This is probably old news to many but there is work dedicated to the attempted factorisation of such "double-Mersenne" numbers. The status of these can be found at
http://www.garlic.com/~wedgingt/MMPstats.txt Basically, the first 8 double-Mersenne's have been checked for primality. As far as I can make out M(M(2)), M(M(3)), M(M(5)) and M(M(7)) are all prime while M(M(13)), M(M(17)), M(M(19)) and M(M(31)) are not. Tony Forbes currently has a page dedicated to the search for "small" divisors of the ninth double-Mersenne - MM61 (i.e. 2^(M61) -1). The URL for this is http://www.ltkz.demon.co.uk/ar2/mm61.htm Tony has written a program called MFAC to search for divisors of double-Mersennes - the program incorporates a very large sieve! I wouldn't want to tempt anyone away from GIMPS but I had a spare PIII which I currently boot off a floppy and it suits me to use this for MM61 factorisation at present... The zip file containing the program also contains a text file that explains the maths behind this. Amongst other things, it uses the fact that d divides 2^(2^p - 1) - 1 when 2^2^p == 2 (mod d). However, Tony does say that MFAC is not suitable for very large exponents, e, as they would benefit from much more sieving and possibly an attempt to factorize candidate divisors by p-1 or ECM before testing them. (Apologies for any copyright breaches incurred Tony!) Happy New Year to all! Keith >>Date: Tue, 25 Dec 2001 14:54:49 +0100 >>From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> >>Subject: Mersenne: Re: 10 million digit overkill >> >>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. :-) -------- The information in this email is confidential and may be legally privileged. It is intended solely for the addressee. Access to this email by anyone else is unauthorized. If you are not the intended recipient, any disclosure, copying, distribution or any action taken or omitted to be taken in reliance on it, is prohibited and may be unlawful. When addressed to our clients any opinions or advice contained in this email are subject to the terms and conditions expressed in the governing Ark Life agreement. This communication represents the originators personal views and opinions which do not necessarily reflect those of Ark Life. If you receive this email in error, please immediately notify Ark Life's Networking team at +353 (0)1 6681199. _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
