A small but valuable group of members of the Mersenne list have been running the elliptic curve method to factor small Mersenne numbers, with some impressive results so far. The outstanding example is Conrad Curry's discovery of the record-holding 53 digit factor of M677, and still the only factor with more than fifty digits to be found by ECM I would like to request that one particular number be concentrated on. That number is P773, also known as 2,773+ by the Cunningham project and as 2^773+1 by everyone. Two small factors are known, 3 and 533371. The composite cofactor has 227 digits. The reason for this request is that it is a candidate for a SNFS factorization (as are several others) and before embarking on a large-scale computation, we want to be sure that it doesn't have a small factor --- under fifty digits or so. George's ECM page (http://www.mersenne.org/ecm.htm) records only the work done by his prime95 program and reported to him. Other work in the past (I've done well over a thousand curves at B1=1M, for instance) suggest that there are very probably no factors under 40 digits and that you should start with the B1 value set to 3 million. If you join in, please report progress back to George so that we can move on to higher values of B1 when appropriate. Prime95 is so efficient at factoring numbers of the form 2^n +/- 1 that non-Intel machines are at a significant disadvantage. Nonetheless, they are a valuable resource and owners of such might find the ECMNET page http://www.loria.fr/~zimmerma/records/ecmnet.html useful. I will be adding P773 to the ECMNET master server shortly. Paul ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
