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 2008-11-08, 04:10 #45 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×7×479 Posts Ben, you are not alone with the 3-split (on 11,226+). (My near-repunit is only sweetened by a hidden "nice split".) Code: (25·10^223-1)/3 = 83333...3333 = 157 · C222 C222 = P55 · P55 · P114 P55 = 1306957603596747155756205207527556392595787608690473329 P55 = 3610883731712362153383889046706233893569388374490811951 P114 = 11247...19111 You're right, now we should all wait for the 4-splits!
 2008-11-08, 04:25 #46 bsquared     "Ben" Feb 2007 3,733 Posts I knew I kept good company ;) Nice work!
 2008-11-10, 07:52 #47 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 274B16 Posts And another 3-split! (this one gave us some pain. Two (week-long) BLs in a row finished with trivial dependencies, but ...per aspera ad astra, or whatever. The third one, after some tinkering and hopefully useful future tricks, finished happily.) Factored (with maxal) two numbers: 2^743-3 = 5 . 919915458916081 . p53 . p76 . p80 p53 = 63529018304787469595760994544568916542616709131721179 p76 = 6161956699502951972272816735739214671420490437899755803072697139814876537011 p80 = 25696742367308592212803153065407421670388916498379493992349439722903096813916169 ...and earlier, rather uneventfully, 2^745-3 = 23 . 53 . 59063 . 8186919763171 . 30496310582253756085729536479 . p67 . p109 p67=1574940336399388867361064992577820311163112464508298354353403078649 Now, I'll say, only two factors? That's a surprise, these days. --Serge and maxal
 2008-11-11, 20:28 #48 themaster     Dec 2007 110112 Posts 148655129312786366154326965873005541392573294151300967 i just found this 54 digit factor using ecm with B1=2000 how lucky can u get
2008-11-11, 21:39   #49
bsquared

"Ben"
Feb 2007

3,733 Posts

Quote:
 Originally Posted by themaster 148655129312786366154326965873005541392573294151300967 i just found this 54 digit factor using ecm with B1=2000 how lucky can u get
Apparently pretty lucky, since gmp estimates that it would take an infinite number of curves to find that size factor with that B1. Even finding a 40 digit factor would take on average 3 Teracurves. What magical sigma was used, and what was the input number?

 2008-11-12, 04:21 #50 jrk     May 2008 21078 Posts I call shenanigans.
2008-11-12, 05:51   #51
Andi47

Oct 2004
Austria

2×17×73 Posts

Quote:
 Originally Posted by themaster 148655129312786366154326965873005541392573294151300967 i just found this 54 digit factor using ecm with B1=2000 how lucky can u get
Can you please post the details of the lucky curve?

 2008-11-12, 07:19 #52 10metreh     Nov 2008 91216 Posts If it was on the Alpertron applet, the factor could have been found by the Lehman method, not ECM.
2008-11-12, 07:37   #53
themaster

Dec 2007

33 Posts

Quote:
 Originally Posted by Andi47 Can you please post the details of the lucky curve?
unfortunately i cant i was using a program i had written to call gmp-ecm so i dont have the logs
it was an extremely lucky find
it was a RHP composite

Last fiddled with by themaster on 2008-11-12 at 07:38

 2008-11-24, 19:23 #54 kenta   May 2006 22 Posts My hobby: factoring n-1 for large primes n My hobby: factoring n-1 for large primes n. Consider the twentieth Mersenne prime M20 = 2^4423-1. Then M20-1 = 2*(2^4422-1) = Code: 2 * 3 * 3 * 7 * 23 * 67 * 67 * 89 * 683 * 1609 * 2011 * 4423 * 9649 * 13267 * 20857 * 22111 * 39799 * 283009 * 599479 * 6324667 * 7327657 * 193707721 * 12148690313 * 12371522263 * 361859649163 * 761838257287 * 6713103182899 * 224134035919267 * 3556355492892313 * 5157050159173695487 * 17153597302151518561 * 17904041241938148871927 * 59151549118532676874448563 * 1647072866431538116058878617811 * 87449423397425857942678833145441 * 1963672214729590922916323781834466879 * 49929707724752567469731915956762751258933207272739486748238351859309991348433 * 40393566547943595749562506243285884534929026356774912763863482259566537671583290150415083011252727505582091 * 245646981125691497673324668265536334044341262452177697864695233686173498977525877540362298849614068695233671 * 29792282327632127192280512714312339494458105715740509816040019161219528270861465666941470299423164525021764760664757557501816665197191248140710453823079834899917278481203481942074120698987141443607970695192539694488469929529584413885826254451155851081784465332583575562462448913571987013144129130422035667076921 * 81306434126435390369376308017426816467338589074376606953450887738659949122190481971292960301001128628269985908910250733571484380927682097166969483636698401864705393738719321415525908871375830643489767976984133538274257006197857712319103629206245907496601803359738478994241731519997695185318284051254656008033048015655006605203258597365919579712675545019366698923697429439095730189943 The one notable new factor comes from the primitive part of 2^2211+1, namely 1647072866431538116058878617811 (p31), which was found via ECM. I sent e-mail to Brent. The factorization of the primitive part of 2^2211-1 turned out to be easy: 39799 * 12371522263 * P383 For nineteenth Mersenne prime M19 = 2^4253-1, the factorization of M19-1 is not complete because of (2^1063+1) C281 and 2126M C219. For all smaller Mersenne primes, the factorization of M-1 may be accomplished from the Cunningham tables and other known sources. Of particular note are M18-1 (2^3217-2), which uses Arjen Bot's continuation of the Cunningham tables for 2^1608+1. M16-1 (2^2203-2) was made possible by this year's factorization by Silverman of 2^1101+1. For the next Mersenne prime, 2^9689-2 looks out of reach. I found 8683987649357777 * C1227 for the primitive part of 2^4844+1 (assuming I calculated the primitive part correctly). For the thirty-first Mersenne prime 2^216091-2 = 2*(2^216090-1), and 216090 = 2*3*3*5*7*7*7*7 which is 7-smooth, so 2^216090-1 might be an entertaining target for an ElevenSmooth-like project.
 2008-11-25, 12:08 #55 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3·7·479 Posts taliking about lucky... (32·10^145+13)/9 = 355..557 = 37 · 3197004779 . C135 So, while cracking this C135... Code: > echo 300581646694173102754989957730357512537506582488896855340284419687744533384371572427030444849066320698471799488342573090961576245101059 | ~/bin/ecm -nn -B2scale 2 -sigma 1379705753 3e6 GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 300581646694173102754989957730357512537506582488896855340284419687744533384371572427030444849066320698471799488342573090961576245101059 (135 digits) Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1379705753 Step 1 took 18333ms Step 2 took 15497ms ********** Factor found in step 2: 1331962064897051431769453993617935390404440387816273704654346513 Found composite factor of 64 digits: 1331962064897051431769453993617935390404440387816273704654346513 Probable prime cofactor 225668323907862446214856345291670054173175166345927281111241519005977043 has 72 digits Exit 10 Interesting, huh? P.S. C64 = P30 . P34 (this is not important)

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