Mersenne: Prime95 as a windows service
This may be a silly question but I've only recently had the need for Prime95 having used the NT service version before. If Prime95 is running as a service, how does one get at the user interface? It doesn't have a separate interface executable like the NT service version. Do I just start the executable manually? I don't want to just go ahead and do that because it *used* to corrupt the safe file and I'm not sure that it still doesn't. :-) Even still, I don't want to start another copy crunching. If anyone can let me know, I'd appreciate it. Rick. - [EMAIL PROTECTED] http://www.alienshore.com/ _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Worth it?
Heya Lucas > P-1 factoring is based upon Fermat's little theorem which states that > with gcd(a,p)=1, p prime, a^(p-1)==1 mod p > What if we use 2 as a base? Well, for mersenne numbers, this might be to > our advantage. Note that 2^n==1 mod Mn, hence 2^q==2^(q mod n) mod Mn. Unfortunately we're in a circular argument at this point. The factors of 2^p-1 are of the form 2kp+1 - also, even for n composite, the 'new' (primitive) factors of 2^n-1 are of the form kn+1. So any prime factor q has q-1 divisible by n, and we already have 2^n=1 mod Mn and hence mod q... Alternatively, think of the values 2^0, 2^1, 2^2... 2^(n-1), which would be ALL the values 2^q mod Mn can possibly take. So if this method found a factor, it would be a common factor of 2^q-1 and 2^n-1, in other words, just one of the known algebraic factors 2^gcd(q,n)-1. P-1 is good up to a point... the prime factors P it finds will by definition either have ALL factors of P-1 very small, or your initial base is already a high power (which is very unlikely). It's good to find the 'smooth' P-1's - put it another way, the factors the P-1 algorithm finds are themselves very easy to prove prime or composite. While the vast majority of primes (and thus potential factors) certainly do not always have small factors in P-1. It will catch a few several digit factors - after that, you've pretty well exhausted the lowest cherries off the tree. Chris _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Mersenne Trivia (was Re: p-1 algorithm)
On Fri, 23 Jul 1999 [EMAIL PROTECTED] wrote: > > EXERCISE: which movie is the following quote from? > > "...and three shall be the number of the counting. Four shalt thou not count, > nor two, excepting thou then proceed to three. Five is right out..." > > -Ernst Too easy. Here's more of a challenge, who wrote this about the perfection of the number six? "For six is the first number that is filled by conjuction of the parts, the sixth, the third, and the half: which is one, two, and three; all which conjoined are six. Parts in numbers are those that may be described by how many they are, as a half, a third, a fourth, and so forth. But four being in nine, yet is no just part of it: one is the ninth part, and three the third part. But these two parts, one and three, are far from making nine the whole. So four is a part of ten, but no just part: one is the tenth part, two the fifth, and five the second: yet these three parts one, two, and five, make not up full ten, but eight only. As for the number of twelve, the parts exceed it. For there is one the twelfth part, six the second, four the third, three the fourth, and two the sixth. But one, two, three, four, and six, make about twelve, namely sixteen. This by the way now to prove the perfection of the number of six, the first (as I said) that is made of the conjuction of the parts..." _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: p-1 algorithm
A small observation, maybe even trivial: Viewed over a finite ring (field) of Mp = 2^p - 1 elements the polynomial x^p - 1 splits (completely, of course) into linear factors of the form (x - 2^r) for 0 <= r <= p-1. Alternatively, x^p - 1 = (x-1)(x-2)(x-4)(x-8)(...)[ x - 2^(p-1)] (mod Mp) As a buddy once asked, "So what?" I rarely had a good answer for him and I do not have one now. Joth - Original Message - From: <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, July 23, 1999 11:36 AM Subject: Mersenne: Re: p-1 algorithm > Lucas Wiman wrote, about the p-1 algorithm: > > >What if we use 2 as a base? > > Unfortunately, 2 is not an eligible base for the powering. > > Example: let's attempt to factor 2^11 - 1 = 23*89 via p-1. The smaller > factor has p-1 = 22=2*11, so raising the base to the powers 2 and 11 > and gcd'ing should reveal the factor. Let's denote the product of the > small primes used for the powering by #, and try bases A = 2 and 3: > > A=2: 2^22 mod M11 = (2^11)^2 mod M11 == 1. You can continue