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 2019-08-16, 07:40 #331 axn     Jun 2003 123D16 Posts 133k-134k Code: 2^133087+1 = 453329102262294084723811 2^133109+1 = 3351248134854989099561 2^133109+1 = 36736921530912909763 2^133121+1 = 104201581276589219755481 2^133153+1 = 330553571607227777 2^133283+1 = 3549308659841553779607377 2^133283+1 = 7682849126487918604777 2^133319+1 = 250385176098144673 2^133319+1 = 4829643637184032939 2^133387+1 = 6342848219618436741377 2^133417+1 = 400313097624860129151977 2^133439+1 = 543243902132295186407161 2^133451+1 = 1612955449488790027 2^133481+1 = 99391448451815168641 2^133543+1 = 18663661033020198715202993 2^133543+1 = 36147461494085054457910529 2^133583+1 = 35456297117032534187 2^133649+1 = 49522392533768721059 2^133669+1 = 1114178544553122193 2^133709+1 = 719007773784874667 2^133831+1 = 151360784493193073 2^133843+1 = 1602938397236867909251339 2^133843+1 = 264072449460645848369 2^133853+1 = 41882464188467210441624291 2^133873+1 = 94516718399025953 2^133877+1 = 13538203739965294014649 2^133949+1 = 276349827110954772712561 2^133963+1 = 149899857045836076961 2^133993+1 = 54661018474564521924097 2^133999+1 = 136699326402532043 2^133999+1 = 83173639538609169883
 2019-08-31, 13:38 #332 axn     Jun 2003 7×23×29 Posts 134k-135k Code: 2^134047+1 = 458551050120241153 2^134053+1 = 27938326875565281641 2^134089+1 = 66344718054731194051 2^134089+1 = 92566509206414883037797577 2^134161+1 = 7886156762440588666577 2^134171+1 = 266530723582396614123473 2^134257+1 = 197415670685852491 2^134257+1 = 3165550681360518348419 2^134263+1 = 53318470364671215113 2^134269+1 = 128604613958729177 2^134339+1 = 406367116822645339 2^134399+1 = 1463074782954436535969 2^134399+1 = 388878093712809981717990841 2^134437+1 = 167164161088501937267521 2^134591+1 = 271039207452607646489219 2^134591+1 = 405747390664898489 2^134593+1 = 41855356193894704121 2^134677+1 = 593955502467205138859 2^134681+1 = 63836537872015054200411956411 2^134731+1 = 20152946935171133641 2^134807+1 = 1415822143214064270259 2^134807+1 = 1738726745448518513 2^134837+1 = 3237446683991379428879923 2^134837+1 = 445780390413190969009 2^134873+1 = 1458440525691571848850219 2^134873+1 = 205758686362155200584964723 2^134909+1 = 413735673912308929
 2019-09-14, 11:33 #333 axn     Jun 2003 7×23×29 Posts 135k-136k Code: 2^135043+1 = 123303916692400034900377 2^135043+1 = 46932312558114182811329 2^135049+1 = 951114340402710131 2^135089+1 = 198042930307632426296689 2^135101+1 = 88923883105222936307 2^135277+1 = 13844776221479612391359371 2^135277+1 = 679855536257354497 2^135329+1 = 88819179686681454611 2^135353+1 = 539390878052607511081 2^135367+1 = 1424221120037978369 2^135403+1 = 404374137201466757974720371218930399789339 2^135409+1 = 10075388732614430321 2^135467+1 = 3048199543152586499 2^135497+1 = 4087170515698284803 2^135497+1 = 59754231852741041281 2^135533+1 = 64503922863684527202961 2^135581+1 = 1637695521606285073 2^135593+1 = 2477273653317372437085403 2^135607+1 = 2317576572399241082939 2^135607+1 = 45893256909212164394587537 2^135617+1 = 226425059354163492883 2^135617+1 = 6828708088740832339 2^135623+1 = 5408603765659842193 2^135647+1 = 5025057265217846077583569228961 2^135649+1 = 11312844108831608873 2^135649+1 = 2021824423274156793806011 2^135661+1 = 714971474894103017 2^135719+1 = 960126630499930509804401 2^135727+1 = 468768835964743987 2^135757+1 = 6036810497331614963 2^135781+1 = 511534316793850921222153 2^135787+1 = 4158839988816074835153523 2^135829+1 = 276641211647482515499 2^135851+1 = 37648782586804124475299761843528048620693787079441528872193 2^135851+1 = 9912215698640939767969 2^135851+1 = 991795322102135777 2^135893+1 = 176202089257358120329 2^135913+1 = 1007816287916049673 2^135913+1 = 166555091819125207118299 2^135977+1 = 63277326542273164817
 2019-09-29, 02:05 #334 axn     Jun 2003 123D16 Posts 136k-137k Code: 2^136027+1 = 3027599141758609819 2^136043+1 = 325842482373398219 2^136139+1 = 951503412092958217915913 2^136189+1 = 11563589698961263993 2^136189+1 = 959641937031951347 2^136193+1 = 37733407716702752009 2^136303+1 = 23265971948486843561 2^136303+1 = 3580357798007590183217 2^136319+1 = 82470779166238979216473 2^136397+1 = 144776139445280228105641 2^136453+1 = 156711957441178049 2^136453+1 = 474287986813848073609 2^136541+1 = 8476499283711862241 2^136603+1 = 15402453301791689027 2^136651+1 = 192707313094821563 2^136693+1 = 1044830121654814211 2^136727+1 = 109985911945908882195547 2^136753+1 = 17817248396750009861539618273 2^136753+1 = 29847412617949680673 2^136813+1 = 2413491717791990987 2^136841+1 = 303916128847568363717659 2^136849+1 = 1009138986256845482763787 2^136849+1 = 36274808869332645467 2^136861+1 = 230307114859192177 2^136889+1 = 13199868500333955928121 2^136889+1 = 149116525235882371 2^136889+1 = 947513007463808816916433 2^136897+1 = 278362767808056634481 2^136949+1 = 725457158703046706530409 2^136951+1 = 206772060714324753397681 2^136963+1 = 5027181616178147347 2^136979+1 = 983224043380450049 2^136991+1 = 13724303468553156379 2^136993+1 = 288960060670846541203 Taking a temporary break.
2019-09-30, 04:05   #335
GP2

