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

[paulunderwood]

Congrats again

time ./pfgw64 -k -f0 -od -q"(2^9181+1)/3/3011369/76784137749059091145875053513/830850377585029456002515680049587" | ../../coding/gwnum//bpsw-2 - 1 2 9181 1
                                               
Testing (2*x)^((n + 1)/2) == -2 (mod n, x^2 - 9*x + 1)...
Likely prime!

real	0m0.600s
user	0m0.328s
sys	0m0.024s

[paulunderwood]

Originally Posted by axn

ECM found a factor in curve #160, stage #1
Sigma=54626733384473, B1=1000000, B2=100000000.
2^9181+1 has a factor: 76784137749059091145875053513 (ECM curve 160, B1=1000000, B2=100000000)
Cofactor is a probable prime!

So, (2^9181+1)/3 = 3011369 · 76784137749059091145875053513 · 830850377585029456002515680049587 · PRP2695

Note that the p33 was already known, but the p29 was missed. And the p29 was found in stage 1 !!

Someone want to take a crack at a juicy PRP2695?

That should not take Primo a long time to prove.

[axn]

93k-96k

2^93001+1 = 13744425055923816992411
2^93059+1 = 812334798111654241
2^93077+1 = 63299563986510730633
2^93083+1 = 68259027888543693457
2^93103+1 = 34207268600198531
2^93103+1 = 37071449024261357842249
2^93169+1 = 5727062687274848779
2^93179+1 = 20078412822489768841
2^93229+1 = 939584799186068466947
2^93241+1 = 3778521656575496325128443
2^93251+1 = 930577510290473
2^93283+1 = 740870310129969137
2^93287+1 = 5764428381514513
2^93287+1 = 7718689223866507
2^93307+1 = 15285653767400751934097
2^93307+1 = 9321950497097470297873523
2^93323+1 = 143496334074667267
2^93323+1 = 2208565311452188807883
2^93383+1 = 162580840485131
2^93407+1 = 1546390279590512009
2^93479+1 = 513851049050083
2^93497+1 = 2583904067662441499
2^93503+1 = 344775577707073
2^93503+1 = 8664649853494518347
2^93523+1 = 13847764441619833
2^93563+1 = 103295270378059
2^93581+1 = 697903278768926809
2^93701+1 = 239765148153331
2^93701+1 = 7517720098185022217
2^93719+1 = 399089727103655633
2^93761+1 = 651243774388169
2^93761+1 = 9830883632650343666930411243
2^93763+1 = 524346886103897
2^93811+1 = 3199129231931715083726115593
2^93893+1 = 7143473692046833
2^93901+1 = 13019341692860473
2^93901+1 = 623317986153275275307
2^93937+1 = 3999457171091361327377
2^93979+1 = 2117005202117483198539
2^93997+1 = 143538967266923
2^93997+1 = 37108584799857279489073
2^94007+1 = 11949964406685420794963
2^94009+1 = 166243987228940611
2^94049+1 = 147520930173737902547
2^94049+1 = 1514914601287301017
2^94049+1 = 5650364380795577
2^94117+1 = 2243895624665402921
2^94121+1 = 248992472375703769
2^94153+1 = 261476009935867845011683
2^94169+1 = 887910193812993097407337
2^94219+1 = 15179209059689799826312411
2^94219+1 = 28782004487799189156113
2^94219+1 = 7269028858966928563
2^94219+1 = 75651401056749949143481
