Mersenne Digest Wednesday, 10 March 1999 Volume 01 : Number 527 ---------------------------------------------------------------------- From: "George Strohschein" <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 08:01:35 -0500 Subject: Mersenne: AMD CPU My new AMD CPU reported a sum check error while double checking. I suppose you would change to Intel while it's still possible? Anybody comment? George ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Marc Getty <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 09:23:18 -0500 Subject: Mersenne: Mersenne Machine & Single Floppy LL Tester > And so I have an idea: would it be possible and feasible to build the > main memory from SRAM? I would expect this to give a bigger improvement > than most of the processor advances that are on the horizon, including > the Pentium III, and only 8 or 12 MB per system should be needed. Can > anyone comment on how much this would help, what it would cost, and > whether it is possible with existing motherboards? I doubt that what you propose is possible with off the shelf components. Chipsets are designed to accommodate certain types of memory, and I don't believe that current chipsets support SRAM as main memory. If a chipset does not support the type of memory you put into the machine, then it will not work. Supposing that you can get SRAM in DIMM or SIMM form, it would not work in any off the shelf motherboard. Sure, SRAM in the form of cache memory works, but a variation of DRAM whether it be SDRAM or EDO DRAM, all main memory is still DRAM. If you could use SRAM as main memory, I'm sure that server manufacturers would offer it standard or at least an option. Hell I would buy it! Single Floppy LL Tester? ======================== What would be good to have is an all in one magic Prime95 bootable floppy disk. I would find it incredibly useful to have a bootable disk that runs LL tests w/o an Windows operation system on the hard disk of the machine. Currently I have >40 new PII 400's in the box to be distributed in various departments here at work. If I could open them up out of the box, give them power without keyboard, mouse, monitor, or network and let them run Prime95 off of a bootable disk that would be great! Many of these machines have been sitting for a month already, and may sit for another month or two longer. If I could use these completely idle CPUs I could get perhaps 160 LL tests done that would not be done otherwise. I would also "burn-in" these machines at the same time. If anyone out there has a configuration like this already, please let me know! What I propose is to do one of the following: Method One - ---------- 1. Make a bootable disk using MS-DOS or MS-Windows95's DOS, the end user must provide this for software licensing reasons, GIMPS can't go around giving out MS software. Win95 B or Win98 bootable would be preferred so FAT32 partitions can be "seen". 2. Have a program not unlike Prime95, but runs under a DOS that runs LL tests. I have been thinking about this for the past few hours, and have come to the realization that a TCP/IP stack would be too awkward and cumbersome, so this would be limited to manual testing. 3. Being that rather large temporary files are created, often greater then a floppy disk, they can be temporarily redirected to the hard drive of the computer. Method Two - ---------- Use a linux bootable disk with mprime on it set to automatically load on boot, again only manual testing, with temporary files redirected to the hard drive of the computer. The linux kernel would have to be both FAT32 aware, because most new machines ship with FAT32 formatted hard drives now. Hell, if you are really good network support could also be built into this disk! I am not a linux guru by any means, but I'm pretty sure this is possible, and can then be freely distributed as a disk image. Any ideas people? Marc Getty - [EMAIL PROTECTED] - [EMAIL PROTECTED] - ICQ: 12916278 http://www.getty.net - http://www.vwthing.org Work: 215-204-3291 http://etc.temple.edu/ Home: 215-322-8363 ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Paul Leyland <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 07:14:49 -0800 Subject: RE: Mersenne: Fabs. > >Eh? My first job after finishing my DPhil... > > Your what? It's what Oxford and a bunch of other universities call a PhD. They doctor us differentlyin