Mersenne Digest Thursday, October 21 1999 Volume 01 : Number 650 ---------------------------------------------------------------------- Date: Thu, 21 Oct 1999 10:20:56 -0700 From: "Joth Tupper" <[EMAIL PROTECTED]> Subject: Re: Mersenne: RE: PI and other periods A little number theory.... Expressed in base 10 (or anything) notation, rational numbers have a repeating pattern of _fixed_ length. (Sometimes the repeating digit pattern is '0' as in .50 for 1/2 in base 10 -- but this gets very close to a quibble). If n is relatively prime to 10 (not divisible by 2 or 5), and if phi(n) is the 'totient' function or the number of integers between 1 and n that are relatively prime to n, then 10^phi(n) has residue (reste) 1 on division by n or 10^phi(n) = 1 (modulo n). This is a variant on the Little Fermat Theorem and the Chinese Remainder Theorem or the group of units in a finite ring (or several other ways of constructing the same thing). For example, 10^12 = 13k + 1. Actually, 10^6 = 1 + 13*76923. The period of 1/13 is 6. We are guaranteed to get a repeating pattern for 1/n of length dividing phi(n). Now, phi(9) = 4 and the period of 1/9 is just 1 so phi(n) is a maximum period length. Back to pi: pi is not just irrational, it is transcendental. The square root of 2 is irrational but is a solution to X^2 - 2 = 0. Numbers which solve some polynomial (with integer coefficients) are called algebraic. Numbers not algebraic are called transcendental. JT - ----- Original Message ----- From: Joth Tupper <[EMAIL PROTECTED]> To: GIMPS <[EMAIL PROTECTED]> Sent: Thursday, October 21, 1999 7:33 AM Subject: Re: Mersenne: RE: PI and other periods > Anyone remember Louisville numbers? > > The simplest I recall is .110001000000000000000001000000... = sum of > 0.1^(n!) for n=1,2,3,... > > Many such numbers and constructions exist which share strange properties: > > 1) the digit patterns exist and are well-defined > 2) the numbers, like pi, are transcendental [i.e., cannot be roots of any > polynomial in one variable with integer coefficients]. > > [Recall that the rational number p/q is a root of the "polynomial" qX - p > = 0.] > > Showing pi transcendental takes a lot of effort. Showing the Louiville > numbers transcendental > takes a lot less effort (but maybe a lot more memory than I seem to have!). > > Joth > > > > ----- Original Message ----- > From: Philippe Trottier <[EMAIL PROTECTED]> > To: <[EMAIL PROTECTED]> > Sent: Wednesday, October 20, 1999 10:39 PM > Subject: Mersenne: RE: PI and other periods > > > > HI, > > > > Again if you look from a human eye, we can see (imagine) a nearly possible > > period in that number ..., again that's human brain doing overtime... But > > again MAYBE, there is a real period to that number... and this number also > > start to have a considerable amount of known digits (We would have to > share > > multiple generation just to say it) > > > > Philippe > > > > At 12:09 20.10.1999 +0100, you wrote: > > >Value of pi is the product of the infinite series ... > > > > > >pi = 4 (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 -1/15 + 1/17.........) > > > > > >Hope this helps.. > > > > > >Regards, > > >Ian McLoughlin, Chematek U.K. > > > > > >Tel/Fax : +44(0)1904 679906 > > >Mobile : +44(0)7801 823421 > > >Website: www.chematekuk.co.uk > > > > _________________________________________________________________ > > 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 > _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 13:40:49 -0400 (EDT) From: Darxus <[EMAIL PROTECTED]> Subject: Re: Mersenne: RE: PI and other periods On Thu, 21 Oct 1999, Philippe Trottier wrote: > Yes, I have learned math in French and its very far away. And my english > start to get rusted in Finland. sorry for the confusion, I know that PI is > irrational, but like the mersenne grouping , if you look at pi your brain > might force you to see some period or bunch of digits that seems to be > repeating... So you're not actually talking about a set of exact digits repeating, but some other repeating pattern ? Hmm. __________________________________________________________________ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Join the Great Internet Mersenne Prime Search http://www.mersenne.org/prime.htm _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 13:01:39 -0500 From: Tony Pryse <[EMAIL PROTECTED]> Subject: Re: Mersenne: estimating mersenne primes >At 08:56 PM 10/20/99 -0400, you wrote: >... snip ... >>I believe the first thing to do in finding an exponential curve fit is to >>take the log of the data, then apply a linear fit. (?) That is how I would >>do it anyway. This would produce identical results to the accuracy of the >>logarithm. >> >>-Lucas