2^94291+1 = 14975308419198577
2^94291+1 = 39624005418646739
2^94327+1 = 262563619758217
2^94327+1 = 41335816463415570472531
2^94351+1 = 1347675889558089313
2^94379+1 = 297986408742294123113147
2^94397+1 = 167208522114896626153
2^94399+1 = 2755437910877074523
2^94433+1 = 19451309034942216527681
2^94439+1 = 40325948381469680051
2^94447+1 = 3490043240442217
2^94483+1 = 436836185755839179371
2^94543+1 = 653553905209889107
2^94547+1 = 421574522878459
2^94547+1 = 825879298992830824556838787
2^94559+1 = 38075714101039232001193
2^94561+1 = 2450234300530533930419
2^94597+1 = 40383937842417123855161
2^94603+1 = 272610652737971
2^94621+1 = 310400785659639179
2^94649+1 = 1597990066629779
2^94687+1 = 663056134955097538763
2^94709+1 = 701891799284859736692206051
2^94727+1 = 2497919529511829483
2^94771+1 = 48874108171142525897
2^94771+1 = 787227040800658820617
2^94777+1 = 11602183099371209083
2^94789+1 = 21038773316323938121
2^94793+1 = 1879568282825730551617
2^94811+1 = 2148329961202874458601
2^94823+1 = 591804735425585270376211
2^94933+1 = 22940108546427063731
2^94933+1 = 369594467953793
2^94949+1 = 1369840871938840129
2^94961+1 = 152074402717024975512683
2^94961+1 = 98703644485855792651
2^94999+1 = 12436250356844428987779779
2^95063+1 = 155748361152563203291
2^95063+1 = 1564962497411674084187
2^95107+1 = 107715190508581379
2^95111+1 = 104048433818617
2^95143+1 = 198701843233339993
2^95153+1 = 1260883994234698320451
2^95153+1 = 69720179311951900939
2^95177+1 = 1138543230950999827
2^95239+1 = 307811488616758707697
2^95257+1 = 1738711857617699
2^95257+1 = 3555040961482880173657
2^95279+1 = 17594484882340685873
2^95287+1 = 19980712161844006732307
2^95327+1 = 12790940787309931
2^95327+1 = 3791160361770572230681
2^95339+1 = 342564658515118673
2^95383+1 = 848606186094905959979
2^95401+1 = 1741112842144619
2^95401+1 = 30612399784386075176467939
2^95443+1 = 1355682230259985415295611
2^95467+1 = 12161752843008694019
2^95467+1 = 256013403506887046949937
2^95467+1 = 724794291236158327153
2^95471+1 = 49562804389443080227
2^95483+1 = 787120775213401
2^95507+1 = 1004943086851001
2^95507+1 = 3416046669680459
2^95527+1 = 1242714171842737811963
2^95569+1 = 74325704889242493209
2^95581+1 = 65884124564130113
2^95581+1 = 9592936004391958187491
2^95603+1 = 776479891078135290247667
2^95633+1 = 32055938578310360699
2^95651+1 = 1088744548112142119908921
2^95651+1 = 48573029969233013830784083
2^95707+1 = 38143394293510890550619
2^95731+1 = 2458185244296307
2^95737+1 = 15096455641830881
2^95737+1 = 214849044042811769
2^95737+1 = 660419822807929
2^95783+1 = 10751699252886713825603
2^95819+1 = 390809021486801
2^95869+1 = 132886331574353823385939
2^95869+1 = 854145482660425913
2^95971+1 = 4969917621352679729

