From:   franke@math.uni-bonn.de
Date: November 11, 2005 04:07:26 CET
To:   NMBRTHRY@LISTSERV.NODAK.EDU
Reply-To:   franke@math.uni-bonn.de

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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