This is **not** the correct way to fit an exponential when you have "real" (i.e., experimental) data. The reason is that for least-squares fitting to be a maximum likelihood estimator of the "true" function, the measurement errors for each data point must be independent and normally distributed with constant standard deviation. Thus, if your data confrom to these requirements, doing a non-linear transformation (such as taking the log) will result in "data" that do not conform to these requirements. In practical terms, there is usually little difference between a nonlinear fit to exponential data and a linear fit to the same logarithmically transformed data, but sometimes there is a difference, so to be sure, one should never transform the data before fitting. How this applies to "fitting" Mersenne numbers is not clear, since the concept of measurement errors, or uncertainty, doesn't really apply, as best I can see. A maximum entropy method might be just as good as a least-squares approach. (Of course, another fundamental underlying assumption of any fitting procedure is that you are using the correct, or "true", functional form, which is not known in this case, or perhaps doesn't even exist!) Tony Pryse ***************************************************** * Kenneth M. (Tony) Pryse * Department of Biochemistry and Molecular Biophysics * Washington University School of Medicine * St. Louis, MO 63110 * [EMAIL PROTECTED] * 314-362-3345 ***************************************************** _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 13:36:51 -0500 From: Herb Savage <[EMAIL PROTECTED]> Subject: Mersenne: PI At 01:40 PM 10/21/99 -0400, Darxus wrote: >On Thu, 21 Oct 1999, Philippe Trottier wrote: > >> Yes, I have learned math in French and its very far away. And my english >> start to get rusted in Finland. sorry for the confusion, I know that PI is >> irrational, but like the mersenne grouping , if you look at pi your brain >> might force you to see some period or bunch of digits that seems to be >> repeating... > >So you're not actually talking about a set of exact digits repeating, but >some other repeating pattern ? Hmm. The current record for number of decimal digits of PI is 206 billion. See: http://www.cecm.sfu.ca/personal/jborwein/pi_cover.html The record time for a million digits of PI on a PC is 52 seconds. The record for most digits of PI on a PC is 2.5 billion digits in a little over 10 days. http://home.istar.ca/~lyster/pi.html I remember reading an interview with the Chudnovsky brothers a long time ago. I think they had computed about 4 billion digits at the time. Then they felt that there would be something interesting in the digits of PI if you computed them out far enough. They thought that this might happen by the time you got to 1 trillion digits. The article never hinted at what they thought that they might find. By the way, these are real mathematicians versus the fiction that was in the Sagan book Contact. Herb Savage _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 21:26:42 +0200 From: "Yves Gallot" <[EMAIL PROTECTED]> Subject: Mersenne: Re: Mersenne Digest V1 #648 > For these reasons (and for the fact that among the only other class of > numbers known to admit DWT arithmetic, the Fermats, there are vastly fewer > primality candidates than among the Mersennes), I predict that a Mersenne > prime will hold the record for a long time to come. Not true - DWT can be applied to any polynomial of the form x^n+/-1. - - If n > 1 and x^n-1 is prime, then x=2 and n is prime. With the form x^n-1, only the Mersenne numbers can be tested. - - If x > 2 and x^n+1 is prime, then x is even and n=2^m. With the form x^n+1, a large set of numbers can be tested the Generalized Fermat numbers. In a fixed range, they are more numerous than Mersenne numbers. Because n=2^m, we only have to use a FFT of length a power of 2. We have to use a base representation which is not a power of 2. If we consider that the advantage cancels the drawback, the test of a GFN is about as fast as a test of a Mersenne number. > There are two further reasons why non-DWT classes of numbers will be less > likely to yield a world-record-sized prime: > > (1) volunteers for distributed computing efforts will always tend to find > the prospect of findng a world-record size something more interesting > than something arcane like 'the largest known irregular Huffergnu"ten > prime octuplet,' i.e. GIMPS will attract more compute cycles because > it holds the current prime record, and by a whopping margin; and True. > (2) Among the Proths, the fact there are so many possible kinds of > candidates dilutes the effort, i.e. makes it vastly more > time-consuming to