[QUOTE=axn;520434]This would go as #2 on [url]http://www.ellipsa.eu/public/primo/top20.html#PrimoRecord[/url] (if it were to be attempted).

How many core years do you estimate to prove this one?

EDIT:- Just missed paul's edit. The question still stands.[/QUOTE]

I took some 14 months on a 48 core AMD 6174 @ 2.2GHz for similarly sized numbers -- but now Primo is quicker. 14 months is an upper bound -- say 1 year on such a machine. Much quicker on a 64 core AMD 7 series EPYC.

Congratulations on the PRP for 114743

There are smaller Wagstaff exponents with uncertified PRPs: 31601, 32369, 32377, 35677, 35851, 41269, 53759, 62581, 70921, 80819, 83423, 85517, 91159, 102299

There are also these uncertified Wagstaff prime exponents: 95369, 117239. Also the prime for 42737 has an old-fashioned certificate (that maybe can be verified with the Maple program, I'm not sure) rather than a Primo certificate.

A lot of work if anyone wanted to tackle it.

PS,
Also Mersenne PRPs with exponents 78737, 82939, 84211, 86137, 86371, 87691, 106391

Well, can Phi(2^n-1,2) or Phi(2^n+1,2) be prime for any n>7?

W5261 has a 48-digit factor: 726665169300701944892064737622954607252115216339

The [URL="http://factordb.com/index.php?id=1100000001321603291"]cofactor is a probable prime[/URL].

[QUOTE=GP2;520639]W5261 has a 48-digit factor: 726665169300701944892064737622954607252115216339

The [URL="http://factordb.com/index.php?id=1100000001321603291"]cofactor is a probable prime[/URL].[/QUOTE]

:w00t: Now [B]there's[/B] an easily provable PRP

[QUOTE=axn;520645]:w00t: Now [B]there's[/B] an easily provable PRP[/QUOTE]

And it's already proven.

It was an extremely lucky hit. I was only doing t=40, yet it found a 48-digit factor after less than 700 curves. The recommended curves for GMP-ECM version 7 are 2753 for t=40, 5208 for t=45, and 8704 for t=50.

[QUOTE=GP2;520442]Congratulations on the PRP for 114743

There are smaller Wagstaff exponents with uncertified PRPs: 31601, 32369, 32377, 35677, 35851, 41269, 53759, 62581, 70921, 80819, 83423, 85517, 91159, 102299
[/QUOTE]

I have done the Primo certification for the cofactor of W31601: [url]http://factordb.com/index.php?id=1100000001188126321[/url]

[QUOTE=Dylan14;520971]I have done the Primo certification for the cofactor of W31601: [url]http://factordb.com/index.php?id=1100000001188126321[/url][/QUOTE]

How long did it take? What about doing the next few in the list!

[QUOTE=paulunderwood;520975]How long did it take? What about doing the next few in the list![/QUOTE]

It took 476222s or about 132.3 hours to do on an Intel i5-6400. I’ll tackle the next one after I finish doing the factorization of 7*2^705+1.

