GIMPS' second Fermat factor! - Page 4

sean · 2010-02-03, 18:56

Congratulations. Any factor of F14 was certainly one of the most wanted.

ewmayer · 2010-02-03, 20:50

Very nice - congrats, Tapio, on this exciting discovery!

I'm guessing running lots of ECM is actually a pretty good use of electricity during the cold Finnish winters ... get some useful workout of those voltage pulses before they're converted into heat. ;)

philmoore · 2010-02-03, 22:04

Thanks for the group order. Looks like that factor of F19 did not need a very high B2 bound either.

Here is graph showing all known prime factors of Fermat numbers up through F32. Note the sparsity of factors from F20 through F24, with only two known factors, for F21 and F23. I'm guessing that region is where the next one will show up!

bdodson · 2010-02-04, 02:14

Quote:

Originally Posted by ewmayer

Very nice - congrats, Tapio, on this exciting discovery!

I'm guessing running lots of ECM is actually a pretty good use of electricity during the cold Finnish winters ... get some useful workout of those voltage pulses before they're converted into heat. ;)

Me too, in addition to a reply on the email thread, following Brent's (F11,
F10 by p40). PaulZ's added this to the "news" on the front page of
ECMNET. -Bruce

2010-02-08, 13:32

Does anyone know if this is the smallest factor of F_14? That is, if this new factor is the fourteenth member of this sequence: http://www.research.att.com/~njas/sequences/A093179

/JeppeSN

jasonp · 2010-02-08, 23:03

With all the ECM poured into F14 for so long, I'd be amazed if there was a smaller factor than yours.

philmoore · 2010-02-09, 01:44

On the other hand, with only 1/3 of the curves run at the 55-digit level (15,909 out of 46,500) there certainly would be a reasonable chance of a 51 to 54 digit factor escaping detection so far. I would be surprised of anything 50 digits or less, but even the 35-digit factor of F19 only showed up halfway through the 40-digit level. Only time will tell!

Samidoost · 2010-02-10, 08:42

Congratulations
But I can't believe it yet

congratulations

alpertron · 2010-02-16, 15:30

Me neither.

F14 = a^2+b^2

Code:

a = 1077024116311342878508929288079858580394807158149909786595824390778885788826071410321460933414750884838611087449591864146054131078459423513986857964414131863669675446042967577699582842258400947219447640826319533784515766323634680405593278312680164338559589017695377601614666215969955780060497512245487515758305025120849327064882811515530515033421707678248911625615791787351289639953572500114101283340665834870417650881172383493347222798649836083106802728723457971800991289441629199789378902608107569521233378631850220649211388660777780839653333869070593929561523106674322077571661195493940366092795573327396649577247245099107878410621040281231291953673542851715731096780018733300225579931375623881813212562777850626687340617061634214167697376775489773135314956000669913460476357884216517210253022571286233961898659740467510812600844558542040321240640789153364163050176609911446812574474126064279772757907997107161572536281412138935785386270481491976380871219153288816299340096368503242778300876868247755838816861341855777660444388475431848865509700154504707366782498294266329842320933062744663161217819583698882799032149664330953241194928639805107185122679021637856893621601365009391358429008394356379280469250679643481348278925784426176132918689527822061665458251258341016730557343656453334741345125823876589094855499568443986997105027458080782769227008187990054466707374130845668234507933523304361574044875303862694917648296541590831889808181693445799881780588389672004958764856475561572957165421702438382114973327037963366790269802414104675847767835880257462857589461784615143973754327956936297379223243544575493303508164078042231821062782028040445098282837494288346461938329336402454401839945118277523468026494519099127804112653340995340086637864569538861270212764634620583893845977586421499309568731628875985000078309644234808830512272618078378229890696969436928330797820294152155933466243316476557877051919367400867472605666376885867780362134609224274531352549654988771672807532159143465041495886682546656593043671548611684046165514097426477025250708221388074609220561790116156716088966201308202374708592897082857926169463920642466412402457073518477080890570496135568272621666474892900875617738028933020242093301005821679084666136193968789002538692392931896395087640670098844788566989852243058566527813128033979667238581552166690032163185745664283555910081768978425879987703893059496379932427579769376707336654932118715708638655803894248481259181536111411568104
b = 172483472370551295064279397026888829881698650469875293373390248658975611380374308650127318621548690068096061724869916161363196571311245191740907652499305057760934091915918229051680432261541823347292669818359975238997227368800408856593971277122292419378910107327203046289795635022377008262600604276167410454147332909277203273640244731359559167785721271725060494583440562741372521300731226881558600835799668803097675456387826684172472101488160537448999719869845343850690645740482448554427185680376202124835390818510157740280283741867509074560490991907850277557988045383019704740803161368336345128450457710305478339952628193550646485971262550523273285738259791625259709162634673820910242858711057498618710277763781273935130955819798744107483663534414018212099014288659284654196837195026147486750819814056720948028954094518326624513541854323173098320773892233472663727769307532683875095831031585127890106298987259532797554328360551532547744130527129190179296171808685867731841824786532218780966149615282983976952579855978153815215480731338215620000522042447605086152902202628841349049445528827764843190401315427519993680535022763082487167524376084223057301199971379234767827993158644752100413328876778568460315599117206599955719332594465021891480355349698961196148593692163192476848597318982442823773259077454657804645763037577966726972937684736999081508210983809579649322314568260191835723927325030274762811023108015667567359452225822634173720015701335609136678847524928304711794481225220625094603862953699323089817647595003786610609165995450229469957492182190316653632551345926703978872105431276624995790130777075650450193609604887397844828458866332864191711805284433330305202321429577717431619777525144428931173509775780793708249017242026540253421118712790386952927736122894255303080315162093100237959631205617099294678598480253043323055072337689137791060325039281761606294094949790412810703335158641146285557175109891697182863845711904735615025158674268836530333517860348273776289407191140302948235226737034762758510585086855071326429294553416599299862018692076986467335199981140212057135176296664299715076314837428147191579468638156698310717424830315694641216554453349892212276417174180989561103343865553591237742904656606867960271827583608973344079667605763753635427443050161185018971650919934946323045829030258703548982524893481695467920874097201104813574750179577883235606476610361907400816221036582815754769890755348372463404808959504402404715253177998098174751

