GIMPS' second Fermat factor!

rajula · 2010-02-03, 07:18

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

Andi47 · 2010-02-03, 08:03

Quote:

Originally Posted by rajula

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

Woha!!

Nice P54 factor - and the first factor of F14! Congrats!!

ckdo · 2010-02-03, 08:06

Congrats, Tapio!

Of course, this simply had to happen while George was on vacation...

Raman · 2010-02-03, 08:07

27122070644729388256659993² + 340870179330807226620457708²
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!

wblipp · 2010-02-03, 08:15

Congratulations!

F14 was the smallest Fermat with no known factors! The 4880 digit cofactor is composite.

http://www.prothsearch.net/fermat.html

debrouxl · 2010-02-03, 09:57

Congratulations indeed !

How much RAM do ECM curves at B1=11e7 on such a monster number eat up ?

philmoore · 2010-02-03, 10:03

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!

akruppa · 2010-02-03, 10:04

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!

p-1 = 2^16 * 3^3 * 9959563 * 761145015334071629 * 8717008205877092841673
p+1 = 2 * 9661881871 * 77508526903108177 * 78068824171447136188657471

Both unrealistic to find with P-1 or P+1. P-1 would have needed B1=10^18, B2=10^22; P+1 would have needed B1=10^17, B2=10^26.

Alex

Batalov · 2010-02-03, 10:06

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.)

R.D. Silverman · 2010-02-03, 11:16

Quote:

Originally Posted by akruppa

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!

p-1 = 2^16 * 3^3 * 9959563 * 761145015334071629 * 8717008205877092841673
p+1 = 2 * 9661881871 * 77508526903108177 * 78068824171447136188657471

Both unrealistic to find with P-1 or P+1. P-1 would have needed B1=10^18, B2=10^22; P+1 would have needed B1=10^17, B2=10^26.

Alex

Has the cofactor been checked?

ET_ · 2010-02-03, 11:19

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

2010-02-03, 07:18	#1
rajula "Tapio Rajala" Feb 2010 Finland 100111011₂ 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

2010-02-03, 08:07	#4
Raman Noodles "Mr. Tuch" Dec 2007 Chennai, India 3×419 Posts	Bingo! 27122070644729388256659993² + 340870179330807226620457708² 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 2010-02-03 at 08:40

2010-02-03, 11:19	#11
ET_ Banned "Luigi" Aug 2002 Team Italia 3·1,619 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 2010-02-03 at 11:24

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2010-02-03, 08:06	#3
ckdo Dec 2007 Cleves, Germany 530₁₀ Posts	Congrats, Tapio! Of course, this simply had to happen while George was on vacation...

2010-02-03, 08:15	#5
wblipp "William" May 2003 Near Grandkid 2×1,187 Posts	Congratulations! F14 was the smallest Fermat with no known factors! The 4880 digit cofactor is composite. http://www.prothsearch.net/fermat.html

2010-02-03, 09:57	#6
debrouxl Sep 2009 1723₈ Posts	Congratulations indeed ! How much RAM do ECM curves at B1=11e7 on such a monster number eat up ?

2010-02-03, 10:03	#7
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2⁵×5×7 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!

2010-02-03, 10:04	#8
akruppa "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! p-1 = 2^16 * 3^3 * 9959563 * 761145015334071629 * 8717008205877092841673 p+1 = 2 * 9661881871 * 77508526903108177 * 78068824171447136188657471 Both unrealistic to find with P-1 or P+1. P-1 would have needed B1=10^18, B2=10^22; P+1 would have needed B1=10^17, B2=10^26. Alex

2010-02-03, 10:06	#9
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10060₁₀ 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.)