116k-120k
 

[CODE]2^116027+1 = 1094948183730961067
2^116041+1 = 875417328300133222062491
2^116107+1 = 33626844482729187593
2^116131+1 = 739645302376182091
2^116159+1 = 179145631566848627
2^116167+1 = 41899885901495539086683
2^116201+1 = 2407642862916145633
2^116257+1 = 138257604673229579
2^116269+1 = 19150533962363051561
2^116269+1 = 720083625776105056559113
2^116329+1 = 12216621437032852097
2^116341+1 = 10062744754478490220067
2^116381+1 = 127062909322205450715203
2^116387+1 = 205592347123322633
2^116443+1 = 3114110896328363999633
2^116447+1 = 111184444974432443
2^116507+1 = 1591460436684305286377
2^116537+1 = 75228214722812123929163
2^116657+1 = 1818929739775860043
2^116687+1 = 295829766978263867
2^116747+1 = 374622899681277683
2^116791+1 = 62613492812492702137
2^116797+1 = 1081653129441765543731
2^116819+1 = 3366170498848051547
2^116819+1 = 5106576796786142819
2^116827+1 = 55771861387027615307
2^116833+1 = 468588970251220033
2^116849+1 = 279134565031287987169
2^116911+1 = 103678486688819575699
2^116911+1 = 2249530050218151929
2^116927+1 = 30752583258150148123
2^116933+1 = 394113607716969035840921
2^116959+1 = 2083333502281749852097
2^116969+1 = 8582767342918392361
2^117041+1 = 3572912173607115501737
2^117071+1 = 1688736755086524313
2^117163+1 = 5000015678314113109763779
2^117191+1 = 3653937140571010802441521
2^117209+1 = 40631584084964272450660963
2^117223+1 = 1805225763028126814377
2^117251+1 = 4170691322154920027
2^117269+1 = 55133324588505798121
2^117269+1 = 5704547556095894792651
2^117319+1 = 31987648662520046153113777
2^117329+1 = 137372153092377817
2^117331+1 = 132682310882544744883
2^117353+1 = 320759980930197529354649
2^117361+1 = 309908197417095938483
2^117373+1 = 329429988641312969
2^117413+1 = 32955651356054043707
2^117427+1 = 2003014686302828025497
2^117511+1 = 332288325402446836963
2^117511+1 = 6674162418797361113
2^117541+1 = 887345979788572702609
2^117671+1 = 206536857424011203
2^117703+1 = 213676532369079817
2^117731+1 = 75432528690664859975803
2^117751+1 = 3038575121094904529
2^117773+1 = 7766103721887637105769
2^117779+1 = 4231200140792321611
2^117787+1 = 13080610077166964659
2^117833+1 = 56942952127191081180397699
2^117841+1 = 221156122802321317379
2^117841+1 = 287862923757807787
2^117881+1 = 2328991366385630539
2^117881+1 = 25194006846584492840841881
2^117899+1 = 13015499294608066378901079137
2^117911+1 = 53492712431598453931
2^117973+1 = 4023022306412156923
2^117979+1 = 1075710170288319043
2^117979+1 = 166315609681197959977087081
2^117991+1 = 47194043904265092217
2^118037+1 = 13896405384590865601
2^118043+1 = 2737140250271512931
2^118081+1 = 33529997052604238980291
2^118093+1 = 329186739812397017690233
2^118127+1 = 1345536558742490507
2^118147+1 = 676354058229929539
2^118211+1 = 13822173369178444847323
2^118213+1 = 60261385225871872907
2^118249+1 = 248640562949083849
2^118277+1 = 420988692530926441
2^118409+1 = 788201449342169179
2^118411+1 = 33209953725170651502937
2^118457+1 = 100403275081323002128409
2^118571+1 = 24775852199867639549199717419
2^118619+1 = 21671515740250258601
2^118669+1 = 608865230673060783725763888313
2^118687+1 = 173547405203339249
2^118709+1 = 91405902970136389321
2^118739+1 = 4656171238367965139
2^118799+1 = 179478376173077813267
2^118843+1 = 190133356384827784339
2^118901+1 = 2271967370902372706267
2^118907+1 = 266012175155350846656700249
2^118973+1 = 43549919260451553335857
2^119033+1 = 373629052645234003
2^119047+1 = 1396308816561565112177
2^119057+1 = 21486798664432140043
2^119069+1 = 141784855234764587599406251
2^119069+1 = 221721729748451909371
2^119101+1 = 20097879346272135085107611
2^119159+1 = 20077616943792160494160067654230691
2^119183+1 = 359198876945936529776250707
2^119191+1 = 8849852009221809357001
2^119227+1 = 5768395206976039241
2^119243+1 = 583144619442294945932497
2^119299+1 = 8373217461424855163353
2^119321+1 = 1211599729053906402673
2^119389+1 = 43768762857937907819
2^119447+1 = 23089647113601483083
2^119513+1 = 34635552772941576423937
2^119549+1 = 80627231877070169
2^119551+1 = 65849176302934384980883
2^119569+1 = 1694762095697562740969
2^119611+1 = 3950578164333541369
2^119671+1 = 12792891279373416923
2^119677+1 = 141030535859196289
2^119677+1 = 280653631721040307
2^119689+1 = 265185385790827550541403
2^119689+1 = 930524117144940089
2^119737+1 = 12677551905220734593
2^119737+1 = 271976908307887259
2^119737+1 = 2762925719490783233051557961
2^119747+1 = 185763013501621418657
2^119747+1 = 22441276635930409578611
2^119771+1 = 13520193560065116593
2^119773+1 = 478383994637331292403
2^119809+1 = 5140221356489006546747
2^119813+1 = 629737739428024219
2^119839+1 = 22340608462138988994257
2^119891+1 = 536348139222587514817
2^119971+1 = 23586149201893829699
2^119971+1 = 334101038086380794210483
2^119981+1 = 29211163456925200704553
2^119981+1 = 3320252131980218843[/CODE]
114k-116k is being worked on on a slower 'puter

