From: Brian J. Beesley Sent: ti 26-11-2002 00:20 >A more sophisticated cheat would be to run through to 2^63 or 2^64 (which is >fast and will find most of the factors) then start again at 2^65. This would >be a lot harder to spot.
You are as usual such a cunning mean guy. :-) And I have to agree it would be unspottedly.Unless doubleproven and that time is probably better spent doing p1. >Even hacking into the save file so that you run >the assignment for a few seconds, stop, edit the save file so that it will >restart just shy of 2^66 then letting it finish is going to be a lot more >effective than simply frigging the start exponent. I believe that could be done (even by me) and it would probably have that nice feature that any checksum or whatever would be automatically calculated right. >I think it was 1998 or possibly 1999 when the exponent limit was raised from >~20 million to ~80 million. Anyway it was related to the EFF reward for a 10 >million digit prime being announced. So now we stick with the 79.3 million limit until somebody finds a 10M digit prime? Is a price available for a 100M digit prime? And will Gimps raise the level once more to make this possible to achieve? In that case it looks like the new candidates are above M332.192.000. Well maybe we have to live forever or we may believe in P5 with SSE7 :-) It's kind of easy to see you are right about the 20M going to 79.3M and it is kind of easy to see the "desparate" programmer calculating that the letters of the alphabet X, Y and Z will keep us going into at least M35.999.999 for the save files. What will happen when Z is used out? I very well know we have a couple of years to rethink but the day is going to come. >This is a THEOREM; there is a proof on Chris Caldwell's Prime Pages site. Tnx, I read to little and ask to much. :-) >Because of this, it's (reasonably) easy to find titanic primes (over 1000 >digits) which are a factor of some particular Mersenne number. All you have >to do is to find a pair of primes p, q such that p+1 is divisible by 4 and >q=2p+1. Then 2^p-1 is divisible by q. Proth.exe is very useful for finding >this sort of prime pair. I've used Proth.exe but I find it boring. Gimps has a ranking system that is fine! Though you find find these 2 p,q you don't really believe these will be the only factors of that number? 2^p-1 might have several factors (of which 2q+1 is the smallest). eg. M179 is: (2*179+1) * 1433 * 14894...................... So some more effort than just finding a 4x-1 and a responding 8x-1 prime and then a divide must be done. br tsc PS.: A very happy day ends now I have found 3 factors in the 20M range. 3 numbers need no more computing power. That is unusual. _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
