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来源:
http://mersenneforum.org/showthread.php?t=4957
RSA-640 factored
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Apologies if this has been seen elsewhere. I've only just returned from a 4-day trip to find the mail below in my inbox.
Another impressive result from Franke et al.
Quote:
Originally Posted by Jens Franke et al.
We have factored RSA640 by GNFS. The factors are
16347336458092538484431338838650908598417836700330\
92312181110852389333100104508151212118167511579
and
19008712816648221131268515739354139754718967899685\
15493666638539088027103802104498957191261465571
We did lattice sieving for most special q between 28e7 and 77e7
using factor base bounds of 28e7 on the algebraic side and 15e7 on
the rational side. The bounds for large primes were 2^34. This produced
166e7 relations. After removing duplicates 143e7 relations
remained. A filter job produced a matrix with 36e6 rows and columns,
having 74e8 non-zero entries. This was solved by Block-Lanczos.
Sieving has been done on 80 2.2 GHz Opteron CPUs and took 3 months.
The matrix step was performed on a cluster of 80 2.2 GHz Opterons
connected via a Gigabit network and took about 1.5 months.
Calendar time for the factorization (without polynomial selection)
was 5 months.
More details will be given later.
F. Bahr, M. Boehm, J. Franke, T. Kleinjung
Yep, congratulation to Franke et al. again!
I believe the all time top 10 for GNFS is now:
Code:
RSA-200 2005 2799 C200=P100*P100 GNFS Bahr/Franke/Kleinjung/et al.
RSA640 2005 3107 C193=P98*P98 GNFS Bahr/Franke/Kleinjung/et al.
11^281+1 2005 1009 C176=P87*P89 GNFS Aoki/Kida/Shimoyama/Ueda
RSA-576 2003 1881 C174=P87*P87 GNFS Bahr/Franke/Kleinjung/Montgomery/te Riele/Leclair/Leyland/Wackerbarth
2^1826+1 2003 9758 C164=P68*P97 GNFS Aoki/Kida/Shimoyama/Sonoda/Ueda
RSA-160 2003 2152 C160=P80*P80 GNFS Bahr/Franke/Kleinjung/Lochter/Bohm
2^953+1 2002 3950 C158=P73*P86 GNFS Bahr/Franke/Kleinjung
RSA-155 1999 1094 C155=P78*P78 GNFS te Riele/CWI et al.
Code Book 2000 1074 C155=P78*P78 GNFS Almgren/Andersson/Granlund/Ivansson/Ulfberg
HP49(95) 2003 2651 C153=P68*P85 GNFS Kruppa/Leyland
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