120k-125k
 

[CODE]2^120017+1 = 39071791252947189017
2^120067+1 = 15983024328677785993
2^120079+1 = 6845714964170128939
2^120079+1 = 79735112578475952331
2^120091+1 = 4560192026327877113
2^120121+1 = 3329137765337185043010331
2^120163+1 = 3746432206888058082713
2^120167+1 = 412318403576107204593779
2^120181+1 = 217160370505065521
2^120199+1 = 2213378176385917217092291
2^120199+1 = 3858499736845275715690001
2^120277+1 = 1245766777845727513
2^120293+1 = 1083950572768438552643
2^120299+1 = 134720134464355922227
2^120319+1 = 17982344164275868483
2^120331+1 = 2965410264358240853353
2^120397+1 = 5571107416909689116405246803
2^120401+1 = 169348138478806841653793
2^120511+1 = 26055186938975045301233233
2^120551+1 = 81349070127459649
2^120569+1 = 260942838791334043
2^120619+1 = 4299835901357861897083
2^120623+1 = 1107110847220040059
2^120623+1 = 117663335121127441
2^120671+1 = 224262498752590931
2^120677+1 = 26696521478492684747
2^120689+1 = 1180225456101339371
2^120691+1 = 87378383989222342417
2^120709+1 = 252840731214797881
2^120713+1 = 53933721700181677187123
2^120713+1 = 651282378973209517867
2^120739+1 = 44181797757191946887449
2^120767+1 = 13837647510757656403
2^120767+1 = 5848308331971222851
2^120779+1 = 255785654792484169
2^120779+1 = 29103964035990653291
2^120811+1 = 60845463996880937603
2^120851+1 = 1433092016799833165089
2^120877+1 = 261667141414722486259
2^120889+1 = 4952116122519865729
2^120907+1 = 5325573807272687083
2^120929+1 = 12055994725031690734287843979
2^120929+1 = 2416978350479852507
2^120929+1 = 82478601287117450883161
2^120941+1 = 565236633048027209803
2^120941+1 = 71939119934628226393123
2^120947+1 = 5700742623890364303552713
2^120977+1 = 1048606264957915268248531
2^121001+1 = 13972679292375693833
2^121001+1 = 3624038016747135773282291
2^121013+1 = 163954660356148877080427
2^121081+1 = 4451816223089256713
2^121081+1 = 741944793257913359845067
2^121139+1 = 617928598904413561
2^121157+1 = 3936270279370822861987
2^121169+1 = 44765272162840196147
2^121181+1 = 6558521264321548427
2^121189+1 = 638877403433201450657
2^121229+1 = 3195685569749564621827
2^121267+1 = 1521907641774009863938403
2^121271+1 = 1124216602994929206307
2^121283+1 = 1946167783555619371987
2^121283+1 = 3438700117191194729
2^121333+1 = 51568528891031573208779
2^121343+1 = 26331988270490965483
2^121379+1 = 12296426529426281267
2^121403+1 = 12388495725094498282650323
2^121447+1 = 6034204864641947559953
2^121487+1 = 10256245172773264437775338913
2^121493+1 = 383780071653380166883
2^121501+1 = 50782766985321694553731
2^121523+1 = 12612705932592106239427
2^121523+1 = 3744662291963733987290011
2^121547+1 = 1365917940095463449
2^121571+1 = 244070468504740070233
2^121577+1 = 75711182320655009
2^121591+1 = 6248582637105021620260859323
2^121607+1 = 497252638229898233
2^121609+1 = 111998316776585100163
2^121637+1 = 172542708522574535002298741185465054896721
2^121661+1 = 535272823375092377483
2^121697+1 = 103879866058868428171
2^121763+1 = 579284672367160607297
2^121843+1 = 385942423874258759539
2^121883+1 = 15219318721364049663460661254609
2^121909+1 = 2147224090110499112683
2^121909+1 = 380521287390164879169492961
2^121993+1 = 2482267850659025183250859507
2^121997+1 = 547652447522824206481033
2^122033+1 = 13295973934566202272251
2^122039+1 = 1875751493205301286857
2^122081+1 = 90671880070452569627
2^122149+1 = 45716890977294117121
