mersenneforum.org New Fermat factors
 Register FAQ Search Today's Posts Mark Forums Read

 2011-03-24, 12:24 #12 akruppa     "Nancy" Aug 2002 Alexandria 46438 Posts 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.
 2011-06-23, 10:31 #13 rogue     "Mark" Apr 2003 Between here and the 23×739 Posts 9*2^2543551+1 Divides F2543548, found by PrimeGrid.
 2011-06-23, 21:44 #14 rogue     "Mark" Apr 2003 Between here and the 23·739 Posts 7333*2^138560+1 Divides F(138557), also by PrimeGrid
 2011-07-02, 23:58 #15 rogue     "Mark" Apr 2003 Between here and the 23×739 Posts 3771*2^221676+1 Divides F(221670), by PrimeGrid.
 2011-07-06, 13:53 #16 ET_ Banned     "Luigi" Aug 2002 Team Italia 2·2,383 Posts 43714055 · 2^3337 + 1 divides F(3335), by Nikolay Kamenyuk (FermatSearch). Luigi
 2011-07-09, 00:38 #17 rogue     "Mark" Apr 2003 Between here and the 23·739 Posts 4479*2^226618+1 divides F226614, again by PrimeGrid.
 2011-07-09, 02:08 #18 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 72×47 Posts Dayam, PrimeGrid is sure on a roll...
 2011-07-09, 06:27 #19 JohnFullspeed   May 2011 France 7×23 Posts Please 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
2011-07-09, 06:47   #20
Ralf Recker

Oct 2010

191 Posts

Quote:
 Originally Posted by JohnFullspeed 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.

2011-07-09, 10:54   #21
ET_
Banned

"Luigi"
Aug 2002
Team Italia

2×2,383 Posts

Quote:
 Originally Posted by rogue 4479*2^226618+1 divides F226614, again by PrimeGrid.

Luigi

2011-07-09, 12:16   #22
Ralf Recker

Oct 2010

191 Posts

Quote:
 Originally Posted by ET_ Any official announcement link? Luigi
Not yet.

 Similar Threads Thread Thread Starter Forum Replies Last Post Batalov Factoring 149 2017-02-20 12:06 yourskadhir Miscellaneous Math 5 2012-12-12 04:18 siegert81 Factoring 1 2011-09-05 23:00 Merfighters Factoring 0 2010-04-13 14:16 UberNumberGeek Factoring 6 2009-06-17 17:22

All times are UTC. The time now is 17:52.

Fri Sep 25 17:52:17 UTC 2020 up 15 days, 15:03, 0 users, load averages: 1.50, 1.51, 1.48