20100203, 07:18  #1 
"Tapio Rajala"
Feb 2010
Finland
100111011_{2} Posts 
GIMPS' second Fermat factor!
I decided to finally register to this forum (which I have actively read for a year or so) after I first checked that what I read this morning from my recent results list is indeed true. I simply could not keep this to myself.
F14 has a factor 116928085873074369829035993834596371340386703423373313 I found this after approximately 750 curves ran on F14 with B1=110M. Tapio Rajala Department of Mathematics and Statistics University of Jyväskylä Finland 
20100203, 08:03  #2  
Oct 2004
Austria
9B2_{16} Posts 
Quote:


20100203, 08:06  #3 
Dec 2007
Cleves, Germany
1000010010_{2} Posts 
Congrats, Tapio!
Of course, this simply had to happen while George was on vacation... 
20100203, 08:07  #4 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
1257_{10} Posts 
Bingo!
27122070644729388256659993^{2} + 340870179330807226620457708^{2}
That's a Bingo! Come on, please go after F20, F22, F24 next! Have a try for M1237, M1277 as well. M1061 has certainly be ECMed enough..., as well as P1123 probably... By the way, how long does it take up to run up one ECM curve upon F14, F20, F22, F24 with some B1, B2 values? The thread title with "F14 factored!" (with 54 digit prime factor) would be much more nicer as well, in my opinion only though, actually! Last fiddled with by Raman on 20100203 at 08:40 
20100203, 08:15  #5 
"William"
May 2003
New Haven
2,371 Posts 
Congratulations!
F14 was the smallest Fermat with no known factors! The 4880 digit cofactor is composite. http://www.prothsearch.net/fermat.html 
20100203, 09:57  #6 
Sep 2009
2·3·163 Posts 
Congratulations indeed !
How much RAM do ECM curves at B1=11e7 on such a monster number eat up ? 
20100203, 10:03  #7 
"Phil"
Sep 2002
Tracktown, U.S.A.
10001011111_{2} Posts 
Very nice! This is the 11th Fermat factor discovered by ECM, and only the second since 1999. Wilfrid Keller's page informs us that F14 was proven composite in 1963 by John Selfridge and Alexander Hurwitz. I think it was Bob Silverman who pointed out awhile back that we could only expect a 50% chance of such as number with no factor below 50 digits to have a factor between 50 and 100 digits, so we should consider ourselves lucky! Time for a Fermat number party! George certainly has permission to take as many vacations as possible! 
20100203, 10:04  #8 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Wonderful discovery! I've spent a bit of cpu time on this one myself, as have many others here, and it's quite satisfying to see this number cracked at last. Congratulations, Tapio!
p1 = 2^16 * 3^3 * 9959563 * 761145015334071629 * 8717008205877092841673 p+1 = 2 * 9661881871 * 77508526903108177 * 78068824171447136188657471 Both unrealistic to find with P1 or P+1. P1 would have needed B1=10^18, B2=10^22; P+1 would have needed B1=10^17, B2=10^26. Alex 
20100203, 10:06  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·5·983 Posts 
Great catch. Congratulations!
You may want to submit it to the ECM record table  ...and could you please find the sigma in the results.txt? (it is good to know for testing the programs and for the group order calculations.) 
20100203, 11:16  #10  
Nov 2003
2^{2}·5·373 Posts 
Quote:


20100203, 11:19  #11 
Banned
"Luigi"
Aug 2002
Team Italia
2^{2}·7·173 Posts 
Congratulations!
The second Fermat factor of 2010 comes just one week after the first!!! And WHICH ONE! F14 !!! We all hope this will be a great year for Fermat factors! Luigi Last fiddled with by ET_ on 20100203 at 11:24 
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