On Friday 02 November 2007 13:52, Ian Halliday wrote: > > Elsewhere, there is the Lenstra–Pomerance–Wagstaff conjecture, > suggesting that the number of Mersenne primes with exponent p less > than x is asymptotically approximated by > > e^y x log_2(x) where y is the Euler-Mascheroni constant. > > The mainstream view over the years in this mailing list seems to have > been that there is an infinite number of MPs,
Because that is the way that the data that we have and hand-waving or heuristic arguments (i.e. based on what appears to be common sense, but is not provable at the moment) tend to point. Of course the data that we have at the moment is not a representative sample, it's really very little better than the argument that "3 is prime, 5 is prime, 7 is prime, 11 is prime ... obviously all odd numbers are prime". The "law of small numbers" is particularly misleading when it is based on incomplete data sets. The L-P-W conjecture is based on an apparently sound heuristic argument; it's going to be (at the very least) hard to prove, and from its formulation is actually completely impossible to disprove by the best method of all (construction of a counterexample). > and those (like me) who > think otherwise have sometimes been treated like flat-earthers. Hopefully without any malice! Life would be very dull if we all agreed on everything. > But if a > proof should appear, one way or the other, I'd be happy to take it on > board. > Same here. Regards Brian Beesley _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
