On 25 Dec 2001, at 14:54, Steinar H. Gunderson wrote: > On Tue, Dec 25, 2001 at 01:41:31AM -0500, Paradox wrote: > >If the computer above could do each iteration in > >0.000000000000000000000000000000000000000000000000000000000000001 seconds, > >the amount of seconds required to complete the task would still be > >significantly more than 4,000,000 digits. Thats incomprehensible. > > Unless we find something more efficient than the Lucas-Lehmer test before > that. :-)
Testing to see if 2k(2^p-1)+1 divides 2^(2^p-1)-1 for small values of k _is_ feasible in a reasonable time and _may_ result in a positive refutation of the theory. As I (and others) have pointed out, LL testing on numbers of this sort of order is impossible (in this universe) because there simply isn't enough matter to build sufficient temporary storage- whatever speed we can manage to achieve. This is an excellent example of the sort of theory which it _may_ be possible to refute but may never be possible to prove. Theories based on samples involving "small numbers" of terms are always dangerous ... look, 3 is prime, 5 is prime, 7 is prime, 9 isn't prime but it does happen to be a perfect square, 11 is prime, 13 is prime ... it looks like all odd numbers which aren't perfect squares are prime ... or just look at the Fermat numbers ... Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