[DukeBG]

Ok, since noone still uploaded a cert for that PRP2695, i'll do it then.

[axn]

96k-100k

2^96001+1 = 29767258628107316819
2^96013+1 = 1074062209085419541841673
2^96059+1 = 162271396235077769
2^96059+1 = 20512561145349960215675737
2^96079+1 = 39853885691623733272441
2^96149+1 = 1267670031135796879290547
2^96181+1 = 1562575760853467
2^96181+1 = 4007722130435761
2^96221+1 = 44037051941095219
2^96233+1 = 1185623668212455203
2^96263+1 = 160566383673660547939
2^96263+1 = 3158222404244412047329
2^96269+1 = 1548599154891831184721
2^96269+1 = 1860502872298768793
2^96337+1 = 435649543301037672707
2^96353+1 = 314407631381596999426811227
2^96401+1 = 2802994608065303519689
2^96401+1 = 5711563827628019
2^96443+1 = 292171176753089
2^96443+1 = 5615664589725452306953
2^96451+1 = 3368804501343929513
2^96461+1 = 155013189693361
2^96461+1 = 231703520947331
2^96469+1 = 320787082864072929109211
2^96479+1 = 14286832806147281360579
2^96493+1 = 3144148189426106687137
2^96527+1 = 214317110285594417
2^96553+1 = 142572499472297
2^96589+1 = 178693936137068179
2^96589+1 = 457065989038013497
2^96661+1 = 334575205692201996331
2^96731+1 = 4093111383382080931
2^96739+1 = 14272248893509138536689
2^96757+1 = 10906820693119187
2^96757+1 = 6475518092372133264569
2^96763+1 = 484745206418193961
2^96763+1 = 68704402071619676498528059
2^96847+1 = 16278825648714713496179
2^96893+1 = 21860035804117719347
2^97001+1 = 6323433518478887453009
2^97007+1 = 2919520998904749881
2^97073+1 = 13108033656310688129
2^97073+1 = 28188797235272619766259
2^97073+1 = 9863128724570411009
2^97081+1 = 37997114714506275971
2^97103+1 = 646582148549901711361
2^97169+1 = 192580760045809
2^97177+1 = 726564097045651
2^97241+1 = 212246581189403
2^97241+1 = 6973894407688699889
2^97259+1 = 1557828531578176056833
2^97283+1 = 213350641219987
2^97303+1 = 17360942024884000019
2^97367+1 = 394359267905704628281
2^97387+1 = 1184686534292445731
2^97429+1 = 60175019356103987
2^97441+1 = 1670478734921369810188185521
2^97459+1 = 565306383931518998497
2^97459+1 = 67427656986769546969
2^97499+1 = 1026481948021709054213579
2^97499+1 = 347130741513187
2^97499+1 = 36284001069947387
2^97501+1 = 328557552611617072938553
2^97501+1 = 43283615473583504939
2^97501+1 = 7902421905950283211
2^97547+1 = 5494965405945903024091
2^97549+1 = 3207878769085809763883
2^97553+1 = 22356781474632417519812251
2^97571+1 = 23608466666870205161
2^97571+1 = 770583394973772403
2^97577+1 = 46931258519544749459
2^97583+1 = 224554429504671907
2^97583+1 = 2955030691318006678043
2^97609+1 = 25687897097511983641243
2^97613+1 = 181964747330961479587
2^97613+1 = 338773060886835769
2^97649+1 = 2021994048123593310579083
2^97777+1 = 280868367534778339
2^97787+1 = 483780424355370043729
2^97813+1 = 936727200377960867
2^97843+1 = 2234972710366886629038569
2^97919+1 = 492417738210785603
2^97943+1 = 426494208265479313
2^98011+1 = 39106146691855183489
2^98017+1 = 302038062458172328321507
2^98047+1 = 67049977459938481149793
2^98123+1 = 1878817043441920993
2^98123+1 = 3667334414342827
2^98129+1 = 2484647951593393
2^98129+1 = 50060806747597721
2^98179+1 = 454899938128553841947
2^98207+1 = 14227482997804963
2^98227+1 = 60938591664197241322955489
2^98251+1 = 1113136956482270075347
2^98251+1 = 641202077069369
2^98297+1 = 14501842174986825374003
2^98299+1 = 110868633842069531
2^98321+1 = 160239344512375953890050217
2^98327+1 = 1254709843262062153
2^98347+1 = 298337992547059337
