Re: Mersenne: Like missing baby's first step
Jeff Woods wrote: At 01:11 PM 7/30/01 -0500, you wrote: I stepped away from my machine at 99.92% completion of its iterations, and when I came back it was 0.04% into processing the next number. Is there some way I can see what happened? Some sort of log file? Check the file RESULTS.TXT in the Prime95 (or mprime) directory. At minimum, at the end, it will have the actual results. If you didn't hear it do anything, long odds are that it was not a prime number. HI, I think it is more the following situatiuon: 95+% done, connecting to prime.net - GET NEW WORK !! - start with new work ! After 5-7% the old workfile gets it's active flag back and will be completed. This situation is really b*llsh*t, imagine the new number is very high, it tooks 1 week to complete the 7% mark and complete the old nonprime. Christian _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Like missing baby's first step
I think it is more the following situatiuon: 95+% done, connecting to prime.net - GET NEW WORK !! - start with new work ! After 5-7% the old workfile gets it's active flag back and will be completed. This situation is really b*llsh*t, imagine the new number is very high, it tooks 1 week to complete the 7% mark and complete the old nonprime. Christian It is more like n days work left (where n is configurable) get new work New work not tested for P-1 factors then first do P-1 factoring, as we know that this is done relatively fast and we cannot guarantee that we will have work after P-1 factoring (you may even find a factor!). No more exponents without p-1 factoring - continue with first item in worktodo list (i.e. the old work) Kind Regards, Martijn _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Like missing baby's first step
Hi, At 04:37 PM 7/31/2001 +0200, Christian Goetz wrote: 95+% done, connecting to prime.net - GET NEW WORK !! - start with new work ! This situation is really b*llsh*t, imagine the new number is very high, it tooks 1 week to complete the 7% mark and complete the old nonprime. I've already fixed this in version 21 (but it isn't uploaded yet). The old behavior, which many find undesirable, will be available with a prime.ini setting. Regards, George _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Like missing baby's first step
I think it is more the following situatiuon: 95+% done, connecting to prime.net - GET NEW WORK !! - start with new work ! After 5-7% the old workfile gets it's active flag back and will be completed. The work done on the new exponent is either trail factoring or P-1 factoring. Trail factoring on the new exponent is unlikely because the trail factored exponents are way ahead of the first time LL tests. When the P-1 test is finished or when there is not enough memory available to complete the test the LL test on the old exponent continues. The LL test on the new exponent will be started after the LL test in the old exponent is finished. This situation is really b*llsh*t, imagine the new number is very high, it tooks 1 week to complete the 7% mark and complete the old nonprime. This is done to make sure your computer has always some work queued up in case a factor is found and your computer is not online or the primenet server is unavailable. In this situation there is more time to get a new exponent after the factor is found. Sander _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: M(2) - composite?!
Hi all, I'm a bit puzzled. The other day, I donated blood and kept my mind busy by doing LL tests on a few exponents mentally. I kept getting the result that the LL test for M(2) ends up resulting in a repeating value of -1, and certainly cannot ever become zero. Am I missing something really obvious? I confirmed it on paper later to make sure I didn't make a mistake in the mental math. Nathan _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: What is done during a LL and what are the timing
-Original Message- From: George Woltman [EMAIL PROTECTED] To: Jeroen [EMAIL PROTECTED]; [EMAIL PROTECTED] [EMAIL PROTECTED] Date: 31 July 2001 04:01 Subject: Re: Mersenne: What is done during a LL and what are the timing 1% of time - Do something with the result to multiply it with itself Oh, you are a tease. :-) What is it that you do? Regards, George Daran _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M(2) - composite?!
How did you get -1? Lucas-Lehmer Test: For p odd, the Mersenne number 2p-1 is prime if and only if 2p-1 divides S(p-1) where S(n+1) = S(n)2-2, and S(1) = 4. You missed the premise for p odd. And even so, S(p-1)/(2p-1) with p = 2; S(1)/3 = 4/3. Carleton - Original Message - From: Nathan Russell [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, July 31, 2001 2:19 PM Subject: Mersenne: M(2) - composite?! Hi all, I'm a bit puzzled. The other day, I donated blood and kept my mind busy by doing LL tests on a few exponents mentally. I kept getting the result that the LL test for M(2) ends up resulting in a repeating value of -1, and certainly cannot ever become zero. Am I missing something really obvious? I confirmed it on paper later to make sure I didn't make a mistake in the mental math. Nathan _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M(2) - composite?!
