From: "Jens Franke"
Date: Fri, 04 Nov 2005 16:53:08 +0100
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