322699938669_<57> × 2288430712134033890918766355388416570275923127799846184606591_<61> (ebina / GMP-ECM 7.0 B1=3000000, sigma=1:2922274362 for P36 / December 29, 2021 2021 年 12 月 29 日) (Eric Jeancolas / cado-nfs-3.0.0 for P57 x P61 / January 2, 2022 2022 年 1 月 2 日)

2×10²⁰⁴+1349 = (2)₂₀₂52_<204> = 2² × 3 × 257 × 44732388341_<11> × 5878930840423_<13> × 29036978519395785809347297842905889715994250143332756179585149989_<65> × 9436289488884651196895189384611929500388085731875400844351623165576375692908496222946749656648958209160789156039_<112> (Bob Backstrom / Msieve 1.54 snfs for P65 x P112 / February 7, 2022 2022 年 2 月 7 日)

2×10²⁰⁵+1349 = (2)₂₀₃52_<205> = 2² × 301222589 × 7859826119_<10> × 46857982681_<11> × 4701837422649761_<16> × 1065064290270578520584350902128744346078448676963210608726382370551472994871210531170957954666181313783496102353507856743412574813466993517663039864249493193673_<160>

2×10²⁰⁶+1349 = (2)₂₀₄52_<206> = 2² × 13 × 89 × 197 × 130171079 × 210078761 × 1514704601_<10> × 58569899093_<11> × 5319293864321977237_<19> × 2980949272713222069530054700251_<31> × 10312752502905307373460804177360332438572512539_<47> × 61439217076869465290644836719880072439840703205648864181692932566837_<68> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1805790548 for P31 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / cado-nfs-3.0.0 for P47 x P68 / January 1, 2022 2022 年 1 月 1 日)

2×10²⁰⁷+1349 = (2)₂₀₅52_<207> = 2² × 3 × 7 × 19 × 113 × 261765827 × 66366680646594269_<17> × 580530930283659803540977_<24> × 122176518562843613496079407546951821571811349769736243531094749051306155628405131986947055743330858816917828429418419735262699496064555069220267733847299_<153>

2×10²⁰⁸+1349 = (2)₂₀₆52_<208> = 2² × 3678601360913473272948164132944513_<34> × 220210929314546117196556201796068055844489028184922939482712593974574448786899_<78> × 685813291911263850419802221714977491207060272634059074140578291778783324972639624754397475562249_<96> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1682665947 for P34 / December 21, 2021 2021 年 12 月 21 日) (Bob Backstrom / Msieve 1.44 snfs for P78 x P96 / August 6, 2024 2024 年 8 月 6 日)

2×10²⁰⁹+1349 = (2)₂₀₇52_<209> = 2² × 751 × 2043074233_<10> × 15723498318797028937_<20> × 289043606071523063787985346876390459509_<39> × 796692751675360459667031191156057136999084816531022430321276521579463378811644884503818076912156287404563043670863333256805362553990036817_<138> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1:3332107472 for P39 x P138 / February 18, 2022 2022 年 2 月 18 日)

2×10²¹⁰+1349 = (2)₂₀₈52_<210> = 2² × 3² × 179 × 15661 × 30259 × 46401975769951_<14> × 4214659009558293940619663494217_<31> × 31454551266745243301851399471796108257_<38> × 11829747727603682971087104251985525005418937361359605807909912167722051273142792296037509268204029355543720667619793_<116> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1125975627 for P31 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2561244483 for P38 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P116 / December 21, 2021 2021 年 12 月 21 日)

2×10²¹¹+1349 = (2)₂₀₉52_<211> = 2² × 142895746309_<12> × [3887838301038111523171439231617019816572401198246192614421719997873443175926746022195727469011399175109336078113694913062169306421096957438023352404111033946981501226343516738527743739484608170594607_<199>] Free to factor

2×10²¹²+1349 = (2)₂₁₀52_<212> = 2² × 13 × 1087 × 207433 × 945917599926429773_<18> × 2003657304589322373753330080690434667305499432555652023357776209435694771403055781130538252063264242877710022913499286656730911174658839885768479301498606639593853211081493626000405797_<184>

2×10²¹³+1349 = (2)₂₁₁52_<213> = 2² × 3 × 7 × 443 × 587 × 49272312924947420757976443195911631407_<38> × [206473073887396392985764395209746609826624858124182433886059039492763090588246272450979866233872325359955130515710112749908060432394485306760131194793817733990583107369_<168>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4164814324 for P38 / February 7, 2022 2022 年 2 月 7 日) Free to factor

2×10²¹⁴+1349 = (2)₂₁₂52_<214> = 2² × 23 × 89809 × 18232214797_<11> × 14751642181640349923990370076571126983718229463010712849671774241656911057140859456088593417204142085707396495651209950863150133121566054723055444980074954820394347968739726477440789288989447722097_<197>

