Mersenne: Estimates to finishing up to 20500000???
Has anyone calculated (given the current rate of growth) how long it will take to do 1st level LL tests up to 20 million? G-Man Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: More on the FAQ
Chris, on your website http://www.utm.edu/research/primes/notes/faq/NextMersenne.html, you say: "This means that the geometric mean of two successive mersenne exponents is 2 raised to 1/e^gamma or about 1.47576." The definition of geometric mean of two numbers a and b is: sqrt(a*b) Therefore the geometric mean must be between a and b. I think that you mean that the geometric mean of two successive mersenne numbers is 2 raised to the (1/e^gamma) raised to the index of the mersenne numbers. -Lucas Wiman Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: M38 = M6972593
Hi all, As the newspaper should announce the new prime on Monday or Tuesday, I've placed the info on the new prime at http://www.mersenne.org/prime.htm Congratulations to Nayan Hajratwala and all GIMPS members for our fourth success! Each Mersenne announcement is different. This time round I finally figured out how to get the press interested in the new number - tell them its a secret. The Oregonian was doing an article on Richard Crandall and when the found out there was a new prime and we wouldn't tell them what it was, their interest level went way up! I admire the resourcefulness of GIMPS members for going on a "scavenger hunt" and finding out the exponent a few days before this email was sent out. However the resourcefulness award must go to one enterprising GIMPS member that dug through all the cleared and assigned exponent lists and human-readable files and deduced the exponent in early June! (Note to Scott - create a dummy non-zero residue a stick it in the cleared exponents report). Good luck to all in the search for M39! Have fun, George Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: how long to 20.5M
Geoffrey Faivre-Malloy wrote: Has anyone calculated (given the current rate of growth) how long it will take to do 1st level LL tests up to 20 million? Gman, I extrapolated and posted an estimate of April 2007, back in February of this year. If I take a linear model starting 1 Jan 99, I get August 2005. If I use the latest curve fit suggest on the wicked-cool site: http://entropia.com/ips/stats.html I get September 2004. For my newest prediction, I split the difference and estimate spring 2005. spike Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Lehmer question
Problem A3 in Richard Guy's `Unsolved Problems in Number Theory' includes this question, by D.H. Lehmer: Let Mp = 2^p - 1 be a Mersenne prime, where p 2. Denote S[1] = 4 and S[k+1] = S[k]^2 - 2 for k = 1. Then S[p-2] == +- 2^((p+1)/2) mod Mp. Predict which congruence occurs. For example, when p = 3, S[1] = 4 == 2^2 (mod 7). When p = 5, S[3] = 194 == 2^3 (mod 31). When p = 7, S[5] = 1416317954 == -2^4 (mod 127). The sign is + for p = 3 and p = 5 but - for p = 7. Do we have the pattern through M38? Peter Montgomery Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