test all the candidates up below any > reasonably-sized threshold. The major advantage of the other forms is the fact that you don't have to organize the search! Because if the number of candidates is huge, the probability for a number to be tested twice is very small. The Mersenne number form has only one degree of freedom. If some forms with more degrees of freedom are as fast to test, the volunteers also will be more free. Yves _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 14:10:32 -0500 From: "Robert G. Wilson v" <[EMAIL PROTECTED]> Subject: Mersenne: Partial Factorization of M(5014947) Et al, Earlier this month, someone posted a question regarding the Mersenne number 5014947 and asked for its factors. Here is what I've been able to gleam. Sincerely yours, Robert G. Wilson v 5014947 = 3*7*47*5081 and its divisors are 1, 3, 7, 21, 47, 141, 329, 987, 5081, 15243, 35567, 106701, 238807, 716421, 1671649 & 5014947. f(n) = 2^f +1. f(1) = 3. f(3) = (1) * 3. f(7) = (1) * 43. f(21) = (1, 3, 7) * 5419. f(47) = (1) * 283 * 165768537521. f(141) = (1, 3, 47) * 1681003 * 35273039401 * 111349165273. f(329) = (1, 7 ,47) * 659 * 762394321774681 * 359687424377961714750891763743933975334959200103759485840227631801. f(987) = (1, 3, 7, 21, 47, 141, 329) * 5135123689810129 * C151. f(5081) = (1) * 10163 * 243889 * Composite. f(15243) = (1, 3, 5081) * 3048601 * Composite. f(35567) = (1, 7, 5081) * Composite. f(106701) = (1, 3, 7, 21, 5081, 15243, 35567) * Composite. f(238807) = (1, 47, 5081) * Composite. f(716421) = (1, 3, 47, 141, 5081, 15243, 238807) * Composite. f(1671649) = (1, 7, 47, 329, 5081, 35567, 238807 ) * Composite. M(5014947) = 2^5014947 -1 = (factors from f(n)) (1) 3, (3) 3, (7) 43, (47) 283, (329) 659, (21) 5419, (5081) 10163, (5081) 243889, (141) 1681003, (15243) 3048601, (106701) 14724739, (5081) 2478643907, (141) 35273039401, (141) 111349165273, (47) 165768537521, (329) 762394321774681, (987) 5135123689810129, (329) 359687424377961714750891763743933975334959200103759485840227631801, (987) 2169938845890939210595986882453006136908227137290342138096226473293044748893969050207434882048911068413643936897791965117470283570473755493061296806419, time one very large composite which has at least 16 factors. Good luck in finding them. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 16:27:46 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: PI At 01:36 PM 10/21/99 -0500, Herb Savage wrote: > I remember reading an interview with the Chudnovsky brothers a long time >ago. I think they had computed about 4 billion digits at the time. >Then they >felt that there would be something interesting in the digits of PI if >you computed >them out far enough. > They thought that this might happen by the time >you got to >1 trillion digits. I don't know if that makes much sense. If you do get something significant after a finite number of digits, it is probably a statistical fluke and won't hold up in the long run. +---------------------------------------------------------+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +---------------------------------------------------------+ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 16:24:12 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: estimating mersenne primes At 01:01 PM 10/21/99 -0500, Tony Pryse wrote: This is **not** the correct way to fit an exponential when you have "real" >(i.e., experimental) data. What is the correct way? I've been taking logs and then doing a linear regression, but what is the correct way? +---------------------------------------------------------+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +---------------------------------------------------------+ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 16:22:03 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: RE: PI and other periods At 01:40 PM 10/21/99 -0400, Darxus wrote: > irrational, but like the mersenne grouping , if you look at pi your brain > > might force you to see some period or bunch of digits that seems to be > > repeating... > >So you're not actually talking about a set of exact digits repeating, but >some other repeating pattern ? Hmm. I think he means that your mind will think it sees patterns when there aren't any. - - +---------------------------------------------------------+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +---------------------------------------------------------+ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 22:34:06 +0200 From: "tom ehlert" <[EMAIL PROTECTED]> Subject: Mersenne: primenet - stats.html Well, I like ithe statistices want I think is missing (and may be nice to look at): easy(IMHO) number of users number of maschines by time performance/ #of maschines performance/ #of users certainly not so easy: a coloured graph, showing in different colours for each week or month: double checking DONE - -2.000.000 double checking nearly finished(99% has been done) - at 2.200.000 double checking essentially done(95% has been done) - at 2.400.000 double checking starting - at 4.200.000 first time LLT DONE first time LLT nearly finished(99% has been done) - at 4.600.000 first time LLT essentially done(95% has been done) - at 5.500.000 first time LLT starting - at 8.700.000 double checking DONE - up to the current wanted factoring depth factoring nearly finished(99% has been done) - at 9.500.000 factoring essentially done(95% has been done) - at 9.8000.000 factoring starting - at 10.800.000 to program this,I would put easy criteria : 'nearly finished' : the first entry with less then 30 outstandng resuts (in a 100.000 range) 'essentially done' : the first entry with less then 120 outstandng resuts 'starting'; the first entry with more then 1000 entries 'available' the idea behind this: the general project is by far faster in progress then the very last and slowest user.So, to keep us satisfied with the projects general increase in speed , show whats going on. best regards tom ehlert _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 00:55:56 +0200 From: Lars Lindley <[EMAIL PROTECTED]> Subject: Mersenne: mprime startup at boot-time Hi everyone. I have request for help. I run mprime on Linux. What I want to do is to have mprime automatically start when I boot and send the -m output to a tty or something like that. Perhaps tty8? Is this possible?? Happy hunting, all! /Lars _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 16:46:19 -0700 (PDT) From: poke <[EMAIL PROTECTED]> Subject: Re: Mersenne: mprime startup at boot-time So you want the output of mprime to display on a virtual terminal? Unless you are displaying to a virtual terminal your data won't go anywhere, or worse someone who connects will see this extraneous data hit their screen every once in a while. You should be able to display to a virtual termina with a simple redirect: mprime -m > /dev/tty1 - -Chuck On Thu, 21 Oct 1999, Lars Lindley wrote: > Hi everyone. > I have request for help. > I run mprime on Linux. > What I want to do is to have mprime automatically start when I boot > and send the -m output to a tty or something like that. Perhaps tty8? > Is this possible?? > > Happy hunting, all! > /Lars > _________________________________________________________________ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers > -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : WWW: http://www.silverlink.net/poke : : E-Mail: [EMAIL PROTECTED] : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : Ask Mike! Aviation's response to Dear : : Abby. http://www.avstarair.com : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 19:57:11 -0400 From: "St. Dee" <[EMAIL PROTECTED]> Subject: Re: Mersenne: mprime startup at boot-time At 16:46 10/21/1999 -0700, poke wrote: > >So you want the output of mprime to display on a virtual terminal? Unless >you are displaying to a virtual terminal your data won't go anywhere, or >worse someone who connects will see this extraneous data hit their screen >every once in a while. > >You should be able to display to a virtual termina with a simple redirect: > >mprime -m > /dev/tty1 First, wouldn't you want to use mprime -d ? The -m flag simply brings up the menu. Secondly, I used to feed the output to a virtual terminal, but decided that having a hard copy that I could periodically check was better. I've been piping all the output to a file, such as mprime -d >>/home/GIMPS/tracking.txt. When it finishes reporting a result, I delete everything but the result and let mprime continue on to the next LL test using the same file. Just my $.02, Kel _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 19:05:20 -0500 From: Herb Savage <[EMAIL PROTECTED]> Subject: Re: Mersenne: PI At 04:27 PM 10/21/99 -0400, Jud McCranie wrote: >At 01:36 PM 10/21/99 -0500, Herb Savage wrote: > >> I remember reading an interview with the Chudnovsky brothers >> a long time ago. I think they had computed about 4 billion digits >> at the time. Then they felt that there would be something >> interesting in the digits of PI if you computed them out far enough. >> They thought that this might happen by the time you got to >> 1 trillion digits. > > >I don't know if that makes much sense. If you do get something >significant after a finite number of digits, it is probably a statistical >fluke and won't hold up in the long run. To be interesting to a mathematician it would have to be something like some statistical property of the digits of PI changing after a certain number of digits. Regards, Herb Savage _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 22 Oct 1999 01:10:42 +0100 From: "Ian L McLoughlin" <[EMAIL PROTECTED]> Subject: Mersenne: prime 95 version 19 Hi, O.K. I am sad and run the program on a cyrix 333....and before you all tell me I should only do trial factoring....and not hold up the general 'Je ne se quoi'...the new version is a behemoth into allocating weird new computer i.d s and making it very user unfriendly to those that are not 'au fait' with the system....I gain the impression from most listees that they have at least a post doctorate in math, and those that know anything about us poor mortals running Windows...well we are not worth knowing..... p.s ...You can memorise the pi fractionals ...add infinitum...surely...since this is a fractional series? i.e. + fract..-fract..+ fract....if you know them ok.... I think cyclic numbers are more intersting...perhaps? Any thoughts. Anybody out their write could integer stuff? Sorry... Must get back to Seti... Tel/Fax : +44(0)1904 679906 Mobile : +44(0)7801 823421 Website: www.chematekuk.co.uk _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 22 Oct 1999 01:20:08 +0100 From: "Ian L McLoughlin" <[EMAIL PROTECTED]> Subject: Mersenne: Dominoes A closed set of dominoes....take any number out from a set of double 6 type (28 set)and join them end to end....o.k... I'll go for ...er 2.3...what are yu left with digit wise on each end? O.K. Ian McLoughlin, Chematek U.K. Tel/Fax : +44(0)1904 679906 Mobile : +44(0)7801 823421 Website: www.chematekuk.co.uk _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 20:15:31 -0400 From: Pierre Abbat <[EMAIL PROTECTED]> Subject: Re: Mersenne: mprime startup at boot-time On Wed, 20 Oct 1999, you wrote: >Hi everyone. >I have request for help. >I run mprime on Linux. >What I want to do is to have mprime automatically start when I boot >and send the -m output to a tty or something like that. Perhaps tty8? >Is this possible?? Try adding the line 8:2345:respawn:/usr/local/bin/mprime to /etc/inittab. What I do is pipe the output of mprime to a tcl script which keeps the last 25 lines in a file. But then I can't type into it. Another way would be to use the screen program; you can run it on a screen, and attach a tty to the screen when you want to. phma _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 20:29:34 -0400 From: Pierre Abbat <[EMAIL PROTECTED]> Subject: Re: Mersenne: mprime startup at boot-time >Secondly, I used to feed the output to a virtual terminal, but decided that >having a hard copy that I could periodically check was better. I've been >piping all the output to a file, such as mprime -d >>>/home/GIMPS/tracking.txt. When it finishes reporting a result, I delete >everything but the result and let mprime continue on to the next LL test >using the same file. If you delete a file while a program is writing to it, it will keep on writing to the now nameless file, and will keep eating up disk space, until the program quits or closes the file, at which time the file will disappear. phma _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 02:38:34 +0200 From: Lars Lindley <[EMAIL PROTECTED]> Subject: Re: Mersenne: mprime startup at boot-time Thanks for the swift replies! I now have it like I want it. Regards, Lars _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 19:44:31 -0500 From: Herb Savage <[EMAIL PROTECTED]> Subject: Mersenne: Chudnovsky brothers For anyone interested I found the article I was thinking of on the Internet. The article was "The mountains of Pi" from the New Yorker, March 2, 1992. The entire article is at: http://www.lacim.uqam.ca/plouffe/Chudnovsky.html Regards, Herb Savage _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 20:44:34 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Re: Mlucas 2.7 on SPARC Brian Beesley writes: << I loaded Mlucas_2.7y onto a Ultra 10 (128 MB, Ultra IIi @ 300 MHz, Solaris 2.6) & have the following timings. The comparison MacLucasUNIX timings were generated using gcc with options - -O6 -mpcu=v9 -Wa,-xarch=v8plusa, using the same method I used for the timings I sent you for my Alpha system at the weekend. These are about 20% slower than the "production" version compiled with the Sun C compiler (binary provided by Simon Burge; I found the "Ultra 5" version was actually the fastest on my system). I was unable to benchmark MacLucasUNIX at 4096K FFT run length due to insufficient system memory - might _just_ manage with 192 MB. Format: FFT size, Mlucas, MacLucas 64K, 0.040, 0.049 80K, 0.058, n/a 96K, 0.079, n/a 112K, 0.097, n/a 128K, 0.116, 0.142 160K, 0.155, n/a 192K, 0.187, n/a 228K, 0.228, n/a 