2×10²¹⁵+1349 = (2)₂₁₃52_<215> = 2² × 8561058383569_<13> × 34304931303368942141_<20> × 306736703864226579838184994827_<30> × 61670537796861255634083106754252595313157290051328656364864538115754685726818004206498726753996224573517489149546834005627385707480959546368411115879461_<152> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1580677854 for P30 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P152 / December 21, 2021 2021 年 12 月 21 日)

2×10²¹⁶+1349 = (2)₂₁₄52_<216> = 2² × 3 × 244463 × 27341833 × 125780497833339675690187_<24> × 48896788428743273079166163_<26> × [450476180589683771613701466608041294190298372099601711438720465457757782548290406731933638488194404488570698037728293647733249683551413556192205981264879_<153>] Free to factor

2×10²¹⁷+1349 = (2)₂₁₅52_<217> = 2² × 211 × 7177 × 7682684246857_<13> × 1250223697557348171017_<22> × 27075286478918477906541350675546200084459276231_<47> × 1410679391963130202470497707585139314895550290402114853344375800666265955143107700471623991071289977100455599081256352137251986311_<130> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3047425440 for P47 x P130 / February 7, 2022 2022 年 2 月 7 日)

2×10²¹⁸+1349 = (2)₂₁₆52_<218> = 2² × 13 × 17 × 373 × 569 × 65929 × 2384177967679_<13> × 100581807731457235267961_<24> × 7491685326130341130322043074297511932000361870510225862640709577180712100940242777593548824028334773295469303018870293347386492217277846017880329407333676313902562775869_<169>

2×10²¹⁹+1349 = (2)₂₁₇52_<219> = 2² × 3² × 7² × 29² × 433 × 237973733 × 21867553845661811859956550051408627922812263_<44> × 1752671477364422669958767483885753523314245919038985780422997508624038861154721_<79> × 37929338307986330424111038845820181558576594126688086641610204529700921466361609_<80> (Erik Branger / GGNFS, Msieve snfs for P44 x P79 x P80 / December 15, 2022 2022 年 12 月 15 日)

2×10²²⁰+1349 = (2)₂₁₈52_<220> = 2² × 103 × 1297 × 472561 × 51673580903034473096259157_<26> × 4969648392917508616822803905411006200373149282937_<49> × 34268744662255150485998285029022660561218791829487193554224223826749899848765849879308644215821438383524529052486221175238727959551857_<134> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P49 x P134 / December 15, 2022 2022 年 12 月 15 日)

2×10²²¹+1349 = (2)₂₁₉52_<221> = 2² × 128467 × 193409717653_<12> × 223592700609207210529553909877898637245587527459036317238391028974254390277374657661924406449386288397742367887027395330459875381639466022605956774075146931520457542123517047207525554739850483427363602213_<204>

2×10²²²+1349 = (2)₂₂₀52_<222> = 2² × 3 × 47 × 9613 × 38448379 × 4529723582704443811786886151177773_<34> × 235342143433437481742290249641304098131973122079341876968688527994476630260393662381303770282065055223406172452507861738490609997027876436203653660122529730502316769580121133_<174> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:713208016 for P34 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P174 / December 21, 2021 2021 年 12 月 21 日)

2×10²²³+1349 = (2)₂₂₁52_<223> = 2² × 43 × 51263 × 69143 × 180239 × 199053118923668445343_<21> × 101598909401371338791659583892023040455497782283904559876498353934525286308334455394298988365673031599326615883805786793474745139406946962668713819499717546048484446899643708093008771337_<186>

2×10²²⁴+1349 = (2)₂₂₂52_<224> = 2² × 13 × 11273 × 7531206421_<10> × 884540866700111_<15> × [5690654014574691779862832108063989367222675675446288817227325868525802417432311851178239716102215561713184663722297858218427770717333207276896845119960448743498117710053672080275791438093604077_<193>] Free to factor

2×10²²⁵+1349 = (2)₂₂₃52_<225> = 2² × 3 × 7 × 19² × 3128510197_<10> × 6424789489_<10> × 61627603817357_<14> × 1536073548398309_<16> × [3851387606090753904130123722158307136832361408778576736507020966280331111818075162600475108344388272527737260213337803341999971855380647565305009471972082785321288330161787_<172>] Free to factor

2×10²²⁶+1349 = (2)₂₂₄52_<226> = 2² × 61 × 21733516454975879_<17> × [419051750908740572318073776744483166697445351644262309947579090861224804811143393998044069631142584541616496096322512320818396686076083357444981187518569339935409835131924083331144778075083680919155409210177_<207>] Free to factor

2×10²²⁷+1349 = (2)₂₂₅52_<227> = 2² × 71 × 116113 × 552894869 × 18469918461768211661076643_<26> × [65990400231653709311449755573290502800455281562258999678369904660409747092576096819337035557534790259427956796550174699305389633348970335565824695483306530633542138476873591909645637043_<185>] Free to factor