Sep 2003

A1316 Posts

Quote:
 Originally Posted by axn Taking a temporary break.
Thanks for all your efforts up to this point.

As always, Wagstaff-related data is available at http://mprime.s3-website.us-west-1.a....com/wagstaff/

2019-10-10, 21:13   #336
GP2

Sep 2003

2,579 Posts

2^5743+1 is now fully factored. However, M5743 is not.

Exponents 7417 and 8849 are fully factored as both Mersenne numbers and Wagstaff numbers. Almost a year ago, I wondered if that wasn't a coincidence (click on the > icon below to read the reasoning in the original post).

Quote:
 Originally Posted by GP2 (Click on the > icon to read the original post)
I started doing deeper ECM on Wagstaff exponents under 10k, to try to create new cases where the same exponent was fully factored in both cases.

So far I've found 61 new Wagstaff factors for very small exponents, but only two of them resulted in new PRPs: exponents 5261 and just today, 5743. And of course various people including Ryan Propper have been finding new Mersenne factors for very small exponents with much deeper ECM.

But there are still no doubly fully-factored exponents other than 7417 and 8849 (and much smaller exponents where it's hardly unusual for them to be fully factored, the largest of which are 1193, 1279, 1459).

2019-10-11, 16:13   #337
axn

Jun 2003

7·23·29 Posts

Quote:
 Originally Posted by GP2 2^5743+1 is now fully factored
... and certified.