256K, 0.254, 0.306 (Production MacLucasUNIX = 0.228) 320K, 0.328, n/a 384K, 0.400, n/a 448K, 0.481, n/a 512K, 0.542, 0.629 640K, 0.718, n/a 768K, 0.841, n/a 896K, 1.041, n/a 1024K, 1.120, 1.333 1280K, 1.544, n/a 1536K, 1.826, n/a 1792K, 2.063, n/a 2048K, 2.320, 2.781 2560K, 3.152, n/a 3072K, 3.864, n/a 3584K, 4.591, n/a 4096K, 5.209, n/a You will see that, even allowing for the production version of MLU being faster than the instrumented version, Mlucas is about the same speed or faster, except for any exponents for which both programs use the same FFT size. These are fairly rare. >> Hi, Brian, and thanks for the Ultra 10 timings and other comments. Regarding the former, could you provide me with all the 64K-2048K MLU timings using the "production" version of MLU? (Not just 256K). Also, I'd appreciate the cache sizes of your Ultra10/300, if you know them. >There is a documentation bug relating to the environment variable >LD_LIBRARY_PATH for the Solaris version. If you have no setting for >this variable & just point it at the directory containing the >libraries distributed, you will find that most of the Sun utilities >stop working! You will probably want to do something like > >LD_LIBRARY_PATH=/usr/lib:$HOME/lib >export LD_LIBRARY_PATH > >so that the default system libraries are searched first. Mlucas >doesn't mind, and the other utilities seem to prefer things this way! When Bill Rea (who put together the SPARC binaries) told me the LD_LIBRARY_PATH environment variable was named the same on Sun as on Alpha, I assumed all else would work as it does on Alpha Unix, too. I'll correct the documentation as you suggest. >1) Can I use "Prime95" format worktodo.ini files (i.e. >Test=exponent,depth or DoubleCheck=exponent,depth) or must I just >have the exponents, one per line? The latter. We won't need the rest of the Prime95 format until Peter Montgomery's Mfactor code is included as a module. Mlucas doesn't differentiate between first-time tests and double checks, but that is also moot for now. >2) If I want to add/remove/resequence assignments in worktodo.ini, >must I do this with the program stopped, or does it reopen the file You can change anything but the first line (currently active exponent) while the program is running. When the current exponent finishes, the program opens the worktodo.ini file, deletes the first entry, and starts on the next exponent. Now that you mention it, it would probably be a good idea to have the program check the first entry of the worktodo.ini file against the just-completed exponent, to make sure the user didn't inadvertently put a new exponent on line 1 once the old one was started. I'll put that on my to-do list. Keep those timings/suggestions/bugreports coming, - -Ernst _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 20:44:39 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Re: factoring and savefiles (was: blahblah) Brian J. Beesley wrote: >On 19 Oct 99, at 15:05, Ken Kriesel wrote: > > > Surely there are other programs. There must be various factoring efforts > > running on non-Intel processors under non-Microsoft operating systems. > >Indeed there are. There are several factoring programs in the mers >suite, also Ernst Mayer's Mfactor program. Um, That's Peter Montgomery's Mfactor program. I chose a similar name for my Lucas-Lehmer code since Peter and I plan to eventually merge the two, probably along with a p-1 factorer. >Actually there is a _big_ performance gain in using 64-bit processors >(instead of IA32 architecture) to trial factor up to 2^63 (or perhaps >2^64), particularly as Alpha, Sun Ultra etc. have (integer) divide >instructions which are more efficient than Intel's rather weak >effort. (39 clocks ...) Actually, none of the good factorers use integer divide. They all use (to check whether M(p) = 2^p-1 == 0 modulo a candidate factor q) left-to- right binary exponentiation (see Knuth, Vol. 2) and check whether 2^p == 1 (mod q). The modding is usually a Montgomery-style divisionless mod, which (for q up to around 64 bits) needs a 64x64==>128-bit integer multiply. Alpha and MIPS support such a multiply in hardware: Alpha uses MULQ for the lower 64 bits of the product, UMULH for the upper; MIPS uses DMULTU to get both halves. On the Pentium, owing to its 64-bit floating register mantissa, UMULH can be emulated via floating-point multiply. (IA-64 has an explicit machine instruction, xma.hu, which does just that.) On platforms like SPARC, one uses several 64x64==>64-bit integer multiplies to build a 128-bit product. >My guess is that someone really needs to make these existing >factoring programs easier to use in order to make them more popular. Yes, bundling a good factorer with an LL tester