2×10²²⁸+1349 = (2)₂₂₆52_<228> = 2² × 3³ × 447449 × 4815775043_<10> × 18254655823_<11> × 129020402751749_<15> × 236773557298372860361_<21> × 1712335086990340892034807438893681269328297460305144341862791778715397576655241642590780289574331396876205217507998890400974125669253633382331988614999359926052611761_<166>

2×10²²⁹+1349 = (2)₂₂₇52_<229> = 2² × 555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555563_<228>

2×10²³⁰+1349 = (2)₂₂₈52_<230> = 2² × 13² × 2681873 × 4342153 × [2822912781403055196897267754805419983053189442294795735198993322089300415919521352087645301449638188891643610907233639320008741360689061652978978500073429086394656189528854176808627079910336930146429626016132178283_<214>] Free to factor

2×10²³¹+1349 = (2)₂₂₉52_<231> = 2² × 3 × 7 × 1471 × 510836099 × 70873089961627_<14> × 6276596261921537_<16> × 13018518532507634957_<20> × 607920544406514815127854799133160880116198448614768367423373492328760230274863624985881911406461502139491004432902977740253102329570269147396819942912857418760501864949_<168>

2×10²³²+1349 = (2)₂₃₀52_<232> = 2² × 266909 × 1384303 × 497047046689_<12> × 786616156143228379_<18> × 3845676575428100448552058451162854524706497904043606497320200055606782875627490989977652263859037907005245169597414492957360105022199973637295295143511442617215436815011562431402380540343499_<190>

2×10²³³+1349 = (2)₂₃₁52_<233> = 2² × 2857 × 162594258373_<12> × 11959473175658745285863703678615158387093052402528706747740202538324684770607611633000644664209448198574328523122425288080467387809067096231370325292829458213153525295451268205143691400173572502043239955704368924445783_<218>

2×10²³⁴+1349 = (2)₂₃₂52_<234> = 2² × 3 × 17 × 9064019 × 4588351931_<10> × 26192671142387673881359375056611773404601722069632353217854526088574753384851390113839202102440357337795091333957076206701798595712100152501612294242042126482854981348715734533581607109933075030599260661319234063817_<215>

2×10²³⁵+1349 = (2)₂₃₃52_<235> = 2² × 3739961681_<10> × 3270846753286571_<16> × [45415086475972512339489803923063311540816085606704450377183179889215633113891636094678231290349021992243919914264680293430921249845219755780550284666152666113486082637778260620340163854535234313322682366214513_<209>] Free to factor

2×10²³⁶+1349 = (2)₂₃₄52_<236> = 2² × 13 × 23 × 4991249 × 7358866793781848992013558117_<28> × [505866743061574814148205561317597636646307321113285708934824233893774728619636026034832974260196613547343660870113123096218111270694546400078507546503340156720136511790248389373746167357937264384989_<198>] Free to factor

2×10²³⁷+1349 = (2)₂₃₅52_<237> = 2² × 3² × 7 × 71329412621_<11> × 12362841396901238908378564133746962246442893152217655367110978458530274694182725494499743931682672970760064390266307379796872824746910727368913950752021504825290672315211397786402933708159452299725686841559322526591998162281_<224>

2×10²³⁸+1349 = (2)₂₃₆52_<238> = 2² × 1097 × 5813 × 1337701 × 11769847 × 81576263676013_<14> × 146193301546712405314467763753_<30> × 11567676999746247693132534887912676379277401793_<47> × 40110053171752625659636034986599634670879732557078740098059846398379189362632955943275221618908988891749038622432042937265698857_<128> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:749198512 for P30 / December 21, 2021 2021 年 12 月 21 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1:284798725 for P47 x P128 / February 18, 2022 2022 年 2 月 18 日)

2×10²³⁹+1349 = (2)₂₃₇52_<239> = 2² × 337 × 3407 × 268849317202409_<15> × 20058649744130429_<17> × 478693535427318451_<18> × [1874378375096968373262323579562842862856734184680196165396439688920327093140703219119984032623675470892121165110403936813027513265849557750042302420161507347195894149933571948115001387_<184>] Free to factor

2×10²⁴⁰+1349 = (2)₂₃₈52_<240> = 2² × 3 × 468581 × 2375391163233575489_<19> × 215614188107882670710026614716629528058753_<42> × 77162998090532491446773549728748245219211964080060390719712838595405548153302769436536350295731630260079374478730512958970409207731643885046908366126602254744427185040904773_<173> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1:2362572084 for P42 x P173 / February 5, 2022 2022 年 2 月 5 日)

