20090720, 04:29  #34 
Einyen
Dec 2003
Denmark
19×181 Posts 
http://primes.utm.edu/glossary/xpage/FermatNumber.html
http://mathworld.wolfram.com/FermatNumber.html Fermat number F_{n} = 2^{2[sup]n}[/sup]+1 and it can be shown that any factor of a fermat number F_{n} is of the form k*2^{n+2}+1. So you found a factor of 2^{2[sup]19}[/sup]+1 = 2^{524288}+1 and the factor: 37590055514133754286524446080499713 = 17924335248057248252165053406 * 2^{21}+1. ( = 8962167624028624126082526703 * 2^{22}+1 factors are usually written with odd k). Here is a list of all known fermat factors: http://www.prothsearch.net/fermat.html The factor was found by Elliptic Curve Factorization Method (ECM) which is a probabilistic method: http://www.mersennewiki.org/index.php/ECM http://en.wikipedia.org/wiki/Lenstra..._factorization Last fiddled with by ATH on 20090720 at 04:37 
20090722, 20:21  #35 
Dec 2008
179_{10} Posts 
Why hasn't anyone proven the compositeness of the cofactor of F25? It's been over ten years since F24 was proven composite, and computers have gotten a lot faster in that time, so it shouldn't take too much effort.

20090722, 20:40  #36  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
1000010110111_{2} Posts 
Quote:
Unless I did something wrong, this is the line you'd use in Prime95: Code:
PRP=1,2,33554432,1,0,0,"25991531462657,204393464266227713,2170072644496392193" 

20090722, 20:42  #37 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Indeed. I think that this worktodo.txt line would work
Code:
PRP=1,2,33554432,1,"25991531462657,204393464266227713,2170072644496392193" Expected time is 19 days on a 2.16 GHz Core 2. Very feasible, but I can't do it at the moment. Anyone want to have a go? Alex 
20090723, 09:53  #38 
Einyen
Dec 2003
Denmark
19·181 Posts 
I started it, and it looks like that line works and known factors check out.
Btw where is documentation for the PRP= line in Prime95? Nothing in readme.txt or undoc.txt. 
20090723, 12:00  #39  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11·389 Posts 
Quote:
Code:
11) Program can now do PRP tests of (k*b^n+c)/f. Add a line worktodo.txt that looks like this: PRP=k,b,n,c[,how_far_factored,tests_saved][,known_factors] The optional how_far_factored (in bits) and tests_saved values are used to determine if P1 factoring prior to the PRP test would be beneficial. The optional known_factors list is a quoted comma separated list of known factors of k*b^n+c. 

20090723, 12:01  #40 
Jul 2009
Tokyo
2×5×61 Posts 
Hi,
I check 4th cofactor of Fermat 25 is conposite. 3^(((2^(2^25)+1)/(48413*2^29+1)/(1522849979*2^27+1)/(16168301139*2^27+1)1)*48413*2^29*1522849979*2^27*16168301139*2^27) != 1 (mod 2^(2^25)+1). Use Fermat Euler Theorem. http://netnews.gotdns.org/WallStreet/6351/gfn/fermat/ 
20090723, 12:07  #41 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 

20090723, 12:22  #42 
Jul 2009
Tokyo
610_{10} Posts 

20090723, 12:28  #43 
"Nancy"
Aug 2002
Alexandria
4643_{8} Posts 
Oh! Right, you multiply the exponent by p1 for the known prime factors. That works, of course.
Alex 
20090723, 20:40  #44 
Dec 2008
B3_{16} Posts 

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