Congratulations

 2019-12-04, 13:42 #338 axn     Jun 2003 7×23×29 Posts 137k-138k Code: 2^137131+1 = 265192503004348610276393 2^137209+1 = 325448681397255884371 2^137219+1 = 2301308500567444738609 2^137239+1 = 9819212986550632433 2^137251+1 = 111839258802768975126521 2^137359+1 = 19692787436755739729 2^137387+1 = 191500409981045273 2^137437+1 = 12424045758414564820272889 2^137437+1 = 140380469176933313 2^137437+1 = 17273129105552341649 2^137437+1 = 3251904111129641131 2^137443+1 = 518201485359944387 2^137447+1 = 40910441205871188257 2^137453+1 = 38617754679653469401 2^137483+1 = 2645734560747394049 2^137491+1 = 11736790270878540543431051 2^137491+1 = 16122173996427013313 2^137507+1 = 536832885187840618448921 2^137567+1 = 5130855963228473 2^137587+1 = 31331429139299 2^137597+1 = 42510106685163097 2^137653+1 = 17966607213001 2^137707+1 = 13370301643695611 2^137707+1 = 592758373181385446377 2^137713+1 = 678116686045697 2^137723+1 = 7452253650510043 2^137771+1 = 721746915583691 2^137827+1 = 10001873225057422727353 2^137831+1 = 1045210024504627 2^137869+1 = 388943275849304602980612139 2^137873+1 = 1762495764078694161203 2^137983+1 = 5306718932989217 2^137993+1 = 15312867978376758099137 There will be some known factors as factordb was not available while preparing the worktodo.
 2019-12-13, 09:11 #339 axn     Jun 2003 10010001111012 Posts 138k-139k Code: 2^138007+1 = 10582086549836801291 2^138053+1 = 380792657401641191687521 2^138373+1 = 2610131839658149123475611 2^138403+1 = 5736695208051537601 2^138461+1 = 3207292823618646813155881141259 2^138511+1 = 71883818725201402005731 2^138547+1 = 16766226123181039390883 2^138547+1 = 8635412590464642058939 2^138563+1 = 1552890640069632336467 2^138581+1 = 85040022771016627 2^138599+1 = 118700921877185607716041 2^138629+1 = 2094111627438975931 2^138629+1 = 321906673282915619 2^138647+1 = 28163071861713235384403 2^138661+1 = 52676191348661515790969243 2^138683+1 = 7098795005607261331 2^138793+1 = 30267921156976098993953 2^138797+1 = 814989689103951189023617 2^138799+1 = 144772705260460775784401 2^138841+1 = 1723171067798010113 2^138863+1 = 10906437909197106257 Last fiddled with by axn on 2019-12-13 at 09:11
 2019-12-28, 06:06 #340 axn     Jun 2003 10010001111012 Posts 139k-140k Code: 2^139109+1 = 232901527497762293385571 2^139121+1 = 2748135663696293579 2^139123+1 = 144834293192245512587 2^139133+1 = 135249101784022350964739 2^139169+1 = 6833785971336806122647841 2^139273+1 = 403707106206774067 2^139291+1 = 176731201325093882563 2^139303+1 = 21161845438388854327561 2^139333+1 = 3780919371435556323569 2^139393+1 = 41915218600911416707 2^139423+1 = 192692015044480459 2^139423+1 = 7914151425713333513 2^139429+1 = 164938712030987651 2^139457+1 = 1604057597011403803520833 2^139457+1 = 27559316522031652297 2^139483+1 = 16141276954868227553 2^139511+1 = 823522945729052939 2^139547+1 = 168286091283720731 2^139619+1 = 4814315853824769913 2^139661+1 = 22143916187498246166089 2^139663+1 = 3195615102067962988012121 2^139681+1 = 642638717263461947699059 2^139697+1 = 2473244696010346349209 2^139703+1 = 1732287483485125979 2^139709+1 = 80900761562355467 2^139721+1 = 14093748534448965379378753291 2^139729+1 = 425779850240099253523 2^139747+1 = 4435439168292693329 2^139801+1 = 172147453827121182961 2^139837+1 = 133923044162410483 2^139907+1 = 11590132907577462409 2^139907+1 = 2327308434820250857 2^139907+1 = 61337367506195041571 2^139921+1 = 75969755935623092048369 2^139991+1 = 2474496757849085982827
 2020-01-11, 11:56 #341 axn     Jun 2003 7×23×29 Posts Another t25 on 137k-139k Code: 2^137147+1 = 28894310756788960796853689 2^137153+1 = 925985372364737241928601 2^137413+1 = 1403935141664544940921627 2^137413+1 = 4443801572645338006979 2^137483+1 = 190159853041802194800331 2^137597+1 = 43987475667364577473063283 2^137633+1 = 2804620285384763160341723 2^137743+1 = 201474912510791815628126963 2^138163+1 = 18292524171995335882906688539169 2^138449+1 = 525002284628826303656299 2^138563+1 = 14262822575931023754694057 2^138577+1 = 248056677547191379189283 2^138599+1 = 14738540602990299961765057

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