2^98387+1 = 46347629908531249255187
2^98389+1 = 400187257242041
2^98407+1 = 517038810573070638371
2^98407+1 = 82785375216088825801
2^98407+1 = 987418132994436355609
2^98411+1 = 39185070939485121113
2^98429+1 = 2466250991913053767243139
2^98453+1 = 2266725956110324283
2^98467+1 = 1138778298908267
2^98479+1 = 15150366101928966938179
2^98491+1 = 478546518345264619
2^98561+1 = 131909422022394644532379
2^98563+1 = 509536599316961
2^98621+1 = 47029159981184713
2^98627+1 = 1850676398834609179
2^98639+1 = 105531571954139
2^98639+1 = 4612949520652126956933971
2^98689+1 = 171309063220465996729
2^98711+1 = 55377473890208664731
2^98717+1 = 64479879981329803
2^98729+1 = 154621438680906947
2^98729+1 = 6817329680592233610331
2^98779+1 = 99990810853902221601043
2^98809+1 = 7281671108520441346033
2^98873+1 = 1704796827253871587
2^98873+1 = 37084837271396231125507
2^98893+1 = 1706296511260147
2^98893+1 = 71477325864973849
2^98899+1 = 35575692015878171
2^98911+1 = 329434637599762393
2^98911+1 = 627533926598142859
2^98929+1 = 1845544993023440853073
2^98939+1 = 12085096429740050092522577
2^98939+1 = 221098704494393592458659
2^98939+1 = 31542297979461977239008523
2^98953+1 = 11215665208046306057
2^98953+1 = 571657825074737
2^98981+1 = 16811033392044817320158348325259
2^98981+1 = 32438991475815066222313
2^98981+1 = 73277570035096032353634553
2^98993+1 = 91444367272985953
2^98993+1 = 98098060359565102156553
2^98999+1 = 1051299667269040394483
2^98999+1 = 38461666007346763838345473
2^99013+1 = 17279923859372716057
2^99041+1 = 11264740878746521
2^99041+1 = 28843535851083319422403
2^99053+1 = 38926586794750859
2^99079+1 = 11062205977817611
2^99079+1 = 1936502015480521
2^99089+1 = 834465867780470973001
2^99089+1 = 9008408934029613169
2^99133+1 = 1590360090075257
2^99133+1 = 3886669924917862729
2^99137+1 = 4852645561922463979
2^99149+1 = 2806267196992899569
2^99149+1 = 611664983327010241
2^99173+1 = 34117345390446566429876483
2^99181+1 = 1429330789505633472713
2^99191+1 = 2586809772952026403
2^99241+1 = 141936170324449378568443
2^99241+1 = 594534674660569
2^99277+1 = 137735140213676980057
2^99277+1 = 47819621653128877322977
2^99317+1 = 11120228658226147
2^99349+1 = 12181448518519827635339
2^99367+1 = 7682051224167095803193
2^99391+1 = 1799299151631295913
2^99397+1 = 53375555142562615629371
2^99409+1 = 141334122256753
2^99431+1 = 12172936497590971640963
2^99469+1 = 1039733312799687579377
2^99469+1 = 16942130366484989507987
2^99469+1 = 40450480970809649
2^99469+1 = 632609919374777
2^99487+1 = 13874905407710027
2^99523+1 = 34399598608921528523
2^99527+1 = 35435947200240513193
2^99551+1 = 118646658835324603
2^99551+1 = 956620131867689
2^99563+1 = 97559166174873817291
2^99571+1 = 2794271080961462753767169
2^99607+1 = 130373578560167962112307817
2^99623+1 = 3906368490735110522777
2^99643+1 = 17912196731662598513563
2^99643+1 = 448204908352752089827
2^99667+1 = 34872671165705318168507
2^99679+1 = 509833420640384323725001
2^99713+1 = 1408106736245825121017
2^99721+1 = 803326104268803977
2^99793+1 = 345231747036597680656560489989737
2^99793+1 = 57024817298211817963
2^99809+1 = 4144518991661456011
2^99859+1 = 676669031242767095260921
2^99871+1 = 186316649204205313193
2^99871+1 = 26692861657976342060873
2^99871+1 = 3588603004538820773969
2^99881+1 = 53186256007200218401
2^99881+1 = 566631967992209316697393
2^99929+1 = 2530207524851137580146374617
2^99961+1 = 1623728942646841
2^99961+1 = 2902878543528934211

