Date: Fri, 3 Jan 2003 20:09:10 +0100 From: Jens Franke To: ssw@cerias.purdue.edu, Herman.te.Riele@cwi.nl, rpb@comlab.ox.ac.uk, pleyland@microsoft.com, Peter-Lawrence.Montgomery@cwi.nl, Paul.Zimmermann@loria.fr, Scontini@gi.com, woltman@alum.mit.edu Subject: M809 X-Keywords: We have factored M809 by SNFS: 4148386731260605647525186547488842396461625774241327567978137 822976161770972830930301003163428309173701632995322298332566131941218475319456934681317262180441560179196983695741564512962292828041194778466080386250032973003303401916055540200393303 Both factors have been tested for primality by Rabin-Miller tests (assuming GRH) and by the Atkin-Morain ECPP method. Sieving was done at the CWI, at the Scientific Computing Institute and the Pure Mathematics Department at Bonn University, and using private resources of J. Franke, T. Kleinjung and the family of F. Bahr. The linear algebra step was done by P. Montgomery at SARA in Amsterdam. Postprocessing (other than the block Lanczos step) was done in Bonn. More details will follow in a separate message. Jens Franke Date: Thu, 9 Jan 2003 22:50:22 +0100 From: Jens Franke To: Peter-Lawrence.Montgomery@cwi.nl CC: Herman.te.Riele@cwi.nl, F.Bahr@uni-bonn.de, thor@pool9.math.uni-bonn.de Subject: M809 X-Keywords: Do you want me to build another matrix for M809, to see how it would have performed? Also, do you want me to convert the combinable relations for M809 to CWI format and send them to you? There are some difficulties in preparing a more detailed report on M809, since I made a mistake during postprocessing which caused the destruction of most of the log-files of uniqueness checking. For this reason, I do not know how many sieve reports we produced by line lattice sieving. The only way to determine it would be to copy the content of the backup CDs to the hard disk and to count them once again. I think the total number of line siever reports was about 170-180 million, while for lattice sieving it was 250-300 million. About 50% of the line siever relations turned out to be duplicates. This may in part be due to overlapping line sieving regions. F. Bahr has more detailed information about the regions sieved by himself, his brother and A. Schwedt. Line sieving was done at the Scientific Computing Institute and the Mathematical Institute of Bonn University, at the Max-Planck-Institute for Mathematics, at the Institute for Experimental Mathematics in Essen, and using private resources of J. Franke and T. Kleinjung. We sieved most special q between 32 and 64 million on the algebraic side, and between 32 and 100 million on the rational side, using varying factor base and large prime bounds. We had 343952357 relations after removing duplicates, 212317735 of which turned out to be combinable. We added 4098656 free relations. I already informed you about the results of the various filter jobs. The square root program written by F. Bahr uses the NTL library and avoids the use of PARI routines for time critical steps. It needed less than 45 minutes to calculate a squere root on a 930 MHz PIII and apparently outperforms programs using only PARI. Jens