Oxford ;-) > >was microcoding a AMD-2900 series bit slice machine which had a 25ns > >(40MHz) clock. That was in 1983 and it was far from rocket science > >then. > > A 40MHz chip in 1983? How come 40MHz personal computers > weren't available > until the early 1990s? Was someone keeping the technology out > of the hands > of the "peasants"?? Yes, really. The only thing that kept them out of the hands of the peasants was that the peasants didn't, by and large, have enough money to buy them. It was ever thus. I also cheated slightly (and I'm surprised that other old-hands didn't pick me up on it). Although the clock ticked at 40MHz, it took at least four ticks to do anything --- just as the 4MHz Z80A did. > >The good old 1970's Cray-1 had a 9ns (110MHz) clock if I > remember correctly. > > That's a supercomputer. Those don't count. :-) Supercomputers have been defined in many ways. One good way is that a supercomputer is one that is too expensive for more than a few to be sold. Paul ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Pete Evans <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 10:35:33 -0500 (EST) Subject: Re: Mersenne: Milstein On 9 Mar, John R Pierce wrote: >> Dr. Milstein has a background, i.e., a CV somewhere. Can someone please >> provide it? > > I did some poking around the web on his name, found only one thing... > > Various bibliographical references to a couple of journal papers Searching for "Milstein J" in our library's database turned up seven promising items. Three of them are the same as John turned up. Luckily they have abstracts listed. Unluckily, they don't mean anything to me beyond "there's a link between linear algebra and finite automata". Of the seven items,some are old, and may be by another J Milstein. Handle with care. * Moeller TL, Milstein J Generalized algebraic structures for the representation of discrete systems LINEAR ALGEBRA APPL 274: 161-191 APR 15 1998 * Moeller TL, Milstein J Algebraic representations for finite-state machines .2. Module formulation LINEAR ALGEBRA APPL 247: 133-150 NOV 1 1996 * Moeller TL, Milstein J Algebraic representations for finite-state machines .1. Monoid-ring formulation LINEAR ALGEBRA APPL 239: 109-126 MAY 1996 * MILSTEIN J SPLINE AND WEIGHTED RANDOM DIRECTIONS METHOD FOR NONLINEAR OPTIMIZATION MATH BIOSCI 74: (2) 247-256 1985 * MILSTEIN J, BREMERMANN HJ PARAMETER IDENTIFICATION OF THE CALVIN PHOTOSYNTHESIS CYCLE J MATH BIOL 7: (2) 99-116 1979 * MILSTEIN J ERROR ESTIMATES FOR RATE CONSTANTS OF INVERSE PROBLEMS SIAM J APPL MATH 35: (3) 479-487 1978 In more detail these are: - ---------------------------------------------------------------------- Generalized algebraic structures for the representation of discrete systems Moeller TL, Milstein J LINEAR ALGEBRA AND ITS APPLICATIONS 274: 161-191 APR 15 1998 Abstract: General algebraic structures are introduced and used to develop epresentations for discrete systems. Properties of the structures and mappings between the structures are derived. The first general structure presented is based on a free monoid of m-tuples of mappings. A. second general structure is presented that is based on a commutative ring of functions with finite support. These structures are specialized to obtain representations for three models of discrete systems: finite-state machines, Petri nets, and inhibitor nets. Uniqueness of the representations is established, and examples of representations for each type of system are given. (C) 1998 Elsevier Science Inc. Addresses: Moeller TL, M1-123 Aerosp, POB 92957, Los Angeles, CA 90009 USA. Aerospace Corp, El Segundo, CA 90245 USA. Publisher: ELSEVIER SCIENCE INC, NEW YORK ISSN: 0024-3795 - ---------------------------------------------------------------------- Algebraic representations for finite-state machines .2. Module formulation Moeller TL, Milstein J LINEAR ALGEBRA AND ITS APPLICATIONS 247: 133-150 NOV 1 1996 Abstract: We show that finite-state machines can be represented as unique elements of special modules of functions. We obtain a module representation for the machine with the least number of states over a class of equivalent machines. We present a unique factorization of this representation. We construct an array which characterizes all state transitions and is identical for all machines in the equivalence class. Further, we show that the module