2×10²⁴¹+1349 = (2)₂₃₉52_<241> = 2² × 1228589 × 4074277 × 387661663673561227258013_<24> × [286297440066874317384395942972346596759533293418752637777630690294164498705614911427228245613246592288480450325811169741686777307418979646666075672161866114985753005390436303991294316309827843654909753767_<204>] Free to factor

2×10²⁴²+1349 = (2)₂₄₀52_<242> = 2² × 13 × [427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427350427351_<240>] Free to factor

2×10²⁴³+1349 = (2)₂₄₁52_<243> = 2² × 3 × 7 × 19 × 148123 × 16674377 × 4256709803393737249830838031_<28> × [13243672715080137202815579500143621951374812062304973535680327344149300710899212131816056977723189799738390565374946184857980130736173869449303692117175979907697061650252876817890949038590016840169737_<200>] Free to factor

2×10²⁴⁴+1349 = (2)₂₄₂52_<244> = 2² × 43 × 101089107992247887_<18> × [127807010047191709012714657226676778401907334275263225170648440573708570417181315438606566747127193380228316470583781409497763719248789675993483666850188937169214037355029062432752233639728655396526188091849775056548826962543_<225>] Free to factor

2×10²⁴⁵+1349 = (2)₂₄₃52_<245> = 2² × 59 × 463 × 3187 × 17036383955627966712930167_<26> × 62293720502351560664370787_<26> × [60129935699799054132625273516021109945971325454606768804404453922697464139491215399586836248747716973656377081687832673268817178086302932280872506862589857612441657386435182981953807393_<185>] Free to factor

2×10²⁴⁶+1349 = (2)₂₄₄52_<246> = 2² × 3² × 1489 × [4145627606563357626711107794609025860425009742224875423890422771103317331210771998772894228457246142493512092795728345314197116301436874528434859753418069961611488363223308376655141821920420532464409786997653574774685139583281512988251291363_<241>] Free to factor

2×10²⁴⁷+1349 = (2)₂₄₅52_<247> = 2² × 29 × 211 × 2683 × 23528125547_<11> × 77561200592543_<14> × 168022168399117_<15> × [110364126903762885915434198831509733376410442476739397547527562862378364392115920726507393956549113431081613337356153470918324997016475440583948748469119039533848825315258746441798909830331695919086967_<201>] Free to factor

2×10²⁴⁸+1349 = (2)₂₄₆52_<248> = 2² × 13 × 1674396060028387_<16> × 519553008800558354459_<21> × 272138850253248556795589969_<27> × [1805117760888011312954355426873274252942716373246454165640945455476778919700732665465208757315929196980827393081117848448870358169843271520046809099633105022215873626055136487394979863_<184>] Free to factor

2×10²⁴⁹+1349 = (2)₂₄₇52_<249> = 2² × 3 × 7 × 659 × 14769920843_<11> × 12922462443033529_<17> × [21032908821124768751256438250297196048236721011562577150174800326627507957891278878258792314800471808296268672949676809365573271547325190037471671111396109322701891394882381233443463178381334374581126879689009276283911_<218>] Free to factor

2×10²⁵⁰+1349 = (2)₂₄₈52_<250> = 2² × 17 × 89 × 1765706497_<10> × 565401230934327141947208893_<27> × [367801335794913972509850553686330585189133353772598104861689414411940962872049484533602574742119916259824682280436519268096959425444905691847222905998889634405674463074738572569652530296875895750228028994576431_<210>] Free to factor

2×10²⁵¹+1349 = (2)₂₄₉52_<251> = 2² × 1361 × [4081965874765286962200995999673442730018777043023920320026124581598497836558086374397910033472120173075353090048167197322230386153971752796146624214221569107682259776308270062862274471385419217895338394971018042289166462568372928402318556616866683_<247>] Free to factor

2×10²⁵²+1349 = (2)₂₅₀52_<252> = 2² × 3 × 46166998541_<11> × 264696300024161_<15> × [1515398066653098584638898739973001548871524876053594376821157818829326008703347158838590595007301838659944797709146431361538892072537491184305475559183168697755689117491343106563451229089733645908527325810547352720149384447421_<226>] Free to factor

2×10²⁵³+1349 = (2)₂₅₁52_<253> = 2² × 28793 × 8466086401_<10> × 10333396483721165171_<20> × 1215942535793638714927_<22> × 5705687593590504225217748683409_<31> × 6875110889904173081169357442803148583_<37> × 4623959704351355968773815074934359769992016831806088733356502096145121342982325233872653545838725194322598615860506357446927972409_<130> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3919174885 for P31 / December 21, 2021 2021 年 12 月 21 日) (Ignacio Santos / GMP-ECM B1=3000000, sigma=1:1512876810 for P37 x P130 / December 31, 2021 2021 年 12 月 31 日)

