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-   -   New Fermat factors (https://www.mersenneforum.org/showthread.php?t=15449)

 akruppa 2011-03-24 12:24

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.

 rogue 2011-06-23 10:31

9*2^2543551+1 Divides F2543548, found by PrimeGrid.

 rogue 2011-06-23 21:44

7333*2^138560+1 Divides F(138557), also by PrimeGrid

 rogue 2011-07-02 23:58

3771*2^221676+1 Divides F(221670), by PrimeGrid.

 ET_ 2011-07-06 13:53

43714055 · 2^3337 + 1 divides F(3335), by Nikolay Kamenyuk (FermatSearch).

Luigi :smile:

 rogue 2011-07-09 00:38

4479*2^226618+1 divides F226614, again by PrimeGrid.

 ixfd64 2011-07-09 02:08

Dayam, PrimeGrid is sure on a roll...

 JohnFullspeed 2011-07-09 06:27

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

[URL]http://www.prothsearch.net/fermat.html#Prime[/URL]

John

 Ralf Recker 2011-07-09 06:47

[QUOTE=JohnFullspeed;265912]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

[URL]http://www.prothsearch.net/fermat.html#Prime[/URL]

John[/QUOTE]

F[SUB]14[/SUB] is a little bigger than that:

F[SUB]14[/SUB] = 2[SUP]2[SUP]14[/SUP][/SUP]+1 = 2[SUP]16384[/SUP]+1 = 116928085873074369829035993834596371340386703423373313 · C4880

Tests were conducted up to 7*10[SUP]14[/SUP]*2[SUP]16[/SUP]+1

Another way to write the known factor is: 1784180997819127957596374417642156545110881094717 * 2[SUP]16[/SUP]+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
[/CODE]A quick look at the coefficient is enough to see that this factor most likely wasn't found by trial division :smile:
[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
[/CODE]

 ET_ 2011-07-09 10:54

[QUOTE=rogue;265899]4479*2^226618+1 divides F226614, again by PrimeGrid.[/QUOTE]

Any official announcement link?

Luigi

 Ralf Recker 2011-07-09 12:16

[QUOTE=ET_;265937]Any official announcement link?

Luigi[/QUOTE]
Not yet.

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