will help. >Factoring programs need savefiles rather less than LL testers; >perhaps they need their own format savefile, rather than trying to >"overload" the LL savefile format with complications it doesn't >really need. One needs to differentiate between sieve-based factoring (described above), which needs very few bytes in its savefile (exponent, desired factoring depth, current q) and p-1 or ecm factoring, which generates residues of the same size as the LL test. The latter wouldn't require many more bytes to be able to share the same savefile format as an LL test, e.g. assuming one uses 8-byte integers: integer contains - ------- --------------------------- 0 exponent 1 task: 0 = sieveing | 1 = p-1, 2 = ecm | 3 = LL testing 2 desired depth | stage 1 depth | 0=first check, 1=DC 3 unused | stage 2 depth | if DC, -2 offset 4 current q | current prime | current iteration 5:6 unused | if 2, ecurve data | unused 7:7+(p/64) unused | p-1 or ecm residue| LL residue If we were planning to be able to share such files via a PrimeNet repository, we'd want to add a generous amount of space (say 1kB or more) to the header to summarize the residue history, i.e. who did what task, between what dates, to what depth, and on what machine. - -Ernst _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 20:44:40 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Re: Schlagobers, Louisville style Brian Beesley wrote: >On 19 Oct 99, at 1:01, Steinar H. Gunderson wrote: > > >In fact, ask anyone what Pi is, and majority of > >them will instantly reply to you "3.14". > >In my experience, most of them will think of something sitting on a >plate, probably stuffed with apple & destined to be served >"schlagobers". This sounds like an apt description of a somewhat tipsy Viennese coffee house patron. :) In the summer of '83, When I was an undergrad at Michigan, I spent the summer in Europe, much of it working as a waiter at a Weinstube in the quaint wine- growing town of Gumpoldskirchen, about 20 minutes' drive south of Vienna. Among the waiters there was a joke along the lines of, if an obnoxious patron asks for coffee "mit Schlag" (literally, "with beating"), then a conscientious waiter will give him or her exactly what was ordered. :) Joth Tupper wrote: >Anyone remember Louisville numbers? I used to have a girlfriend from Louisville (Kentucky), but must admit that I've forgotten her number... Seriously, I think you mean "Liouville" numbers. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 22 Oct 1999 03:33:25 +0200 From: "Otto Bruggeman" <[EMAIL PROTECTED]> Subject: Mersenne: Alot of small exponents for double checking will be reassigned tonight and the following days Hi, If you want small exponents you better try to get them tonight and the following days cause a lot of them are going be released again tonight... I skimmed through the assigned exponents list and counted about 20 exponents that are (almost) overdue... So be there when you want them... 2.1 - 2.6 million range. Otto. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 03:38:59 +0200 From: Lars Lindley <[EMAIL PROTECTED]> Subject: Re: Mersenne: mprime startup at boot-time If anyone is interested I added this line to the inittab file: 8:2345:respawn:/mersenne/mprime -d > /dev/tty8 where /mersenne is my 30MB dedicated prime-partition...Just to be a little safer. :) This works great! :) I get the output to Alt-F8 and mprime restarts if killed for any reason. I'm also thinking of putting in an old hd i have lying around to back up the gimps-files at a regular interval. One more question. Can I by simple means redirect tty8 to an xterm-session?? Thanks again for the helpful tips! Happy hunting! /Lars _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 23:19:41 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: prime 95 version 19 > p.s ...You can memorise the pi fractionals ...add infinitum...surely...since > this is a fractional series? > i.e. + fract..-fract..+ fract....if you know them ok.... > I think cyclic numbers are more intersting...perhaps? > Any thoughts. This is a very easy thing to memorize. The alternating series of the recipricals of odd natural numbers is equal to pi/4. (that is to say 1-1/3+1/5-1/7...). Cyclic numbers are rational numbers. While easier to predict the behaviour of, they aren't (as a whole) more or less interesting or useful. Though, pi is more useful than most rational numbers (with the possible exceptions of 0,1/2,1,2). > Anybody out their write could integer stuff? Eh? What are you talking about? - -Lucas _________________________________________________________________ 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 #650 ******************************