-Original Message- From: Nathan Russell [EMAIL PROTECTED] To: [EMAIL PROTECTED] [EMAIL PROTECTED] Date: 31 July 2001 19:51 Subject: Mersenne: M(2) - composite?! Hi all, I'm a bit puzzled. The other day, I donated blood and kept my mind busy by doing LL tests on a few exponents mentally. I kept getting the result that the LL test for M(2) ends up resulting in a repeating value of -1, and certainly cannot ever become zero. Am I missing something really obvious? I confirmed it on paper later to make sure I didn't make a mistake in the mental math. From http://mersenne.org/math.htm (brackets and exponentiation added for the sake of clarity) The Lucas-Lehmer primality test is remarkably simple. It states that 2**P-1 is prime if and only if S(p-2) is zero in this sequence: S(0) = 4, S(N) = S(N-1)**2 - 2 mod 2**P-1. If P=2 then S(P-2) is S(0) is 4 which is clearly not 0. It's not even 0 mod 3 However http://www.utm.edu/research/primes/mersenne.shtml#test does state the P must be odd. So I guess the mersenne.org page is wrong. Nathan Daran _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Managing factor lists
I'm after a simple program that can manage a list of factors. With some expression dependant on a single variable such as n, I'd like it to be able to accept new factors for a given n, check they are factors, then rewrite the factor list including the length of the remaining cofactor. I'd be suprised if one wasn't already in use for the Mersenne numbers. My reason for asking is that I'd like to go through my current lists of factors for n!+-1 (n=400) and for NSW numbers (similar to Mersennes!), checking for any possible typos or missing small factors. Thanks, Andrew Walker _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M(2) - composite?!
From: Nathan Russell [EMAIL PROTECTED] Hi all, I'm a bit puzzled. The other day, I donated blood and kept my mind busy by doing LL tests on a few exponents mentally. I kept getting the result that the LL test for M(2) ends up resulting in a repeating value of -1, and certainly cannot ever become zero. Am I missing something really obvious? I confirmed it on paper later to make sure I didn't make a mistake in the mental math. One proof of the LL test notes that if we define a[0] = 4 a[j+1] = a[j]^2 - 2(j = 0) then a[j] = (2 + sqrt(3))^(2^j) + (2 - sqrt(3))^(2^j) (j = 0) This is a simple induction argument. Next, if alpha = (1 + sqrt(3))/sqrt(2) beta = (1 - sqrt(3))/sqrt(2) then alpha^2 = 2 + sqrt(3) beta^2 = 2 - sqrt(3) alpha*beta = -1 so a[j-1] = alpha^(2^j) + beta^(2^j)(j = 1) If N = 2^p - 1 is prime, and p = 3 is odd, then N == 7 (mod 24). Therefore 2 is a quadratic residue (indeed, 2^((p+1)/2) is a square root of 2 modulo N) but 3 is a quadratic nonresidue. alpha and beta are algebraic conjugates in GF(N^2). So alpha^N = beta and beta^N = alpha (mod N). Since alpha*beta = -1, this implies alpha^(N+1) == beta^(N+1) == -1 (mod N) and a[p-1] == alpha^(N+1) + beta^(N+1) == -2 (mod N) . Therefore a[p-2] == 0 (mod N). When p = 2 and N = 3, we can neither claim that 2 is a quadratic residue nor that 3 is a non-residue. Both alpha and beta reduce to 1/sqrt(2) mod 3. As in the case where p is odd, alpha and beta are in the extension field GF(N^2) and not the base field GF(N). Unlike that case, alpha = beta rather than alpha = beta^N and beta = alpha^N. The proof falls apart. Peter Montgomery _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Suggestion for mprime documentation
I would have just sent this to George, but I thought others might want to comment. I think the -m (menu) option of mprime deserves better press. The only negative about starting mprime with it it is that the menu choice of 6 is needed to start LL checking (or whatever). After that the -d option is active (and I like to see what's going on), and more importantly, ^C does not terminate the program, but brings up the menu again. This allows easy checking of completion dates, and I like to see which way they are moving. For me, it's -m rather than -d from here on out. I apologize to the real mathematicians here who may be offended by something this plebeian. Gerry -- mailto:[EMAIL PROTECTED] Gerry Snyder, AIS Symposium Chair, Region 15 RVP Member San Fernando Valley, Southern California Iris Societies in warm, winterless Los Angeles--USDA 9b-ish, Sunset 18-19 my work: helping generate data for: http://galileo.jpl.nasa.gov/ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Like missing baby's first step
Christian Goetz wrote: 95+% done, connecting to prime.net - GET NEW WORK !! - start with new work ! This situation is really b*llsh*t, Not BS at all; the replies to this original post have taught me a bit about how Prime95 maximizes the resources of the client pc, particularly those on dial up connections (like mine). George Woltman wrote: I've already fixed this in version 21 (but it isn't uploaded yet). The old behavior, which many find undesirable, will be available with a prime.ini setting. Too bad it needed to be 'fixed'. This thread has shown me that the problem is only in the user's imagination. Still, I'm not a math guru, I'm in this for the ability to participate in a distributed computing project and to also see my id in the Top Producers list. I guess we all get something different from our association with GIMPS and maybe the orderly completion of exponents is more important than efficiency to some. Cheers... Russ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
