In Primeform Digest Number 258, on Wed, 27 Sep 2000 Chris Caldwell <[EMAIL PROTECTED]> writes > >Subject: Re: Gaussian-Mersenne numbers > >I took a break from other duties to take time to decide what to do with >your primes. I have decided they are (by my definition) archivable, at >least the norms are with no shortage of publications related to the >Cunningham project. So I changed the comments to > Gaussian Mersenne norm \d+ >and have added a page on them in the glossary. >[snip] I have today found (with PFGW) and verified (with an independent program) the 34th in this series of Gaussian primes, of form s[n] = (1+i)^n-1. Its "Gaussian Mersenne norm" is 2^203789+2^101895+1, which has 61,347 decimal digits and is currently the 88th largest known prime. It is slightly smaller than Mersenne 31 (2^216091-1). The geometric mean of the ratio of successive exponents for the first 34 terms of this series is 1.4183. The corresponding ratio for the first 34 Mersennes is 1.4987. The most cogent heuristic argument, due to Wagstaff and others in the 1980s, would predict for both series the theoretical value (for large n) of 2^(exp(-gamma)) = 1.47576, which is in reasonable agreement with the present sparse data. In particular, the value of 1.5 sometimes advocated looks less likely than it does if the Mersenne series alone is considered. Mike Oakes _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt
