Mersenne: Prime95 a bit faster in Win2K than Win98...
Oh well, since it's so quiet on the list, I'll post this little comparison of Win98 vs Win2K. I've been playing around with a free copy of Win2K RC2 I got from a mag, and decided to compare Prime95 performance to Win98. Prime95 19.1.1 with a PentiumPro-233MHz/64Mb RAM, M8984771: Win98 0.463s Win2K 0.456s It's not a big difference. but 1.5% better performance in Win2K is nothing to sneeze at. That's one more reason for me to migrate to Win2K... It's rock solid, fast and with some cool GUI enhancements. With 64Mb it's faster than NT4, and about as fast as Win98 as long you don't load many apps. I think the minimum recommendation for memory would be at least 128Mb. Have a nice holiday, -- Petri H. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: Mersenne Digest V1 #672
That's certainly the 'obvious' way of trying to construct such starting values. Can anyone think of any other ways to come up with them? It seems 'likely' that if there is no finite covering set of divisors there are an infinite number of primes... but my intuition is more likely a negative endorsement than a positive one ;-) This is indeed a great unknown, but a familiar situation. Our heuristics and our instincts tell us we expect an infinite number of Mersenne (and a finite number of Fermat) primes. Neither of which are proven... perhaps may never be. The important thing about constructing such a provable sequence of composites is it shows that 'expecting an infinity' doesn't necessarily 'guarantee any'. The constructions may seem a little 'artificial', but they're valid 'islands' of counterexamples in a sea of subjects where heuristics is currently the best we have. As for the finiteness of the covering set, again it's currently the limit of our knowledge. Which is more likely, the existence of an infinite covering set, or of a single prime? Chris Nash Lexington KY UNITED STATES _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Mersenne Digest V1 #672
Date: Sat, 18 Dec 1999 08:34:06 - From: "Brian J. Beesley" Subject: Re: Mersenne: v19 and priorities The valid range is 0-15. If you specify 0, you will lose half your CPU to the OS's native cycle sink. This is probably not what you want. Which OS is this (some win32 obviously, but which)? In both windows 9x and 2k, the idle thread has priority far below zero; I have never seen it get any time slices while a priority zero (idle process, idle thread) task was running. Date: Sat, 18 Dec 1999 22:34:10 -0500 From: "Chris Nash" Subject: Re: Mersenne: Fibonacci Series U(1) = 1786772701928802632268715130455793 U(2) = 1059683225053915111058165141686995 U(N+2) = U(N+1) + U(N) I checked a few thousand terms, and they were all composite. There is almost certainly a 'covering set' of divisors. In essence you need to find a set of primes P and a modulus M, then prove that U(N) has a factor in P specified by the value of N mod M. That's certainly the 'obvious' way of trying to construct such starting values. Can anyone think of any other ways to come up with them? It seems 'likely' that if there is no finite covering set of divisors there are an infinite number of primes... but my intuition is more likely a negative endorsement than a positive one ;-) Colin Percival _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Fibonacci series..
"Ian L McLoughlin" [EMAIL PROTECTED] asks Since the list is quiet... Does a Fibonnacci series contain a finite or an infinite number of primes? From what I understand.. In a gen.F sequence if the first two numbers are divisible by a prime all its numbers are divisible by the same prime, if the first two numbers are co-prime is there a generalised sequence that contains NO PRIMES This is part of problem A3 in Richard K. Guy's `Unsolved Problems in Number Theory', Second Edition, Springer-Verlag, 1994. This book could make a good Christmas gift to your number theory friends. Richard Guy gives solutions starting with 1786 772701 928802 632268 715130 455793 1059 683225 053915 111058 165141 686995 (Graham) and 49463 435743 205665 62638 280004 239857 (Knuth) _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: high factoring bug in prime95
George Woltman wrote: This is primarily directed at the 4 or 5 users dedicated to factoring exponents above 35 million. Prime95 version 19.1 has a bug that causes it to miss some factors for these large exponents. If you are one of the 4 or 5 affected users, please download version 19.2 to fix the problem. One ugly fact about this too... exponents already tested above 35.79M may need to be re-tested! Within 10 seconds of starting v19.2, two new small factors were found for exponents already tested and found to have factors (just not that small)... Six new smaller factors were found testing just 24 exponents previously tested that had factors. And for exponents that have had no factors found yet, there might be a smaller one that wasn't discovered :( Eric Hahn _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: high factoring bug in prime95
Aargh!! I've spent *weeks* trial factoring some of those, time which could have been better spent in ECMNET. Unhappy. Ah well, it's going to have to wait. I've got other things to do. In the meantime, I'll just stop the programs. Paul -Original Message- From: Eric Hahn [mailto:[EMAIL PROTECTED]] Sent: 20 December 1999 17:52 To: George Woltman Cc: [EMAIL PROTECTED] Subject: Re: Mersenne: high factoring bug in prime95 George Woltman wrote: This is primarily directed at the 4 or 5 users dedicated to factoring exponents above 35 million. Prime95 version 19.1 has a bug that causes it to miss some factors for these large exponents. If you are one of the 4 or 5 affected users, please download version 19.2 to fix the problem. One ugly fact about this too... exponents already tested above 35.79M may need to be re-tested! Within 10 seconds of starting v19.2, two new small factors were found for exponents already tested and found to have factors (just not that small)... Six new smaller factors were found testing just 24 exponents previously tested that had factors. And for exponents that have had no factors found yet, there might be a smaller one that wasn't discovered :( Eric Hahn _ 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: high factoring bug in prime95
