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Old 2010-03-27, 19:33   #1
Xyzzy
 
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Post F12

F12 has a factor:

568630647535356955169033410940867804839360742060818433

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Old 2010-03-27, 20:06   #2
Batalov
 
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Nice!

568630647535356955169033410940867804839360742060818433 =
1 + 215 * 17353230210429594579133099699123162989482444520899 (a prime)

Cofactor is still composite.

Last fiddled with by Batalov on 2010-03-27 at 20:12
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Old 2010-03-27, 20:14   #3
Prime95
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Wow!! Congratulations!

Last fiddled with by Prime95 on 2010-03-27 at 20:14
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Old 2010-03-27, 20:18   #4
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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 2010-03-27 at 20:27
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Old 2010-03-27, 20:42   #5
ET_
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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 2010-03-27 at 21:08
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Old 2010-03-27, 21:11   #6
Andi47
 
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Quote:
Originally Posted by ET_ View Post
P.S. is the cofactor composite?
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 2010-03-27 at 21:13
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Old 2010-03-27, 21:12   #7
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Quote:
Originally Posted by Andi47 View Post
Yes - Batalov has tested it (and I verified it 14 minutes later.), see posts above.
Whoops, I was too much in hurry, sorry...

Luigi
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Old 2010-03-27, 23:02   #8
warut
 
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Let C be the 1133-digit cofactor of F12. Since gcd(3^(C-1)-1, C) = 1, C is not a prime power. This means that F12 has at least 8 distinct prime factors.
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Old 2010-03-28, 01:13   #9
Xyzzy
 
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Code:
GMP-ECM 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
http://caramel.loria.fr/f12.txt

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Old 2010-03-28, 01:19   #10
jrk
 
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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]
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Old 2010-03-28, 02:06   #11
Mini-Geek
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Quote:
Originally Posted by jrk View Post
obligatory group order:
For once, the successful group order wasn't ridiculously smoother than the bounds.
23759413 vs
43000000
and
45947380867 vs
199103726650
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