to power until > you're blue in the face, and all you'll ever get is one, i.e. gcd(a^#-1, M11) > = 0. > > A=3: 3^22 mod M11 = 1013, so gcd(a^#-1, M11) = gcd(1012,2047) = 23. > > For Mersennes you can in fact use any base you like, as long as it's not > a power of 2. > > EXERCISE: We wish to attempt to find an odd prime factor p of a number N > via the p-1 method. What is the mathematical requirement for A to be an > eligible base for the powering? > > EXERCISE: which movie is the following quote from? > > "...and three shall be the number of the counting. Four shalt thou not count, > nor two, excepting thou then proceed to three. Five is right out..." > > -Ernst > _ > 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
Mersenne: Re: p-1 algorithm
Lucas Wiman wrote, about the p-1 algorithm: >What if we use 2 as a base? Unfortunately, 2 is not an eligible base for the powering. Example: let's attempt to factor 2^11 - 1 = 23*89 via p-1. The smaller factor has p-1 = 22=2*11, so raising the base to the powers 2 and 11 and gcd'ing should reveal the factor. Let's denote the product of the small primes used for the powering by #, and try bases A = 2 and 3: A=2: 2^22 mod M11 = (2^11)^2 mod M11 == 1. You can continue to power until you're blue in the face, and all you'll ever get is one, i.e. gcd(a^#-1, M11) = 0. A=3: 3^22 mod M11 = 1013, so gcd(a^#-1, M11) = gcd(1012,2047) = 23. For Mersennes you can in fact use any base you like, as long as it's not a power of 2. EXERCISE: We wish to attempt to find an odd prime factor p of a number N via the p-1 method. What is the mathematical requirement for A to be an eligible base for the powering? EXERCISE: which movie is the following quote from? "...and three shall be the number of the counting. Four shalt thou not count, nor two, excepting thou then proceed to three. Five is right out..." -Ernst _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Worth it?
Lucas Wiman wrote: > P-1 factoring is based upon Fermat's little theorem which states that > > [...] > What if we use 2 as a base? Well, for mersenne numbers, this might be to The problem is that 2 is not a primitive root (mod Mp). From a computers point of view, the mod Mp operation is a rotate and add, so if you start with a single bit set (2d = 10b), that bit will rotate around the p possible positions like mad but you´ll only ever get values of 2^n, 2^E == 2^n (mod Mp). So you could only find factors of the form 2^n-1. Ciao, Alex. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne Digest V1 #602
Mersenne Digest Friday, July 23 1999 Volume 01 : Number 602 -- Date: Thu, 22 Jul 1999 11:26:03 -0400 From: Pierre Abbat <[EMAIL PROTECTED]> Subject: Mersenne: Computing noises; was Worth it? > (Off topic, when I computed that value in Landon's Calc program, my computer > PII/233 started making a weird humming noise. The noise stopped when the > calculation finished. Very strange indeed...) I'm running Prime95 on a computer at the office, and it emits faint cricketish noises from the speakers while it's working. phma _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Thu, 22 Jul 1999 16:50:34 +0100 From: Gordon Spence <[EMAIL PROTECTED]> Subject: Mersenne: Re: Allocation of Prize Fund I have watched with interest the ideas flowing around for the distribution of the prize money awarded by the EFF and how we should try and reach an equitable distribution. In fact the answer is simple, the person who discovers it is *entitled* to it, end of story. I would hope that they would *choose* to donate some to George and Scott, but if they decide not to well then that is up to them. Direct quote from eff page > > Through the EFF Cooperative Computing Awards, EFF will confer prizes of: > $50,000 to the first individual or group who discovers > a prime number with at least 1,000,000 decimal digits Seems clear to me, the GIMPS s/w is given away free to the individual who runs the test. If we want to amend that then George will (or have to get drawn up) a legally binding software license. Now of course if the next winner comes from a country who doesn't recognise US laws... Now that would be interesting, what would the EFF do then given that they are entirely about freedom and the rights of the infividual. As a Mersenne prime discoverer it would appear that I would be on the panel(s) that have been suggested, and my vote goes to allowing the discoverer to keep it and do what their conscience tells them is the right thing to do. I don't agree with Luke's sentiments about orderly progress, having already tested one number in the 20m range. As soon as V19 is available I'm jumping up into the 33-35m