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c137 factored with GNFS

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• Factorization of 2^643-3 was initiated by Joe Crump back in 2001 in search for new solutions to the congruence 2^n=3(mod n). At that time he ended up with a
Message 1 of 1 , Mar 2, 2006
Factorization of 2^643-3 was initiated by Joe Crump back in 2001 in
search for new solutions to the congruence 2^n=3(mod n). At that time
he ended up with a composite co-factor c137 which became a target of
my factorization efforts.

So, this c137 number happens to be the product of two primes:
r1 = 170890017904359186727050262036995846555074348155602036792130577971
r2 =
398085096927875650079602480935994493287846516042673558096821977233071517

implying the following complete factorization:

2^643 - 3 = 5 * 19 * 97 * 239 * 401953 * 1739009003318072377 *
348517228735983022805545699 *
170890017904359186727050262036995846555074348155602036792130577971 *
398085096927875650079602480935994493287846516042673558096821977233071517

Unfortunately, this factorization does not lead to a solution of
2^n=3(mod n). Anyway, it is good to know that.

Everything except sieveing (that was distributed among friends) was
done on my Opteron linux box. Rough timing is about a day for
polynomial selection and about 2 days for matbuild/matsolve/sqrt
stage. Sieving took about 2 weeks for 3 CPUs.

As Andrei Belenko before ( see
http://groups.yahoo.com/group/ggnfs/message/863 ) I faced the problem
with infinite loops in sqrt, and it has been fixed the same way Andrei
did.

Besides that I also noticed that 64-bit version of sqrt sometimes
hangs up and sometimes segfaults (that should be investigated and I
have a testcase for that). So I used 32-bit version (athlon-optimized)
of sqrt. All other programs were k8-optimized and were running smoothly.

Max
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