> >We discussed the observation (not a conjecture) that so far no two > >consecutive gaps between Mersenne primes (in terms of exponent ratio) > >were greater than two
Far be it from me to add to a discussion started under the influence of much beer. However, we note that the exponents of M(13) and M(14) differ by more than a factor of 2, as do the exponents of M(15) and M(16). Similarly for M(35) and M(36) with M(37) and M(38). Conjecture: with very weak evidence. If M(n-2) and M(n-1) are closer in exponent factor than twice and M(n) and M(n+1) are further apart than twice, then M(n+2) and M(n+3) are also further apart than twice. I'll have a crack at restating this hypothesis more formally another day, but I'm sure you know what I'm getting at (and I'm sure you can't prove it wrong yet). Nevertheless, I'm sure that whether true or false, this conjecture probably won't change the world. Regards, and Happy New Year to you all Ian -- Ian W Halliday, BA Hons, MIMIS, AAIBF Snr, ATMB, CL +64 27 245 6089 (GMT+13) http://baptism.co.nz Focus On Success -- Word documents not accepted -- see http://baptism.co.nz/word.html _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
