From: morain@lix.polytechnique.fr (Francois Morain)
Newsgroups: sci.math.numberthy
Subject: New ordinary primality proving record
Date: 30 Oct 97 21:04:12 GMT

We are pleased to announce that the remaining cofactor of 2^7331-1,

        MC7331 = (2^7331-1)/458072843161

has been proven prime. This number has 2196 decimal digits and is the
new record for general purpose primality proving (as far as we know).

Note that the previous record was hold by the first author for a while
(1510 digits and later 1549, both in 1997), succeeding  the second author
who had been holding it with 1505 digits since 1992. Note that all of these
records were done with the new version of ECPP which can be found at
FM's web page:

        http://www.lix.polytechnique.fr/~morain/

The certificate for MC7331 can also be found at this address.

(People interested in small numbers -- and not afraid by complicated
theory -- may be interested to learn that this new version is able to
prove the primality of 512 bit numbers in less than 40 seconds on a
quite old 125 MHz alpha workstation.)


E. Mayer & F. Morain

PS: for more Mersenne factorizations, see

        ftp://ftp.ox.ac.uk/pub/math/factors/mersenne

EM's web page: http://k2.scl.cwru.edu/cse/emae/faculty/mayer