2×10²⁵⁴+1349 = (2)₂₅₂52_<254> = 2² × 13 × 103 × 167 × 427307 × 5223148025189031063719455063_<28> × [11131613155666210227945087112345648124110380606850664560297541680581427398018387530084900127504464920383748313444514872364907095241331154500491402466993366287950182502458990055977813730299081181811669805095558135411_<215>] Free to factor

2×10²⁵⁵+1349 = (2)₂₅₃52_<255> = 2² × 3³ × 7 × 677² × 40430390925475571_<17> × 3034972943244485470091_<22> × 1263252723075254371187584601153_<31> × 8390772875407258555299356340719612351_<37> × 493098158207823522248596051067945799416602744921092153289119212904626956104100975631337571911531397744358923466556612353483635379564257818481_<141> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1796757950 for P31 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1327302031 for P37 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P141 / December 21, 2021 2021 年 12 月 21 日)

2×10²⁵⁶+1349 = (2)₂₅₄52_<256> = 2² × 379 × 2797 × 186247 × 7145498282917609_<16> × 75492045431444099122151_<23> × [5216423235861423217978119996127574245680225964854650077542788427058451696003169068042664272097541145822028223845870191993978236794813701408537453760264238235284266815850256964965382901924587069375725841437_<205>] Free to factor

2×10²⁵⁷+1349 = (2)₂₅₅52_<257> = 2² × 13896397 × 56915229473_<11> × 7024198741374165155465244026169251191456744264563522929643949314435383479284694537454593809054574207325806014927833390333270347830318863441782261081234118301023358519756503029024016837476267742587488875105823151300147724614875193337085623_<238>

2×10²⁵⁸+1349 = (2)₂₅₆52_<258> = 2² × 3 × 23 × 1426553 × 51654671 × 2019491125251499_<16> × [5410519218140313600126187063757312668543870756442303305450360090848901443715116738388600754025139361480841994782916406216193060787091205402996665964067977296593986989432112228139473444690657753673902678093598084530763654214971_<226>] Free to factor

2×10²⁵⁹+1349 = (2)₂₅₇52_<259> = 2² × 1289 × 1867 × 129833903230062522444278183689_<30> × 1778042534518391126241498788901000197820575534468436193010653942898900778470010020878597876289972032745944309543576609648544206666202623800833159553270948282896801432376133931649665619617135987427885367207749336874549688209_<223> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1683653238 for P30 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P223 / December 21, 2021 2021 年 12 月 21 日)

2×10²⁶⁰+1349 = (2)₂₅₈52_<260> = 2² × 13 × 558629 × 8173049 × 21107351 × 203410073 × 12145299597349439_<17> × 9911993833330125502247_<22> × 181092773077469922330713623433701648814196220447164312093604839331572710690967612114737221695115741319354786859008397631159637193602608803546901740884337855622662504367366057957941040662631909_<192>

2×10²⁶¹+1349 = (2)₂₅₉52_<261> = 2² × 3 × 7² × 19 × 26416214279422248480447356653091369_<35> × 752984402844622709718989329148843716792170866783116558322635731239806261712474196499615058786892855895183191906526341619180991394428948712903785287593673773289982331940245652186163151600245023151999164077830577672565788539_<222> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:396844854 for P35 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P222 / December 21, 2021 2021 年 12 月 21 日)

2×10²⁶²+1349 = (2)₂₆₀52_<262> = 2² × 71 × 1811 × 31609933 × 12008838169255310995127_<23> × 11382197792384456022910013202451774711008296116332848558641058422982327643017241400421385694551517827688723100802036185228185435636608870250737195507130540622049613143943726882544868217094747976695702554216603754031394189710253_<227>

2×10²⁶³+1349 = (2)₂₆₁52_<263> = 2² × 17783 × 134710599377_<12> × 12630126311610129139427273533_<29> × 183617049297926904623605434588168855634195613223349544745894114619261098060159590042821801151089044033703929205017871192699908668460803453565606320445607249624277683181430192733136075247429819029348320290997453119613921_<219>

2×10²⁶⁴+1349 = (2)₂₆₂52_<264> = 2² × 3² × 1237 × 838399426725659_<15> × 15245389904050473467467_<23> × [390414354488226081667188240274273007766457001115867285531322037669694740668568957771910902829391997844509864794802363940782737308221220367991026030695568617412189700978406566433946770415916121385718019481532633225031573487_<222>] Free to factor

2×10²⁶⁵+1349 = (2)₂₆₃52_<265> = 2² × 43 × 199 × 62171 × 83983 × 249454487 × 67674044383656694928264431_<26> × [736568723627360796622602593154196166207113621736281379941640450174063257725246792603453004527762866218503970970483534046794732694153506854779941250261089421440275368083401575698895069797334212720072586672879575668979_<216>] Free to factor

