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

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Default 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
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Old 2010-02-03, 08:03   #2
Andi47
 
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Oct 2004
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Quote:
Originally Posted by rajula View Post
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!!

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Old 2010-02-03, 08:06   #3
ckdo
 
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Congrats, Tapio!

Of course, this simply had to happen while George was on vacation...
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Old 2010-02-03, 08:07   #4
Raman
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"Mr. Tuch"
Dec 2007
Chennai, India

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Thumbs up 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
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Old 2010-02-03, 08:15   #5
wblipp
 
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"William"
May 2003
New Haven

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Congratulations!

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

http://www.prothsearch.net/fermat.html
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Old 2010-02-03, 09:57   #6
debrouxl
 
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Congratulations indeed !

How much RAM do ECM curves at B1=11e7 on such a monster number eat up ?
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Old 2010-02-03, 10:03   #7
philmoore
 
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Sep 2002
Tracktown, U.S.A.

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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!
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Old 2010-02-03, 10:04   #8
akruppa
 
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"Nancy"
Aug 2002
Alexandria

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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
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Old 2010-02-03, 10:06   #9
Batalov
 
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"Serge"
Mar 2008
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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.)
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Old 2010-02-03, 11:16   #10
R.D. Silverman
 
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Quote:
Originally Posted by akruppa View Post
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?
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Old 2010-02-03, 11:19   #11
ET_
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"Luigi"
Aug 2002
Team Italia

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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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