On Wednesday 13 March 2002 00:52, danny fleming wrote: > I saw recently a method of locating a Mersenne Prime.
Please tell us more! We'd all like to know of any better (less computationally expensive) method than computing the Lucas-Lehmer sequence for those Mersenne numbers which cannot be "easily" shown to be composite by finding a factor. > Does anyone know if it includes the expected number > of Mersenne Primes to a given integer? The usual > number of primes to any positive integer n is > n/ln(n)-1. There are more accurate estimates than this of the number of primes up to any given limit, or between any two specific limits, than this. See for example Riesel, "Prime Numbers and Computer Methods for Factorization" (2nd edition), p.50ff. I'm not aware that there is any specific formula for the number of Mersenne primes up to a given limit. In fact the much weaker assertion that there are an infinite number of Mersenne primes still remains to be proved. However the (rather limited) experimental evidence to hand does not disagree with the unproved theoretic assertion (apparently based on heuristics rather than solid logic) that there should be _on average_ exactly one Mersenne prime in the interval (2^x,2^(x+y)) where y is Euler's constant gamma = 0.5772... Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