2×10²⁶⁶+1349 = (2)₂₆₄52_<266> = 2² × 13 × 17 × 229 × 4327 × 52768889 × 174246326966834050927_<21> × [2759124267062962387028062639044405421307812942645929334481851381564802182748602274744125663205426424523062372078866418237761869830284419462380524744479002529518023090046106301114912846699523086571957122417605661739282723885202747_<229>] Free to factor

2×10²⁶⁷+1349 = (2)₂₆₅52_<267> = 2² × 3 × 7 × 720569209 × 3857797888941428311896583909_<28> × 9004927063181579919703302601957870784849_<40> × [105684872889041963741552693833966005779441842054040170137383969668400837699974941353332642547601777091811740173256997930918819030841247273141931155213872339478630788757642176314693416440187_<189>] (Ignacio Santos / GMP-ECM B1=3000000 for P40 / July 28, 2023 2023 年 7 月 28 日) Free to factor

2×10²⁶⁸+1349 = (2)₂₆₆52_<268> = 2² × 47 × 204947 × [57675062183233418785858965255631274837693435381742758356681063631038969759130830353291707856754201377393528057493178107132373876375880422801116049365285363922894393927434228772125264098435366689567126857141327929779827411067620653721222119341446299770449792007_<260>] Free to factor

2×10²⁶⁹+1349 = (2)₂₆₇52_<269> = 2² × 151 × 1307 × 400761926180631887_<18> × [70240647234606781630107985896172899790143237090846548836471887759507805596226416075543353899837405504860024183260598849187768650749395513742302239337619791140650592987548608731134546031739467792032876954038426100360901962238049092190300803196057_<245>] Free to factor

2×10²⁷⁰+1349 = (2)₂₆₈52_<270> = 2² × 3 × 1549 × 36562457179128866369_<20> × 1077135696292488519062971597549_<31> × [303563134779875900417210153188440038664500831444664307386832041236856419387797847294228055965002773671088506120049219747977599225844193921240717329342140431801084542092388803066792441025796014172206953939818907644209_<216>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3556987866 for P31 / December 21, 2021 2021 年 12 月 21 日) Free to factor

2×10²⁷¹+1349 = (2)₂₆₉52_<271> = 2² × 683 × 1733 × 42740748979_<11> × 2519542451323905982536147874349_<31> × 7487039233143621727097890858321087_<34> × 582149208239890662511514352172822770400595092560243138189400608200793946204429342299716762279466475237559805361269377767640995408816942815493210407137656617481971020318131051896261417269221_<189> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:480088507 for P31 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1200183166 for P34 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P189 / December 21, 2021 2021 年 12 月 21 日)

2×10²⁷²+1349 = (2)₂₇₀52_<272> = 2² × 13 × 911 × 3067 × 234919477267311503_<18> × [651077914699252383304872373854970255214984907046787287898003291416530932221137350008888327833707669975972567729592184339493380484469542427665660354433036183375726514379607833381632963955996240989428495955651764810848582498811113211097902554612341_<246>] Free to factor

2×10²⁷³+1349 = (2)₂₇₁52_<273> = 2² × 3² × 7 × 5927 × 1105744090623443119_<19> × [134554241105811279378990129845039687203602822309446165549548549508554615441998558096475570718713249174949115786436512437220639681325906799763554134502887715854267484238661916701865703823993873289681924688331722165210557669114673340556838073189084877_<249>] Free to factor

2×10²⁷⁴+1349 = (2)₂₇₂52_<274> = 2² × 555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555563_<273>

2×10²⁷⁵+1349 = (2)₂₇₃52_<275> = 2² × 29 × 31019 × 22323683 × 690313627 × 171438107820693613_<18> × 286377761773594717_<18> × 907610385351896641_<18> × [8993801517047446996502138653993878249676644113524857213735984467961574198100513261986628644784219757221731419007267514770149462794763984501914690444174672381974936985746342805165693046832962466273613_<199>] Free to factor

2×10²⁷⁶+1349 = (2)₂₇₄52_<276> = 2² × 3 × 4684575583_<10> × 2803479748009957_<16> × 26999111470362232795446401_<26> × [52226280222233480296861526069885016207794670541969300384171430236081514956600711353207888826876977079573246687832357825939711605877120281494026089324984130353442258925557606045417205911465340519078754044797103688020185918491_<224>] Free to factor

2×10²⁷⁷+1349 = (2)₂₇₅52_<277> = 2² × 211 × 2667491129_<10> × [987056597732653657425924847378427013587370312542401358255839445366987112771442252492493669557378579860602469809772891283205824943634807920972493515273704576476690046808704142275332242713043441493351190469696592056769579709734489172525943572737918828997453488743377_<264>] Free to factor

2×10²⁷⁸+1349 = (2)₂₇₆52_<278> = 2² × 13 × 33857 × [12622217779201563943271714190578827138475069478997765615008725739150762041153983736019947143200827815530831155369655532103474921799049748956710589460094732268876463577707042869343132213439683091453774030493763488417474299271268878735576907299150852921121993987280338699543_<272>] Free to factor

