Status of Wagstaff testing? and testing Mersenne primes for Wagstaff-ness

[axn]

2^185027+1 = 1083777842499641953
2^185027+1 = 89787141833932019
2^185057+1 = 282852866698072157681
2^185077+1 = 16919021276013747377
2^185089+1 = 10900699594074604881521953
2^185089+1 = 221798932094409327898715443
2^185123+1 = 249091823540792164193
2^185131+1 = 614631266097437401961
2^185149+1 = 4632054652645851487481
2^185177+1 = 11070289464064123567067
2^185183+1 = 410204248236457001
2^185299+1 = 2726123297546983707881
2^185303+1 = 22030523950409842310815772731
2^185327+1 = 7004644768153282098139
2^185401+1 = 1377284104461902171
2^185401+1 = 44710542352174493027
2^185467+1 = 1570156116294456363238817
2^185467+1 = 55425949518507998201
2^185467+1 = 93286571979743003
2^185477+1 = 623200626015451653236731
2^185483+1 = 170624566503653489
2^185491+1 = 3055170002964841297
2^185519+1 = 226859023207751855611
2^185531+1 = 531996034759495139
2^185539+1 = 929386990693006986364331
2^185567+1 = 932751605797981486313
2^185599+1 = 592285553429279239544919787
2^185599+1 = 854933907480021563
2^185651+1 = 74158574248997652097
2^185683+1 = 697848717937007996393
2^185693+1 = 27819970850774446813219
2^185723+1 = 21118986264580414108696409
2^185749+1 = 90798595301225353
2^185869+1 = 37595098481095045921
2^185873+1 = 824616873826472953
2^185947+1 = 885397338194474559611
2^185959+1 = 460160292352421660563
2^185987+1 = 2089486125043693379

[axn]

2^186013+1 = 15748083763136456177209
2^186023+1 = 2957528297971240769
2^186023+1 = 3402564142067436324961
2^186103+1 = 19771015720037170163
2^186113+1 = 1264254694532649649
2^186113+1 = 1749334182278066622401
2^186163+1 = 222616039509644431342387
2^186187+1 = 13199271202969862921
2^186187+1 = 20019988696652894179
2^186191+1 = 1897101472028076329457131
2^186191+1 = 990277752466980673
2^186211+1 = 122192835705630923
2^186227+1 = 274495111056860933347
2^186239+1 = 50813940129478179431655089
2^186247+1 = 226624428159729731
2^186253+1 = 56961240657650945537
2^186283+1 = 6672183213705107046161
2^186317+1 = 2045450087818948099
2^186317+1 = 80982142529700619
2^186377+1 = 34268714308628897914763
2^186379+1 = 11612837880807314003843
2^186391+1 = 56563876014079737097
2^186419+1 = 28027979928983244920209
2^186419+1 = 494957124478775099
2^186481+1 = 1751994290017631250661457
2^186583+1 = 1184388217657709619005419
2^186601+1 = 461028278059086467
2^186629+1 = 1797521859941530207393
2^186647+1 = 11631782649413914674204313
2^186647+1 = 226623519555038339113
2^186647+1 = 511832426132525161157602049
2^186649+1 = 1964131017769064219
2^186653+1 = 1147521675240936169758979
2^186701+1 = 607703715843134609
2^186709+1 = 5700471557565950178953
2^186733+1 = 3453877838390317145322721
2^186757+1 = 7302570709281500527673
2^186859+1 = 92018509516509165049
2^186917+1 = 887039887286310624322434971
2^186947+1 = 4763529256011569539681

[sweety439]

Can you give a list for factorization for Phi(n,2), like this factorization for Phi(n,2) for n<=1280, but for larger n, or the base 2 analog of https://stdkmd.net/nrr/repunit/Phin10.txt?

[Dr Sardonicus]

The Main tables for the Cunningham Project give all that is known as of October 13, 2020 for 2^n - 1 and 2^n + 1, odd n < 1300; 2^n + 1, n = 4k-2, n < 2600; and 2^n + 1, n = 4k, n <= 1300.

I'm not sure about what's known for n > 1300, apart from factors found for specific reasons, as in this thread.

[axn]

All known factors should be available in factordb.

[axn]

2^187027+1 = 93280062041601923
2^187067+1 = 167657338910185123
2^187073+1 = 1773547043131252961179
2^187091+1 = 7490974414010726201
2^187111+1 = 12085454218928510429154251
2^187123+1 = 15237076331343916532363
2^187129+1 = 13054812070733883811
2^187141+1 = 2767727424596022073
2^187277+1 = 16648130154426565870451
2^187367+1 = 2851213614560745669761
2^187393+1 = 4325900451522429451666409
2^187409+1 = 23682536026839095233
2^187441+1 = 356811465049602822379
2^187507+1 = 136182070752022075763
2^187531+1 = 234824523235406579
2^187547+1 = 21734337743760654848729
2^187559+1 = 119141644147537859
2^187597+1 = 328082017140957356779
2^187631+1 = 135257665033256813773319179
2^187651+1 = 118958604171619114907
2^187699+1 = 16754593966508176403
2^187763+1 = 1594694862869556281
2^187823+1 = 315252188853125984642449
2^187823+1 = 353873670894420161
2^187843+1 = 1611721668010771099
2^187861+1 = 138185409779245238777
2^187927+1 = 1123741668557525881
2^187931+1 = 4158259200700500195538209227
2^187951+1 = 423208240806304897
2^187963+1 = 3539214169878534957289
2^187963+1 = 386995130744702202497
2^187963+1 = 749025383074373851
2^187973+1 = 79294752365737873

