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Old 2011-03-24, 12:24   #12
akruppa
 
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If you want multiplications modulo Fermat numbers, you should call the Schönhage-Strassen code in GMP directly (mul_fft) since it has an implicit modulus 2^n+1. That should give you a factor 2 speedup and asymptotically O(n log(n) log(log(n))) run-time.
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Old 2011-06-23, 10:31   #13
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9*2^2543551+1 Divides F2543548, found by PrimeGrid.
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Old 2011-06-23, 21:44   #14
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7333*2^138560+1 Divides F(138557), also by PrimeGrid
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Old 2011-07-02, 23:58   #15
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3771*2^221676+1 Divides F(221670), by PrimeGrid.
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Old 2011-07-06, 13:53   #16
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43714055 · 2^3337 + 1 divides F(3335), by Nikolay Kamenyuk (FermatSearch).

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Old 2011-07-09, 00:38   #17
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4479*2^226618+1 divides F226614, again by PrimeGrid.
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Old 2011-07-09, 02:08   #18
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Dayam, PrimeGrid is sure on a roll...
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Old 2011-07-09, 06:27   #19
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Could you confirm me that I have well understand

F14= 116928085873074369829035993834596371340386703423373313
the only factor find is 319546020820551643220672513
and all primes less than 700000000000000 have been tested

http://www.prothsearch.net/fermat.html#Prime

John
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Old 2011-07-09, 06:47   #20
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Quote:
Originally Posted by JohnFullspeed View Post
Could you confirm me that I have well understand

F14= 116928085873074369829035993834596371340386703423373313
the only factor find is 319546020820551643220672513
and all primes less than 700000000000000 have been tested

http://www.prothsearch.net/fermat.html#Prime

John
F14 is a little bigger than that:

F14 = 22[SUP]14[/SUP]+1 = 216384+1 = 116928085873074369829035993834596371340386703423373313 · C4880

Tests were conducted up to 7*1014*216+1

Another way to write the known factor is: 1784180997819127957596374417642156545110881094717 * 216+1

Code:
Sat Jul  9 09:28:17 2011 : --------------------------------------------------
Sat Jul  9 09:28:17 2011 : Found a factor for F14: 1784180997819127957596374417642156545110881094717*2^16+1
Sat Jul  9 09:28:17 2011 : 
Sat Jul  9 09:28:17 2011 : Current k  : 1784180997819127957596374417642156545110881094717
Sat Jul  9 09:28:17 2011 : Tested ks  : 94718
Sat Jul  9 09:28:17 2011 : 
Sat Jul  9 09:28:17 2011 : Sieving to : 1742539 [131073. Prime]
Sat Jul  9 09:28:17 2011 : 
Sat Jul  9 09:28:17 2011 : Step       : F14-1 mod (k*2^16+1).
Sat Jul  9 09:28:17 2011 : 
Sat Jul  9 09:28:17 2011 : Work time  : 0:00:00:00
A quick look at the coefficient is enough to see that this factor most likely wasn't found by trial division
Code:
Sat Jul  9 09:35:21 2011 : Speed      :
Sat Jul  9 09:35:21 2011 : 
Sat Jul  9 09:35:21 2011 :             22409390 k / second

Last fiddled with by Ralf Recker on 2011-07-09 at 07:39 Reason: Notation.
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Old 2011-07-09, 10:54   #21
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Quote:
Originally Posted by rogue View Post
4479*2^226618+1 divides F226614, again by PrimeGrid.
Any official announcement link?

Luigi
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Old 2011-07-09, 12:16   #22
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Quote:
Originally Posted by ET_ View Post
Any official announcement link?

Luigi
Not yet.
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