[axn]

9-9.5k to t35

2^9391+1 has a factor: 15053695523301896080196014623082123 (ECM curve 556, B1=1000000, B2=100000000)
2^9397+1 has a factor: 142431182933424549568492130623460569 (ECM curve 863, B1=1000000, B2=100000000)
2^9277+1 has a factor: 43121574137546761051397200211457141787 (ECM curve 558, B1=1000000, B2=100000000)
2^9181+1 has a factor: 76784137749059091145875053513 (ECM curve 160, B1=1000000, B2=100000000)
2^9137+1 has a factor: 3327060733378993953616723390060019 (ECM curve 218, B1=1000000, B2=100000000)

[GP2]

With ECM to t40 on Wagstaff exponents from 3000 to 4000, the following factors were discovered:

2^3011+1=1816619272155487791560717448516519693937
2^3089+1=13839103247628681510101111834057993
2^3109+1=590010984386508367122063204267363841,73386299644848640204126072658168681,83316512557326177817598047246790849469030361
2^3167+1=33152238124362923032373534255518409
2^3319+1=3252360285900453519800855046203605362811
2^3373+1=2542916407539550917982537085402937903019
2^3433+1=166596781182097605569132789924365551329
2^3449+1=1237042874546529851324382493065770076641153
2^3533+1=22073945862359767285266685333132481441427377
2^3571+1=1222019590737291558255575120183884699,276256789208754723404276460523
2^3581+1=148503017368476924146456255256881776747
2^3637+1=4079937169947205097853033549950017
2^3739+1=13394841132851831667530611640122193957306923
2^3793+1=84623495188538318097610966381339248486660083
2^3823+1=3221770714648236848248157965151857
2^3943+1=361015976299864394671296312524737187
2^3947+1=7499425548876402914429380134327605947

Unfortunately, none of them resulted in PRP cofactors. Maybe the 4k range will have some.

[axn]

2^100129+1 = 25688950465586276971
2^100153+1 = 10720388598267921491
2^100153+1 = 5804229203262904241929
2^100169+1 = 5224437302402897057
2^100183+1 = 1788066096394188801297139
2^100213+1 = 56427141679506021889
2^100313+1 = 295567952996905219
2^100361+1 = 346316081878860965891
2^100417+1 = 1079676713189299073
2^100447+1 = 8547924742232949613889
2^100483+1 = 2698219793672669380817
2^100517+1 = 547364738235344753
2^100523+1 = 28611607422832825133073563
2^100523+1 = 503050835622099817487651
2^100547+1 = 10416634164049354099
2^100613+1 = 23139905183450018500441
2^100649+1 = 294840528094662732841
2^100673+1 = 6836026999276557292565963
2^100741+1 = 511058179677748106800931
2^100747+1 = 16014062648121269297
2^100747+1 = 311493111436876123
2^100769+1 = 251704259406499772489
2^100799+1 = 15600106075574524619
2^100847+1 = 10897918234335228638929
2^100913+1 = 113047892664847606451
2^100931+1 = 41855348903947886537
2^100937+1 = 164914506066167955151163
2^101009+1 = 908005007023408875265297
2^101009+1 = 93918088342486619
2^101021+1 = 21562997855965633201
2^101027+1 = 628229657566606649
2^101081+1 = 357475580384275799911963
2^101089+1 = 3619771874989322264378243849
2^101107+1 = 7613068550525042390829227
2^101111+1 = 2584883841472434449659979
2^101113+1 = 330267544782864993851467
2^101159+1 = 6183893989348928753
2^101173+1 = 3277923133271759729
2^101173+1 = 355523335501340051284009
2^101197+1 = 90597010926048481
2^101203+1 = 473122075605766319233
2^101273+1 = 12642834809888473417
2^101279+1 = 5022803416251338281
2^101287+1 = 13540811660726487718969
2^101323+1 = 3100799453710889645579
2^101359+1 = 28938775713646528309193
2^101399+1 = 1534971040557222903499
2^101411+1 = 161002222537092210419
2^101429+1 = 16005524784003474113
2^101429+1 = 181163111425417912817177
2^101429+1 = 5062240980850911964753
2^101477+1 = 587811113797798660102771
2^101489+1 = 1800762843842270840963
2^101489+1 = 40798751767261835647169
2^101513+1 = 2405834159029917937259
2^101527+1 = 12076299431481925159078043
2^101537+1 = 6925989208339669730257
2^101561+1 = 3855946849405070079889
2^101611+1 = 385472013663595196017
2^101611+1 = 647534575861668288991051
2^101611+1 = 769829805249776603
2^101681+1 = 241823992867052143169
2^101693+1 = 4700534847636745529
2^101723+1 = 137144872755949430419
2^101737+1 = 143993392494482339
2^101737+1 = 268867336515506694425479147
2^101737+1 = 556160539329438675713
2^101749+1 = 595442369433608483
2^101749+1 = 980704466315833219
2^101837+1 = 11030690951278414627
2^101869+1 = 6486800532155769521273
2^101921+1 = 3267585635210320049020097
2^101921+1 = 77398645622382749756761
2^101957+1 = 78485507759851289
2^101987+1 = 1688174075177787927803
2^101999+1 = 329009834647766099

[axn]

