> > I think trial factoring is done to 2^68 for an exponent around 33 million. > > Thus your chance is 2 * 68 / 33000000. > > Okay, so as far as we know, each number is equally likely to be prime, and > this probability is just based on how much has already been tested ? Umm, no. The probability that a number is prime is inversly proportional to the number of digits (or more precisely, the probability that a number on the interval [1,x] is prime is asomtotically 1/ln(x)). However, the probability that a number is prime increases with the amount that has been trial factored (without finding a factor). The precise estimation is based on Mertel's theorem. > Ugh... I apparently had bad math teachers, and GIMPS is really making me > feel it. I *really* wanna play with these numbers, but I feel > intellectually cripled. You certainly seem to have done a good job! You found the two big conjectures about Mersenne distribution. That is Curt Noll's (poorly defined) island theory (your pairs observation), and your observation about it being roughly exponetial (a conjecture due to Wagstaff, and others, though Wagstaff's has hueristic evidence to back it up). > I took the numbers from > http://www.utm.edu/research/primes/mersenne.shtml#known See http://www.utm.edu/research/primes/notes/faq/NextMersenne.html, as well as http://www.tasam.com/~lrwiman/FAQ-mers, Q4.2. > Does anybody see what I'm talking about ? Is there any significance to > this ? Has somebody already written extensive papers on this ? Yes, see above. Good work! -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