Raman · 2010-02-16, 15:47

Quote:

Originally Posted by alpertron

Me neither.

F14 = a^2+b^2

a = 2⁸¹⁹²
b = 1

alpertron · 2010-02-16, 16:42

Quote:

Originally Posted by Raman

a = 2⁸¹⁹²
b = 1

That's the trivial solution.

2010-02-03, 22:04	#36
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2137₈ Posts	Thanks for the group order. Looks like that factor of F19 did not need a very high B2 bound either. Here is graph showing all known prime factors of Fermat numbers up through F32. Note the sparsity of factors from F20 through F24, with only two known factors, for F21 and F23. I'm guessing that region is where the next one will show up! Attached Thumbnails

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2010-02-03, 18:56	#34
sean Aug 2004 New Zealand 11011111₂ Posts	Congratulations. Any factor of F14 was certainly one of the most wanted.

2010-02-03, 20:50	#35
ewmayer ∂²ω=0 Sep 2002 República de California 103×113 Posts	Very nice - congrats, Tapio, on this exciting discovery! I'm guessing running lots of ECM is actually a pretty good use of electricity during the cold Finnish winters ... get some useful workout of those voltage pulses before they're converted into heat. ;)

2010-02-08, 13:32	#38
JeppeSN 7,457 Posts	Does anyone know if this is the smallest factor of F_14? That is, if this new factor is the fourteenth member of this sequence: http://www.research.att.com/~njas/sequences/A093179 /JeppeSN

2010-02-08, 23:03	#39
jasonp Tribal Bullet Oct 2004 3,541 Posts	With all the ECM poured into F14 for so long, I'd be amazed if there was a smaller factor than yours.

2010-02-09, 01:44	#40
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 10001011111₂ Posts	On the other hand, with only 1/3 of the curves run at the 55-digit level (15,909 out of 46,500) there certainly would be a reasonable chance of a 51 to 54 digit factor escaping detection so far. I would be surprised of anything 50 digits or less, but even the 35-digit factor of F19 only showed up halfway through the 40-digit level. Only time will tell!

2010-02-10, 08:42	#41
Samidoost Jul 2003 Chabahar, Iran 2₁₀ Posts	Congratulations But I can't believe it yet congratulations