20100327, 19:33  #1 
"Mike"
Aug 2002
7×1,171 Posts 
F12
F_{12} has a factor:
568630647535356955169033410940867804839360742060818433 
20100327, 20:06  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}×7×13^{2} Posts 
Nice!
568630647535356955169033410940867804839360742060818433 = 1 + 2^{15} * 17353230210429594579133099699123162989482444520899 (a prime) Cofactor is still composite. Last fiddled with by Batalov on 20100327 at 20:12 
20100327, 20:14  #3 
P90 years forever!
Aug 2002
Yeehaw, FL
2×3^{3}×139 Posts 
Wow!! Congratulations!
Last fiddled with by Prime95 on 20100327 at 20:14 
20100327, 20:18  #4 
Oct 2004
Austria
2×17×73 Posts 
Nice!
P.S.: 2010  The Year we make Contact with lots of Fermat Factors Edit: When I made no Copy/Paste error, the cofactor is composite. Edit2: Batalov was ~14 minutes faster Last fiddled with by Andi47 on 20100327 at 20:27 
20100327, 20:42  #5 
Banned
"Luigi"
Aug 2002
Team Italia
2·29·83 Posts 
Two in a couple of days!
Mike, was it you that found the factor? Was it with Prime95? PrimeNet didn't record it yet! Congratulations! Luigi P.S. is the cofactor composite? Last fiddled with by ET_ on 20100327 at 21:08 
20100327, 21:11  #6 
Oct 2004
Austria
2482_{10} Posts 
Yes  Batalov has tested it (and I verified it 14 minutes later.), see posts above.
On a P4 the test takes just a few seconds (using Primo). Last fiddled with by Andi47 on 20100327 at 21:13 
20100327, 21:12  #7 
Banned
"Luigi"
Aug 2002
Team Italia
12CE_{16} Posts 

20100327, 23:02  #8 
Dec 2009
89 Posts 
Let C be the 1133digit cofactor of F12. Since gcd(3^(C1)1, C) = 1, C is not a prime power. This means that F12 has at least 8 distinct prime factors.

20100328, 01:13  #9 
"Mike"
Aug 2002
7×1,171 Posts 
Code:
GMPECM 6.2 [powered by GMP 4.2.2] [ECM] Input number is 2296476634...2322001921 (1187 digits) Using special division for factor of 2^4096+1 Using B1=43000000, B2=199103726650, polynomial x^1, sigma=1428526317 dF=32768, k=17, d=324870, d2=11, i0=122 Expected number of curves to find a factor of n digits: 20 25 30 35 40 45 50 55 60 65 2 5 16 60 274 1437 8541 56540 411842 3268425 Step 1 took 3659840ms Estimated memory usage: 848M Initializing tables of differences for F took 8ms Computing roots of F took 2056ms Building F from its roots took 7661ms Computing 1/F took 3720ms Initializing table of differences for G took 212ms Computing roots of G took 1640ms Building G from its roots took 7581ms Computing roots of G took 1648ms Building G from its roots took 7544ms Computing G * H took 2880ms Reducing G * H mod F took 5793ms Computing roots of G took 1648ms Building G from its roots took 7524ms Computing G * H took 2889ms Reducing G * H mod F took 5756ms Computing roots of G took 1652ms Building G from its roots took 7520ms Computing G * H took 2877ms Reducing G * H mod F took 5756ms Computing roots of G took 1668ms Building G from its roots took 7529ms Computing G * H took 2892ms Reducing G * H mod F took 5768ms Computing roots of G took 1648ms Building G from its roots took 7513ms Computing G * H took 2896ms Reducing G * H mod F took 5748ms Computing roots of G took 1648ms Building G from its roots took 7537ms Computing G * H took 2888ms Reducing G * H mod F took 5760ms Computing roots of G took 1648ms Building G from its roots took 7517ms Computing G * H took 2900ms Reducing G * H mod F took 5772ms Computing roots of G took 1673ms Building G from its roots took 7524ms Computing G * H took 2892ms Reducing G * H mod F took 5749ms Computing roots of G took 1648ms Building G from its roots took 7512ms Computing G * H took 2896ms Reducing G * H mod F took 5777ms Computing roots of G took 1644ms Building G from its roots took 7524ms Computing G * H took 2916ms Reducing G * H mod F took 5757ms Computing roots of G took 1648ms Building G from its roots took 7528ms Computing G * H took 2897ms Reducing G * H mod F took 5752ms Computing roots of G took 1668ms Building G from its roots took 7605ms Computing G * H took 2888ms Reducing G * H mod F took 5700ms Computing roots of G took 1640ms Building G from its roots took 7457ms Computing G * H took 2848ms Reducing G * H mod F took 5612ms Computing roots of G took 1628ms Building G from its roots took 7445ms Computing G * H took 2844ms Reducing G * H mod F took 5612ms Computing roots of G took 1628ms Building G from its roots took 7449ms Computing G * H took 2844ms Reducing G * H mod F took 5608ms Computing roots of G took 1628ms Building G from its roots took 7441ms Computing G * H took 2844ms Reducing G * H mod F took 5612ms Computing polyeval(F,G) took 18062ms Computing product of all F(g_i) took 564ms Step 2 took 326281ms ********** Factor found in step 2: 568630647535356955169033410940867804839360742060818433 Found probable prime factor of 54 digits: 568630647535356955169033410940867804839360742060818433 Composite cofactor 40386086203521847842442038116961395908045388225743593887534051882867088867451422279926227658353369309602134937818767935489955578234805439581534625494985324713549730074875381338741302421655631135507379857269344735228428553001352597596691638801743636629329355013511352942721273050339170429834278987040381747960884411851433916486144170476008852597093750739127802680309124526032940172579802008470093339990359384991503503614458710698904103258512429909701566697333753540519871100983916899540657050034590964623607736274756781417764221105569531562147057912826327014822324375878810085123801163054580870423717464500275259286644790292287618742984022979008217487409481420224445378839089353872030913057691176817044086502550278535272750787424451118761716552849620868806555149154293300951201837849814408323169458959040706805689440625767829357238882085766112685307073105174963070427573702738362159098805163558648031695168433171835632969724871377060199849541218845177450315677176119955499412825504179204908105894697957170244421770769366517833025139901383316838896066622320648993411213811241118825043233830644947321875736006536117418021434702300430337 has 1133 digits 
20100328, 01:19  #10 
May 2008
3·5·73 Posts 
obligatory group order:
Code:
[2 4] [3 2] [7 1] [17 1] [293 1] [349 1] [8821 1] [23753 1] [65123 1] [2413097 1] [9027881 1] [23759413 1] [45947380867 1] 
20100328, 02:06  #11 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