2×10²⁷⁹+1349 = (2)₂₇₇52_<279> = 2² × 3 × 7 × 19 × 593 × 3413 × 508259 × 8927423 × 1217958046598357_<16> × 514078506123214458586172513_<27> × 1426672499932416226940550234386839819_<37> × 16973302905350231856433707179669533573081153183833095489855028222289696119184845296045120666194710860304106719874566580389414891708128849508576093446895658328696171038783334050531_<179> (Ignacio Santos / GMP-ECM B1=3000000 for P37 x P179 / July 28, 2023 2023 年 7 月 28 日)

2×10²⁸⁰+1349 = (2)₂₇₈52_<280> = 2² × 23 × 20593 × 25307 × 210658168621_<12> × 574029261203_<12> × 383289602980721503333434141441421617233401033525222562369748582360236722075377601984768916319303320591314292787714454716545005909714887340546694505744715762459701296085626600614997291975409119683668222828501060905031082092368587482305109815930737_<246>

2×10²⁸¹+1349 = (2)₂₇₉52_<281> = 2² × 97 × 2647 × 178223 × 25928413759_<11> × 322075627274749_<15> × 86831588644525168547269_<23> × 167427392248491488499387233271549500836153185120689394632954381765262894701423779437412891617168443414111476144826111910849220520198444216690495959374967971610408625533991023628615737533633091876930329594976222585039117421_<222>

2×10²⁸²+1349 = (2)₂₈₀52_<282> = 2² × 3⁶ × 17 × 3181 × 164432894993_<12> × 1735475757443_<13> × 45058951695155971_<17> × 1278104229357262777_<19> × 207908332908799911833407_<24> × 412440087192483339926861674585303888212604271846893971796933114927467377764057967104471955400298539771419102722418497045169515349053878110709769203919992033854137932025626794511212709505803281_<192>

2×10²⁸³+1349 = (2)₂₈₁52_<283> = 2² × [555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555563_<282>] Free to factor

2×10²⁸⁴+1349 = (2)₂₈₂52_<284> = 2² × 13 × 193 × 1399 × 28955820457690532357251242029_<29> × [54660455189421329849109602241885808135416522184813243924521002270964362434723905804764621668015660361148099745014118061552114340906867916089684712326472026696214634521394668100773606634582500597822160453681091561105982612258549878022352330675085317_<248>] Free to factor

2×10²⁸⁵+1349 = (2)₂₈₃52_<285> = 2² × 3 × 7 × 563 × 1553 × 281321 × 914678987 × 330574401602973027962729_<24> × [35570361137285374087230483435648196146877757670688032336854794856859984776053139693348076872103239799064733971520021070289282390681102911288173449436643066592389254364598207410893489478409568072543147182788430419259810986657297542883042319_<239>] Free to factor

2×10²⁸⁶+1349 = (2)₂₈₄52_<286> = 2² × 43 × 61 × 3388802363_<10> × 9164002559_<10> × 159609070037781515052871_<24> × [42730718372205811614687797444554062297245827441672120832575429982089799507423086122798319708694452925771476773404518948825151190144556685083479547051326071298415878595782148162819777962846855409734160945250066855138686902617791155545865383_<239>] Free to factor

2×10²⁸⁷+1349 = (2)₂₈₅52_<287> = 2² × 8002093831843_<13> × 29535173204353_<14> × 1282845443484777220834211_<25> × [18323566020933155503244257873348729248057414834679063650187743246756624340575060184104065998811418025694742327757466527907730998168450485029581268018836084223345324168299731191896601730190306147814234091613209829574433016201364151259027_<236>] Free to factor

2×10²⁸⁸+1349 = (2)₂₈₆52_<288> = 2² × 3 × 103 × 58477 × 2784719109235097_<16> × 3548386639075253_<16> × 8943575460528548735974513_<25> × 687397449988787190390169736875828217693791_<42> × [50611884526502763312010548350111445977337738507612064389113630752023801503907955681779350348554841813481761518149760350067196175838853120247844581515953443986532896260862449086635497_<182>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:4124596815 for P42 / December 21, 2021 2021 年 12 月 21 日) Free to factor

2×10²⁸⁹+1349 = (2)₂₈₇52_<289> = 2² × 181 × 225581 × 862171 × 5557991 × 1617993677627652239720355196666758857_<37> × [1754924076208674135005603125395075417796260390302646368499178994832038552567197452116168191529017822398807277732667798816307629387216160252600980549857433105900712831277544371292370549804795575532309526186391072428085042289359631679_<232>] (Ignacio Santos / GMP-ECM B1=3000000 for P37 / July 27, 2023 2023 年 7 月 27 日) Free to factor

