Mersenne Digest Saturday, January 22 2000 Volume 01 : Number 682 ---------------------------------------------------------------------- Date: Thu, 20 Jan 2000 03:11:37 -0700 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Doubling PIII (500) Memory To Increase LL Performance > Would increasing PIII (500MHz) memory from 128M to 256M improve > L-L performance? Current exponent being tested is in range 9,xxx,xxx. The best way to find out is to profile your memory usage right now. With NT, it's as easy as bringing up Task Manager when your system is doing what it normally does. Look at the "Performance" tab, and pay attention to the Physical Memory (K) section. For instance, my system shows total 196148, and available as 117332 right now. Obviously, I have plenty of extra memory (this is with Windows 2000 Professional, by the way). Your load will definitely vary depending on what other programs you have loaded. If your free memory is still pretty high, adding more won't be much help most of the time. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 20 Jan 2000 03:14:28 -0700 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: Mersenne: Unusual request... I have a bit of an odd request, but one that is peripherally related to Mersenne Primes. Today (Thursday the 20th of January) at 2:00 PM Mountain time, I will be going in with my lawyer to meet someone from the Attorney General's Office. For those of you familiar with my plight, it would mean *a lot* to me if those of you who are religous would say a little prayer for me. If you're not religious, maybe just cross your fingers and hope for the best. I know it's an odd request, but I'm just a bit nervous about the meeting. Thanks all, Aaron Blosser _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 21 Jan 2000 09:55:03 +1300 (NZDT) From: Bill Rea <[EMAIL PROTECTED]> Subject: Mersenne: LL Test for M7 Gimpsters, A while ago someone posted a demonstration of the Lucas-Lehmer test for, I think, 2^7-1. Would that person be so kind as to email me another copy or point me to an archive if the posts on this list are saved somewhere. Thanks. Bill Rea, Information Technology Services, University of Canterbury \_ E-Mail b dot rea at its dot canterbury dot ac dot nz </ New Phone 64-3-364-2331, Fax 64-3-364-2332 /) Zealand Unix Systems Administrator (/' _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 20 Jan 2000 19:57:20 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Doubling PIII (500) Memory To Increase LL Performance On 20 Jan 00, at 0:36, Stefan Struiker wrote: > Would increasing PIII (500MHz) memory from 128M to 256M improve > L-L performance? Current exponent being tested is in range 9,xxx,xxx. Increasing the amount of memory will have _no effect whatsoever_ unless the system is short of memory. LL testing an exponent in the 9 million range uses less than 10 MBytes of memory in total. I don't know what else you're running on your system, but I'm running similar exponents in a system with 32 MBytes memory (running under linux), and it's just FINE. Windoze will need a tad more memory but 64 MBytes would be more than sufficient so far as running Prime95 is concerned. An easy way to see if you have sufficient memory - irrespective of OS etc - is to look at the disk access light. If it's off most of the time you probably have at least enough memory in the system. If it's constantly or almost constantly on, and you hear lots of clattering from the head actuators, you *may* be short of memory - but, alternatively, it could just be that whatever you're running is doing a lot of file access. Anyway, if the disk isn't being accessed much, it isn't even worth thinking about adding more memory. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 21 Jan 2000 21:58:21 -0800 From: Spike Jones <[EMAIL PROTECTED]> Subject: Mersenne: 1E7 digit primes I did not find in the faq where one can reserve a number of 1E7 digit primes. I was able to sell the notion of running GIMPS to the IT people at my job, but only by offering the possibility of a monetary prize. Please, how may I reserve about 50 1E7 digit primes that have been prechecked for small factors? Thanks! spike _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 21 Jan 2000 12:15:06 -0800 From: Stefan Struiker <[EMAIL PROTECTED]> Subject: Mersenne: Brief But Exclusive Access M-Team: With 2 weeks dedicated access to a PII600/64M, what OS/Prime?? mix would you choose to best M-prime away that time? Such Dreams, Stefan S. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 21 Jan 2000 17:29:03 -0800 From: Stefan Struiker <[EMAIL PROTECTED]> Subject: Mersenne: CORRECTED Brief...Access M-Team: With 2 weeks dedicated access to a PIII 500/64M, what OS, running Prime??, would you choose to best M-prime away that time? Such Dreams, Stefan S. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 22 Jan 2000 11:31:23 -0800 From: Will Edgington <[EMAIL PROTECTED]> Subject: Re: Mersenne: Factoring Mersenne Daniel Grace writes: > Anyway, any mersenne's factor can be written as 2kp+1 <snip> > directly). Call (P-1)/p = Q > > Then 2n = Q mod p > n = Q/2 mod p which is well defined > Therefore we can find the sun of the two factors mod p. I think what you are trying to say is M_p is composite for p a prime iff 1+2kp divides (2^(p-1)-1)/p - k for some k>0. If I am not mistaken factoring this using current methods is harder than factoring 2^p - 1. Yup, almost certainly, if only because k is needed twice. The current trial factoring method does not even use k per se. Remeber it is easy to trial divide 2^p - 1 using bit wise operators, because 2^p - 1=1+2+2^2+...+2^(p-1). Let u be a potential divisor (e.g. u=2kp+1) then let j be smallest int. such that 2^j-1>u then you can try dividing 2^p-1 using just j bits of storage. e.g. start with 1+2+2^2+...+2^(j-1), subtract u, shift to the left appending 1's at the start, until you get v>u, subtract u and so on. I think that the software stops if it gets a residue of 0 before all p bits have been eliminated - in this case u divides some smaller Mersenne. Not quite. My "reverse method" works that way, and will find the smallest Mersenne exponent which is a multiple of a given odd number, but the fastest-so-far trial factoring method actually squares and perhaps multiplies by two modulo the trial factor each loop, starting with two and looping over the _bits_ of the Mersenne exponent, making it quite fast. If the particular bit is one, the multiply by two occurs; if it's zero, it doesn't. That is, it calculates the Mersenne number (two to the exponent power) mod the trial factor. This algorithm is in Knuth, apparently, which I don't have a copy of. Before GIMPS, I was doing something slower; George Woltman told me about this method, speeding up my then-current trial factoring program by a factor of about three (in Jan. 1996 or so). Will _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ End of Mersenne Digest V1 #682 ******************************