ECM found a factor in curve #79, stage #2
Sigma=8182130021064353, B1=50000, B2=5000000.
2^102299+1 has a factor: 338189324089623539623841 (ECM curve 79, B1=50000, B2=5000000)

I guess at this size P95 doesn't do PRP testing of the cofactor, because factordb tells me...
(2^102299+1)/3 = 28439123 · 338189324089623539623841 · PRP30764

No factoring at all, not even trivial division
Primality testing (2^102299+1)/28853423355215000601173363794329 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000001257801520.txt
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX FFT length 10K, Pass1=128, Pass2=80 on A 102195-bit number
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction AVX FFT length 10K, Pass1=128, Pass2=80 on A 102195-bit number
Calling N+1 BLS with factored part 0.05% and helper 0.03% (0.19% proof)
(2^102299+1)/28853423355215000601173363794329 is Fermat and Lucas PRP! (117.4538s+0.0049s)

[GP2]

Originally Posted by axn

ECM found a factor in curve #79, stage #2
Sigma=8182130021064353, B1=50000, B2=5000000.
2^102299+1 has a factor: 338189324089623539623841 (ECM curve 79, B1=50000, B2=5000000)

I guess at this size P95 doesn't do PRP testing of the cofactor, because factordb tells me...
(2^102299+1)/3 = 28439123 · 338189324089623539623841 · PRP30764

Yes, at some point the PRP test is no longer quick and Prime95/mprime no longer does it.

Since we have 2048-bit PRP residues for all Wagstaff exponents under 2M, I automatically run Gerbicz cofactor-compositeness tests whenever new factors are discovered in this exponent range. This test is much faster than a PRP test, although it can only find probable probable primes as opposed to actual probable primes.

[axn]

2^102001+1 = 770957355196573817
2^102079+1 = 24715796754544855891
2^102101+1 = 12170646087469408474433
2^102103+1 = 2851129637373075299332307
2^102107+1 = 87729566611955022309827
2^102149+1 = 17030667459639752873
2^102199+1 = 2371496814296641421393
2^102233+1 = 653638095872549987
2^102253+1 = 601892013365499238937
2^102299+1 = 338189324089623539623841
2^102329+1 = 6366383123951716845872953
2^102407+1 = 792658079943930763
2^102437+1 = 28737481410188638753
2^102481+1 = 2568630649986400787
2^102497+1 = 156684370103469559042723
2^102593+1 = 2835946408661279641702033963
2^102593+1 = 644356899066626499176483377
2^102653+1 = 434623901028640506804688609
2^102667+1 = 4439541201846151702289
2^102673+1 = 278110463166412691
2^102701+1 = 539666767691108505137
2^102763+1 = 1131690627764983729
2^102811+1 = 1613814476488071564011
2^102811+1 = 318299121313111129
2^102859+1 = 484380393296447905171
2^102871+1 = 12506148369290004281467
2^102911+1 = 23662826326380733621578601
2^102911+1 = 305263125371843323
2^102967+1 = 149200424330765900075777
2^103043+1 = 51277801637576309569
2^103091+1 = 152869215642589561
2^103141+1 = 394938112991962822222403
2^103349+1 = 4081333819139643086561
2^103357+1 = 4756568416003264507
2^103391+1 = 68101445363099340166627
2^103393+1 = 10228565389305891542801
2^103483+1 = 545479572042715043545859
2^103511+1 = 25040709626341385243
2^103511+1 = 266028644197546057
2^103529+1 = 17247595841289024490627
2^103529+1 = 558738320230445777
2^103573+1 = 83752106816548187
2^103591+1 = 13101945417247648130243
2^103591+1 = 3385545668142041249
2^103613+1 = 361381298945183177
2^103651+1 = 2644776401279444978683
2^103657+1 = 110200328776177067
2^103657+1 = 33512316529708162073
2^103681+1 = 1177347314478393859
2^103699+1 = 112440922024027952708141417417
2^103723+1 = 1903675371358138162033387
2^103787+1 = 33992952804543935619217
2^103801+1 = 5759197660361442089227
2^103843+1 = 11967141655671278707
2^103867+1 = 55299272873204625443
2^103963+1 = 2186395828481780070721
2^103969+1 = 12889088730074545475083