On 4 Dec 2001, at 1:19, Paul Leyland wrote: > > > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] > > > > > > (Aside - we're rather more likely to find a 75-bit factor than a 75- > > digit factor. In fact, finding a 75-digit prime factor of a > > "no factors > > known" Mersenne number with an exponent under 80 million would > > be a significant achievement in itself. > > Finding a 75-digit prime and non-algebraic factor of any integer with > more than, say, 200 digits would be a significant achievement. The > record today is 55 digits; it reached 53 digits 3 years ago and only a > handful of factors with 50 or more digits have been found ever. I have > precisely one of them to my credit 8-)
Sure. Not quite the same since there appears to be no certificate of primality, but on 30 Aug 2001 there was a message on this list to the effect that M727 (c219) = prp98.prp128. So much ECM work was done on M727 (before the NFS people started work) that it is highly unlikely that there are any factors < 10^50, which means that at least the 98-digit probable prime is almost certainly a genuine prime. (Maybe that's been proved by now. ECPP on general numbers of around 100 digits isn't very expensive.) I think the 55 digit record applies to ECM. A number of much larger factors (not counting cofactors) have been found using number field sieve techniques. > > > At the moment, having found one factor, we quit. That's sufficient > > effort for the purpose of trying to find Mersenne primes. A little > > more work might break the cofactor down further. > > Actually, some of us don't quit. But we're a small bunch of weirdos, > and we only work on tiny exponents anyway. I was speaking for the project rather than myself. I'm also one of the small bunch of weirdos. Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