2^122167+1 = 1424549171933711266819
2^122207+1 = 31962576674946109889
2^122231+1 = 18291091349323833601572397387
2^122263+1 = 24327115811784029401
2^122263+1 = 98994582267383281
2^122273+1 = 102504968015533236563
2^122279+1 = 11523494771756083093889
2^122323+1 = 20506436259404376233
2^122323+1 = 31096848713829790249
2^122363+1 = 3151569707162213459
2^122399+1 = 175018069577117483513
2^122399+1 = 42798575027701262756923
2^122399+1 = 859307981040829039871080427
2^122453+1 = 175018333848423075323
2^122477+1 = 81056019784997603
2^122497+1 = 1967734894337843107
2^122503+1 = 233398034421571639931
2^122509+1 = 164182377375735497
2^122527+1 = 80485862463052153
2^122527+1 = 887619447285557812152165409
2^122579+1 = 2946565906928898920517569
2^122597+1 = 6020473364341837812881
2^122651+1 = 52371757520436335379659
2^122693+1 = 7112574506762220889
2^122701+1 = 115582494910435019
2^122743+1 = 140836708381005976771
2^122753+1 = 20725045499649761414251
2^122819+1 = 21393602588051783135329
2^122849+1 = 23893176794527080544771507
2^123017+1 = 111118002986292793
2^123031+1 = 1400095406682076499
2^123031+1 = 1909319568202697249
2^123059+1 = 125919610809973155233
2^123059+1 = 471262112428028147
2^123121+1 = 3226221698211264144787
2^123127+1 = 7930870541085943036321899211
2^123169+1 = 285513437807029273
2^123191+1 = 32859580075237686523
2^123229+1 = 345467060810506009
2^123269+1 = 152825375598579179
2^123269+1 = 170191612675323611
2^123269+1 = 86666253241166447791577
2^123289+1 = 201452966985911347523
2^123289+1 = 3905265455416896713
2^123289+1 = 729153586235104728544361
2^123311+1 = 823895633369705779
2^123323+1 = 6989359599899046233
2^123373+1 = 19490478928354584979001
2^123379+1 = 2674623067040480757059
2^123407+1 = 151659085914896514667
2^123427+1 = 41702311407108949894793
2^123439+1 = 22356140321377503951553
2^123457+1 = 301183871038130099
2^123517+1 = 22475325310035701436667
2^123593+1 = 4368630713238355307
2^123637+1 = 625201599412133123
2^123653+1 = 248657993660342852774753
2^123707+1 = 817809063261943369251937
2^123803+1 = 15186695433777024483583921
2^123817+1 = 143487431508597289
2^123829+1 = 763968061159561385876633
2^123887+1 = 4274038081285071299
2^123911+1 = 14406550018015417697
2^123953+1 = 11441963493410219914699
2^123953+1 = 8466140130495607559833
2^124021+1 = 3237507914864886624361
2^124067+1 = 657078625778954083
2^124087+1 = 161013434916056369
2^124133+1 = 5072828094915000595481
2^124193+1 = 219541474269980636334563
2^124199+1 = 18596467835523415477871971
2^124249+1 = 173858299304886192101297
2^124303+1 = 35710891007093245113683
2^124303+1 = 407519984834066324713
2^124303+1 = 751593266218284132641
2^124337+1 = 14566581597435247268923
2^124339+1 = 96220904072049534160489
2^124429+1 = 3056167505697890019083
2^124447+1 = 33374452821572406563
2^124541+1 = 1034944733005775086549921
2^124601+1 = 11129786568398675996699
2^124601+1 = 386238465708100187131
2^124643+1 = 126825656591742375217
2^124643+1 = 1882431603335293417249
2^124693+1 = 13615129719355117297
2^124703+1 = 481499969777245667
2^124717+1 = 6987832051499927362856347
2^124721+1 = 13871977244770208507
2^124777+1 = 4883441354464665313
2^124793+1 = 51699052562325677127720833
2^124823+1 = 45410756838701026374368771
2^124909+1 = 74328289301748395737
2^124909+1 = 934861200933283121
2^124987+1 = 17838917614651494631147
2^124987+1 = 311397204222338401[/CODE]