2×10²⁹⁰+1349 = (2)₂₈₈52_<290> = 2² × 13 × 2213 × 193093 × 6806338398869_<13> × [146934121590762212817070852048331516496785326369716643797991460143977242900140105971130130945625883070247848787136761730399666188426837138280087852125561617599147127119709853976562223997907976479382952769307411649211898631874123604875706863652321592016649741326411731_<267>] Free to factor

2×10²⁹¹+1349 = (2)₂₈₉52_<291> = 2² × 3² × 7 × 881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548500881834215167548501_<288>

2×10²⁹²+1349 = (2)₂₉₀52_<292> = 2² × 22726672452757913_<17> × [24445090090086554831740652594299399828647308852991867274211284543141892695660576955496545064277160049785455514459689437786810276271686234739229523979309291333989667720351120257550895288795020816034553853559994042754039503267520107501726209518857536043855580439460141035254051_<275>] Free to factor

2×10²⁹³+1349 = (2)₂₉₁52_<293> = 2² × 14747 × 954623 × 9578952193_<10> × 613347749380859_<15> × [67168730343759154558366480973444955564407538548441102601169395454028464949904839041449705630393931552604095605267671294574463772710866457122249653819821205731794475835429223864330092122548088249839733771518710720539736724578445932209523233045749353573964029_<257>] Free to factor

2×10²⁹⁴+1349 = (2)₂₉₂52_<294> = 2² × 3 × 89 × 2153 × 350570663 × 73692478830669894473_<20> × [3740877340706395704872467194214386226556512481732502596499327514028073791496334820892463810457767007260341659810065045655338942483400881242580409066676536602950910785469803229426923620433743236250661424700018079168136820671459859718365137976774898932231219687_<259>] Free to factor

2×10²⁹⁵+1349 = (2)₂₉₃52_<295> = 2² × 149 × 28934975441087_<14> × 81189536787214780091_<20> × 8882992534454319586001903_<25> × 851426341504908065563422414871261421039_<39> × 209851300686555062695037292465440421198104008936397341875119595358390653679242394136408186636493288762042207689634919940773922653895438146512698308403246491878269039668647057906761266934870057683_<195> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1:219784567 for P39 x P195 / February 5, 2022 2022 年 2 月 5 日)

2×10²⁹⁶+1349 = (2)₂₉₄52_<296> = 2² × 13 × 2903 × 148842748360700954983165846861819_<33> × 989029911193974119455151698826669771470958709643450585487316506697031641728813372081822569399301439873444965623159757235560731100368959314042784786421631362275213553845089200773026851834098432505333301768149751522525354714087723871090133509128304895712216243_<258> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3435866227 for P33 / December 21, 2021 2021 年 12 月 21 日) (Eric Jeancolas / ECM for P258 / December 21, 2021 2021 年 12 月 21 日)

2×10²⁹⁷+1349 = (2)₂₉₅52_<297> = 2² × 3 × 7 × 19 × 71 × 853598143 × [2297432650643623519098352361872638105405329948367513935194879598280272690945233846352341040371617989409585084955873343705486748362334382811916237805700913950078898901909474740007791112442020941755138911697622543806837528827187677751130055477146777523385881219551054665708181201207629_<283>] Free to factor

2×10²⁹⁸+1349 = (2)₂₉₆52_<298> = 2² × 17 × 1953567868547_<13> × 337454489809117_<15> × 894863337341717_<15> × 294431921085981601521609075442408171079_<39> × 188145246882789929411722673717420971543332202105456291981488099706734784271682214553405383672694670508812527975781598179230776537082912698260382595648353933018416827898553270334173825545369688819572837355416580553327_<216> (Ignacio Santos / GMP-ECM B1=3000000 for P39 x P216 / July 27, 2023 2023 年 7 月 27 日)

2×10²⁹⁹+1349 = (2)₂₉₇52_<299> = 2² × 1453 × 596612461 × 2194334242231_<13> × 74528677670190329_<17> × 2935543332087175492884419224397602721_<37> × [13349188608303378841660666525832458622072455417519441628582636987089720710813811182993336419607536593769850377074552417214606330551581183529900099526749672011617435650885143557569965715373619739406432733693257463860601709_<221>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:579649155 for P37 / December 21, 2021 2021 年 12 月 21 日) Free to factor

2×10³⁰⁰+1349 = (2)₂₉₈52_<300> = 2² × 3² × 54063407 × 1366606037_<10> × 2334102492748404700070526726639644930551_<40> × [35794666239996513271384786834929561756030087082327932804449108702553277418362205755023429744788153139213134141476707073373375535492429172542245090234723351549821637895425248726967760927401617015999870866306676998946780291046294611146374784223_<242>] (Dmitry Domanov / GMP-ECM 7.0.5 B1=11000000, sigma=3:600732280 for P40 / January 1, 2022 2022 年 1 月 1 日) Free to factor

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