Gee I wish I could have all of the time back that I spent on "bad" Microsoft software too. ; Alan From: Paul Leyland [EMAIL PROTECTED] To: "'Eric Hahn'" [EMAIL PROTECTED], George Woltman [EMAIL PROTECTED] Copies to: [EMAIL PROTECTED] Subject:RE: Mersenne: high factoring bug in prime95 Date sent: Mon, 20 Dec 1999 10:33:03 -0800 Aargh!! I've spent *weeks* trial factoring some of those, time which could have been better spent in ECMNET. Unhappy. Ah well, it's going to have to wait. I've got other things to do. In the meantime, I'll just stop the programs. Paul -Original Message- From: Eric Hahn [mailto:[EMAIL PROTECTED]] Sent: 20 December 1999 17:52 To: George Woltman Cc: [EMAIL PROTECTED] Subject: Re: Mersenne: high factoring bug in prime95 George Woltman wrote: This is primarily directed at the 4 or 5 users dedicated to factoring exponents above 35 million. Prime95 version 19.1 has a bug that causes it to miss some factors for these large exponents. If you are one of the 4 or 5 affected users, please download version 19.2 to fix the problem. One ugly fact about this too... exponents already tested above 35.79M may need to be re-tested! Within 10 seconds of starting v19.2, two new small factors were found for exponents already tested and found to have factors (just not that small)... Six new smaller factors were found testing just 24 exponents previously tested that had factors. And for exponents that have had no factors found yet, there might be a smaller one that wasn't discovered :( Eric Hahn _ 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 "A programmer is a person who turns coffee into software." Alan R. Vidmar Assistant Director of IT Office of Financial AidUniversity of Colorado [EMAIL PROTECTED](303)492-3598 *** This message printed with 100% recycled electrons *** _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Fibonacci Series
François Perruchaud wrote: An old book of mine gives without proof an example of Fibonacci Sequence that countains no primes, but where U(1) and U(2) are co-prime. The sequence was found by R. L. Graham. Reference : "A Fibonacci-like sequence of composite numbers", R.L. Graham, Math. Mag. 37, 1964. U(1) = 1786772701928802632268715130455793 U(2) = 1059683225053915111058165141686995 U(N+2) = U(N+1) + U(N) I only verified with Mapple that U(1) and U(2) are co-prime and that U(N) is composite for N10. Unfortunately, Graham made a computational error in calculating U(1) and U(2), and the above values don't work as desired. The following will correct the error: U(1) = 331635635998274737472200656430763 U(2) = 1510028911088401971189590305498785 U(N+2) = U(N+1) + U(N) The trick is to create a "covering" of the indices, i.e. a set of congruences such that every index satisfies at least one of the congruences. The best way to understand this is by this example. Note that F(4) is divisible by 3, and that every 4th term in the Fibonacci sequence is also divisible by 3, i.e. the period of 3 is equal to 4. Using the U() series instead of the F() series, it can be verified that U(4n+2) is divisible by 3 for all n. Similarly, U(8n+4) is divisible by7 U(16n+8) is divisible by 47 U(32n+16) is divisible by 2207 U(64n+32) is divisible by 1087 U(64n)is divisible by 4481 This assures that U(2n) is composite for all n, since every even number is either 2 mod 4, 4 mod 8, 8 mod 16, 16 mod 32, 32 mod 64, or 0 mod 64. Note that F(8)/F(4) = 7, F(16)/F(8) = 47, F(32)/F(16) = 2207, F(64)/F(32) = 1087*4481. For the odd indices, consider separately the cases 6n+1, 6n+3 and 6n+5. First, the period of 2 is 3, and U(6n+3) is divisible by 2 for all n (in fact, U(3n) is divisible by 2, but at this point we only need the odd values). For 6n+5, we have U(18n+5) is divisible by 17 (actual period = 9) U(18n+11) is divisible by 19 U(54n+17) is divisible by 53 (actual period = 27) U(54n+35) is divisible by 109 (actual period = 27) U(54n+53) is divisible by 5779 which covers all the cases U(6n+5). For 6n+1, we have U(30n+7) is divisible by5 (actual period = 5) U(30n+13) is divisible by 11 (actual period = 10) U(30n+19) is divisible by 61 (actual period = 15) U(30n+25) is divisible by 31 U(60n+1) is divisible by 2521 U(60n+31) is divisible by 41 (actual period = 20) which covers all the cases U(6n+1). This completes the coverage of all cases, thus U(n) is composite for all n. Graham's error was that his original U(1) and U(2) gave U(64n+33) divisible by 1087, rather than U(64n+32). This doesn't mean necessarily that any U(n) was prime in his original sequence, only that U(n) could not easily be proved composite. Regards, Bill _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Looking for a new maintainer for OS/2 version
A few weeks ago the PC I used for maintaining the OS/2 version of George Woltman's Prime program broke down and since that was it's only reason to stay in existence I decided not to replace it. So I am lokking for a new maintainer of the PRIMEOS2 program. All source code of the latest version (3.3.1 dd 3/4/1999) are available. I also have a diff with the mprime version 18.1.2 which formed the basis of this version. Please reply to me when you are interested and I will inform you about more specific issues concerning the port. With kind regards, Michiel van Loon _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
