20110315, 00:58  #1 
Jul 2009
Hobart, Australia
11 Posts 
New factor for F17
Found a new factor for F17 using prime95
[Mon Mar 14 15:03:04 2011] ECM found a factor in curve #3, stage #2 Sigma=10717701036773, B1=44000000, B2=4400000000. UID: Buckle/G826, F17 has a factor: 7751061099802522589358967058392886922693580423169, AID: ECC0BE7A98422FA33606BA70798F5D21 whats the best way to check cofactor status? 
20110315, 01:14  #2 
Bemusing Prompter
"Danny"
Dec 2002
California
2^{3}×3^{3}×11 Posts 
Congratulations. :D
The fastest method for checking the cofactor is probably a Fermat PRP test. If it does turn out to be a probable prime, then we'll need a (slower) deterministic in order to know that it's actually prime. The fastest known deterministic algorithm is ECPP; unfortunately, at around 39,000 digits, such a number would be currently beyond what ECPP can do in a reasonable amount of time. On the other hand, maybe you'll be the lucky discoverer of a Mersenne prime soon! Last fiddled with by ixfd64 on 20191018 at 20:46 
20110315, 01:20  #3 
Einyen
Dec 2003
Denmark
2^{10}×3 Posts 
Congratulations on another Fermat factor!
You can do a Fermat PRP test with Prime95. Add this to worktodo.txt: PRP=1,2,131072,1,"31065037602817,7751061099802522589358967058392886922693580423169" This means it checks 1*2^131073+1 = 2^(2^17)+1 and divides by the known factor 31065037602817 from here: http://www.prothsearch.net/fermat.html and your new factor. 
20110315, 01:22  #4  
Nov 2003
2^{2}·5·373 Posts 
Quote:


20110315, 01:35  #5 
Dec 2009
59_{16} Posts 
Congratulations!
I've added the factor to FactorDB. Can't wait to see if the cofactor is composite or not. 
20110315, 01:41  #6  
Bemusing Prompter
"Danny"
Dec 2002
California
2376_{10} Posts 
Assuming I did this correctly:
Quote:


20110315, 01:42  #7 
Einyen
Dec 2003
Denmark
2^{10}×3 Posts 
Group order is:
[ <2, 2>, <3, 1>, <541, 1>, <2713, 1>, <5153, 1>, <23773, 1>, <152363, 1>, <239387, 1>, <19359383, 1>, <22095751, 1>, <230254627, 1> ] calculation stolen from here: http://www.mersenneforum.org/showpos...0&postcount=69 Factor would have been found with a much smaller B2. 
20110315, 01:58  #8 
Einyen
Dec 2003
Denmark
2^{10}×3 Posts 
p1 = 2^19 * 229 * 9920257 * 49765687 * 860444447189 * 151977745250209
p+1 = 2 * 3^2 * 5 * 7 * 43003 * 286102634397324165621481818300343273307753 P1 would have required B1=10^{12} and B2=2*10^{14} to find the factor. Not *totally* unrealistic but would have taken a very long time on a 39444 digit number. 
20110315, 02:13  #9 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Confirmed with PFGW:
Code:
PFGW Version 3.4.4.32BIT.20101104.Win_Dev [GWNUM 26.4] Generic modular reduction using generic reduction Core2 type1 FFT length 16K, Pass1=64, Pass2=256 on A 130865bit number (2^(2^17)+1)/31065037602817/7751061099802522589358967058392886922693580423169 is composite: RES64: [6EF4AD31682CD751] (95.3671s+0.0139s) Done. 
20110315, 02:33  #10 
P90 years forever!
Aug 2002
Yeehaw, FL
11×673 Posts 
Congratulations! Your hard work has paid off again.

20110315, 02:39  #11 
Einyen
Dec 2003
Denmark
2^{10}·3 Posts 
The last 2 years have been very nice for Fermat ECM factors:
Jul 18th 2009: F19: Buckle (David Bessell). GIMPS' 1st: http://www.mersenneforum.org/showthread.php?t=12168 Feb 2nd 2010: F14: Tapio Rajala. GIMPS' 2nd: http://www.mersenneforum.org/showthread.php?t=13051 Mar 26th 2010: F22: Buckle (David Bessell). GIMPS' 3rd: http://www.mersenneforum.org/showthread.php?t=13209 Mar 27th 2010: F12: Xyzzy. GMPECM: http://www.mersenneforum.org/showthread.php?t=13215 Mar 14th 2011: F17: Buckle (David Bessell). GIMPS' 4th. I'm wondering why Buckle only have 2 success listed: http://www.mersenne.org/report_top_5...&B1=Get+Report Last fiddled with by ATH on 20110315 at 02:40 
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