range. As long as they all get tested does it matter in what order? So a test will take my PII-300 about 3 years, so what, if I've got the patienceI can always switch the intermediate results over to faster processors as I get them. regards Gordon Spence (finder of M2976221 which earned me precisely $0.00 ) _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Thu, 22 Jul 1999 10:47:39 -0600 From: "Blosser, Jeremy" <[EMAIL PROTECTED]> Subject: Mersenne: Squaring algorithm... Just was thinking the other day about this... Forgive me if its been discussed before etc. Aren't there other "better" algorithms for finding the square of a number besides using an FFT? Sure an FFT is great for multiplying two different numbers, but for squaring a number isn't the case a little different. Plus, going off what I've read on FFT's, it runs in O(n log n) time. So wouldn't a summation algorithm work better. For example, to find the square of a number k take the sum of n=1 to n=k of 2n-1. So 3**2 is 1+3+5 = 9 4**2 is 1+3+5+7 = 16 etc... So the sqaure performs in O(n) time. Plus, you could already throw in the sub 2 by starting at -1 instead of 1. And figuring out the mod is just as easy. k is the sum of n=2**p-1 to n=k of 2n-1 (This would give k**2 - 2**p-1). The only hassle is adding *big* numbers up, but I'm not sure how the ramifications of doing carries across boundaries and such would factor into the equation etc. Just a thought. - -Jeremy _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Thu, 22 Jul 1999 19:11:07 +0200 From: "Hoogendoorn, Sander" <[EMAIL PROTECTED]> Subject: RE: Mersenne: The sound of number searching Read the archives, this has been discussed 2 or 3 times before - -Original Message- From: burlington john [mailto:[EMAIL PROTECTED]] Sent: Wednesday, July 21, 1999 19:47 To: [EMAIL PROTECTED] Subject: Mersenne: The sound of number searching Hello Mersenne, Sorry for bad english its not my native language, thanks. I run mprime (or prime95 ntprime) on my laptop. When I start the programm on my notebook it makes a strange mechanical pulsing sound like an old damaged wheel or like an ill cricket. The sound doesn't come out of the speakers
Re: Mersenne: The sound of number searching
Back in 1974 I got a summer job as a night time computer operator for a NCR Century-101 (32K core memory) with two 5 MB 14" Disk Drives. Most things were on cards. The programmer had programs that would play simple tunes on the radio if the radio was on or very near the computer. He had about a dozen different programs in COBOL for different tunes, like Dixie, Swanie River, etc. He would also use the radio as feedback as to whether his program was running correctly or not. He could then monitor the progress from across the room, without looking at the console. Kip Luke Welsh wrote: > > At 11:35 PM 7/22/99 +0100, Brian J. Beesley wrote: > > >Back more or less to topic - > > Oh, this is very much on topic! > > > when I was a computing neophyte, a > >quarter of a century ago, I was told a story by an engineer working > >for a major mainframe supplier. For a laugh, the development team > >wired up a loudspeaker (presumably through a buffer and amplifier of > >some sort) to one of the bits in a CPU shift register. (This was > >easily done in the days when everything was discrete components!) > >The trick was then to code your program so that it performed to > >specification, but, by insertion of extra instructions to tweak this > >particular bit at suitable times, played interesting tunes whilst > >doing so! > > Alex Hurwitz loves this story. They did just that on the SWAC. It > was captured for prosperity in the film 'Magnetic Monster'. I once > made some MPegs and put them on the wwweb. I wonder if they are > still there? Alex says the sounds in the movie were produced by LL > tests. > > I recall the CDC 3150 was so wired from the factory. There was > even a volume control on the operator's console. Probably a very > helpful debug tool as you could not see the console when you were > across the room with your head inside a 32 KB memory bank the size > of a refrigerator, poking away looking for faulty a core memory. > > --Luke > > _ > 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
Mersenne: Links in the FAQ
I added a supplemental resources, and references section to the FAQ. Feel free to send me any links/books that you think should go in there. I'm trying to keep everything at least tangentaly related to the FAQ's on this list (and yes, the sites about general primality proving, and factoring are supposed to be there)... Thank you, -Lucas _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