[axn]

2^188107+1 = 653775933513408919963
2^188159+1 = 246535478649675829249
2^188197+1 = 3126305333546483489
2^188261+1 = 78508796621992867771
2^188281+1 = 1339468462911942839796641
2^188291+1 = 316432399448701708057
2^188299+1 = 1449215641848983990873
2^188317+1 = 20255826347594739689
2^188323+1 = 13626867339374301014939
2^188389+1 = 1152245956325215859
2^188389+1 = 1423100990824458577
2^188431+1 = 383433379800251747318593
2^188437+1 = 452845870835898197731
2^188443+1 = 60139930851023701311451
2^188491+1 = 38929236513778615057
2^188491+1 = 549676633329942342276889
2^188527+1 = 756255254682346708297
2^188533+1 = 2659395280293844144571
2^188563+1 = 8292813314933361016417
2^188579+1 = 688881947613892821953
2^188677+1 = 1489516446916178953
2^188681+1 = 1221572281895537235162823811
2^188687+1 = 717281332499277471659
2^188687+1 = 816834003221119411531305189827
2^188701+1 = 26101615273658551387
2^188701+1 = 62596401317613830263217412139
2^188707+1 = 2492133954971603804033
2^188711+1 = 3624492595018154981772401
2^188779+1 = 31065038697319181537
2^188827+1 = 174513165543868729
2^188827+1 = 20013002096740787411
2^188831+1 = 13097121949498115833
2^188831+1 = 1828434873324785953
2^188831+1 = 6649806620616851281361
2^188833+1 = 1212315784226053540849
2^188843+1 = 123330837316977943362011
2^188869+1 = 217359754451105353313
2^188869+1 = 755425547490511889
2^188911+1 = 27325390561826338337
2^188911+1 = 6229945467543243091
2^188933+1 = 270142109645531707
2^188933+1 = 3972925038423008816779
2^188939+1 = 314063757512756512344619
2^188941+1 = 141027751669759132883
2^188953+1 = 4024513545065700361
2^188983+1 = 32607615694265360899
2^188999+1 = 278952816848830355483639081
2^188999+1 = 31028514562606473370097

[axn]

2^189011+1 = 2507085911135037069449033
2^189017+1 = 91509819679994113
2^189067+1 = 518379693187305883
2^189127+1 = 172362306382997453347
2^189127+1 = 235186328400822452963
2^189139+1 = 564699739349407470019
2^189239+1 = 18700318729635760587899
2^189253+1 = 814719423304107641
2^189257+1 = 42236768932837975600331
2^189347+1 = 2207587847359101209
2^189361+1 = 256035024256050635747
2^189361+1 = 475342587776255066279011
2^189377+1 = 63331044268486688347427
2^189389+1 = 8601556032018421763
2^189421+1 = 115060887756225619193
2^189437+1 = 75899758083816027655793633
2^189473+1 = 195257878771001947273
2^189491+1 = 319477165871282342449
2^189517+1 = 161470381016653649
2^189529+1 = 1345938364415133107
2^189529+1 = 16159541445823648294547
2^189547+1 = 86651282271389107
2^189583+1 = 41442341065252218871602763
2^189583+1 = 50582790450651796147
2^189583+1 = 6611324380294792241
2^189643+1 = 110550538577484863227
2^189671+1 = 2114152432906445401129534601
2^189691+1 = 258188420009499086003536513
2^189701+1 = 2441840025800070251
2^189767+1 = 2600436807019268827
2^189799+1 = 452281133650851883747
2^189817+1 = 21903853750525520843
2^189851+1 = 1008165824700201179
2^189851+1 = 90605075601528767513737
2^189949+1 = 93046626903765627794041
2^189967+1 = 84913293937093744875721

[sweety439]

Have all exponents <= 13372531 (the largest known Wagstaff exponent, found in 2013) been tested?

[paulunderwood]

Originally Posted by sweety439

Have all exponents <= 13372531 (the largest known Wagstaff exponent, found in 2013) been tested?

Unknown. We tested up to 10^7. Ryan worked independently to find the two records.

[axn]

2^190031+1 = 48077710933058669722529
2^190093+1 = 55135981143431058671257
2^190121+1 = 38477336342052106777
2^190147+1 = 7832399627127774994007131
2^190271+1 = 96566573425033830294859
2^190297+1 = 74368920726189611
2^190301+1 = 173366336948763307
2^190321+1 = 93677236942153794073
2^190537+1 = 4439215131533896825193
2^190543+1 = 288142184650394248123
2^190543+1 = 5901989372124472593064363
2^190573+1 = 9453550385425692517739
2^190583+1 = 1638182801273110454304073
2^190633+1 = 1124811022503483353
2^190633+1 = 94536947316200563
2^190667+1 = 1887551580498981451
2^190667+1 = 554561060381422935481
2^190711+1 = 7270624885258188731
2^190807+1 = 1789398360174779668481
2^190811+1 = 96798035688331655203
2^190843+1 = 32984909840919336035804449
2^190843+1 = 362659467865533744368059
2^190871+1 = 24789912272846936441
2^190913+1 = 6449646901771763228449
2^190997+1 = 153084291836130139