From: warwick@mundook.cs.mu.OZ.AU (Warwick HARVEY) Newsgroups: sci.math.research Subject: Re: Mersenne Primes Date: 4 Dec 1997 08:09:52 GMT Brian D Koberlein writes: >I am just wondering if anyone knows if the Mersenne number 2^(2^127 - >1) - 1 is prime. 2^127 - 1 is prime, so the possibility is not ruled >out. For anyone who has any interest in Mersenne primes, I recommend having a look at http://www.mersenne.org/prime.htm . It's the home page of "The Great Internet Mersenne Prime Search" (GIMPS) project, and has links to just about any information you might want to know about Mersenne numbers. From your question, I suspect you are interested in the conjecture which can be found at the bottom of http://www.utm.edu/research/primes/mersenne.shtml There's also a mailing list specifically for discussing Mersenne numbers: details can be found by following links on the web page. To answer your question, 2^2976221 - 1 is the largest prime number known, found by the GIMPS project on August 24. 2^127 - 1 is a 39-digit number, and so is much larger than 2976221, and thus it hasn't been proven prime. On the other hand, it hasn't been proven composite either (to the best of my knowledge). GIMPS is throwing a *lot* of CPU power at trying to prove Mersenne numbers prime, and even a 10-digit exponent is beyond what is practical at the moment. Thus for the forseeable future, trying to prove prime a Mersenne number with a 39-digit exponent is out of the question. Of course, someone may find special properties of this particular Mersenne number that suddenly makes finding the answer practical. Also, I'm sure there are a number of people out there who have or will spend time trying to factor it, hoping that it's composite, and maybe it is and one of them will get lucky. If you really are interested in this stuff, please: read the web pages, and join the mailing list. You might also like to browse the mailing list archives looking for old posts on 2^(2^127 - 1) - 1. Warwick ---------------------------------------------------------------------------- Warwick Harvey email: warwick@cs.mu.OZ.AU Department of Computer Science phone: +61-3-9344-9171 University of Melbourne fax: +61-3-9348-1184 Parkville, Victoria, AUSTRALIA 3052 web: http://www.cs.mu.OZ.AU/~warwick