The 640-bit number RSA640 was factored last week. This is somewhat anticlimactic, since the 200 digit number RSA200 was factored in May. For some reason, this group doesn't post announcements on the NMBRTHRY list. The total work looks like roughly 30 years of 2.2GHz Opterons. This would nominally be 66 Gips-years, but I don't know either the parallelism of the Opteron, or the average number of clocks per instruction. Rich ---------- http://mathworld.wolfram.com/news/2005-11-08/rsa-640/ includes a bit of history http://www.crypto-world.com/announcements/rsa640.txt 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