representation for any finite-state machine is contained in a free submodule, and can be written as a linear combination of elements of submodules obtained from equivalent machine states. Module representations and associated arrays are given for two examples. Addresses: AEROSP CORP, EL SEGUNDO, CA 90245. Publisher: ELSEVIER SCIENCE INC, NEW YORK ISSN: 0024-3795 - ---------------------------------------------------------------------- Algebraic representations for finite-state machines .1. Monoid-ring formulation Moeller TL, Milstein J LINEAR ALGEBRA AND ITS APPLICATIONS 239: 109-126 MAY 1996 Abstract: Special algebraic structures, which are rings of functions with finite support, are introduced. These structures are used to develop representations for finite-state machines. Three equivalent representations for finite-state machines are presented. The first is given in terms of elements of a monoid ring based on a finite set. The second is given in terms of elements of a monoid ring based on n-tuples. The third is given in terms of the polynomial ring in 2n indeterminates. The representations are shown to be unique, and examples of them are given. Addresses: AEROSP CORP, EL SEGUNDO, CA 90245. Publisher: ELSEVIER SCIENCE INC, NEW YORK ISSN: 0024-3795 - ---------------------------------------------------------------------- SPLINE AND WEIGHTED RANDOM DIRECTIONS METHOD FOR NONLINEAR OPTIMIZATION MILSTEIN J MATHEMATICAL BIOSCIENCES 74: (2) 247-256 1985 Addresses: MILSTEIN J, ISRAEL INST TECHNOL, DEPT MATH, IL-32000 HAIFA, ISRAEL. Publisher: ELSEVIER SCIENCE INC, NEW YORK ISSN: 0025-5564 - ---------------------------------------------------------------------- PARAMETER IDENTIFICATION OF THE CALVIN PHOTOSYNTHESIS CYCLE MILSTEIN J, BREMERMANN HJ JOURNAL OF MATHEMATICAL BIOLOGY 7: (2) 99-116 1979 Addresses: MILSTEIN J, UNIV SO CALIF, DEPT MATH, LOS ANGELES, CA 90007. UNIV CALIF BERKELEY, DEPT MATH, BERKELEY, CA 94720. UNIV CALIF BERKELEY, DIV MED PHYS, BERKELEY, CA 94720. Publisher: SPRINGER VERLAG, NEW YORK ISSN: 0303-6812 - ---------------------------------------------------------------------- ERROR ESTIMATES FOR RATE CONSTANTS OF INVERSE PROBLEMS MILSTEIN J SIAM JOURNAL ON APPLIED MATHEMATICS 35: (3) 479-487 1978 Addresses: UNIV CALIF LOS ANGELES, DEPT MATH, LOS ANGELES, CA 90024. Publisher: SIAM PUBLICATIONS, PHILADELPHIA ISSN: 0036-1399 - ---------------------------------------------------------------------- FITTING MULTIPLE TRAJECTORIES SIMULTANEOUSLY TO A MODEL OF INDUCIBLE ENZYME-SYNTHESIS MILSTEIN J MATHEMATICAL BIOSCIENCES 40: (3-4) 175-184 1978 Addresses: MILSTEIN J, UNIV SO CALIF, DEPT MATH, LOS ANGELES, CA 90007. Publisher: ELSEVIER SCIENCE INC, NEW YORK ISSN: 0025-5564 - ---------------------------------------------------------------------- HTH, P. - -- Pete Evans, Gradual Student [EMAIL PROTECTED] "Your luck has been completely changed today. Lucky Numbers 40 16 37 32 19 43" ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Jud McCranie <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 10:32:08 -0500 Subject: Re: Mersenne: Milstein At 09:47 PM 3/9/99 -0800, John R Pierce wrote: >Moeller Thomas L., Milstein Jaime, Generalized Algebraic Structures for the >Representation of Discrete Systems, Linear Algebra And Its Applications This is a journal, and doesn't seem to be a book coauthored by Moshe Goldberg, as was claimed. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Jud McCranie <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 10:29:22 -0500 Subject: Re: Mersenne: Re: Alien stuff At 08:26 PM 3/9/99 -0800, Spike Jones wrote: >This reinforces an earlier notion I posted: that primes are the most >obvious thing to put in a messages bound for exocivilizations. In >retrospect, it is difficult to imagine such a message without reference >to prime numbers and/or mathematics as we know it. That what they used 35-40 years ago. >Consider this: *any* civilization that is capable of receiving our >messages must have developed knowledge of math functions, and >knowledge of division implies knowledge of primes. Postmodern relativists would disagree. +------------------------------------------+ | Jud McCranie [EMAIL PROTECTED] | +------------------------------------------+ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Jud McCranie <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 10:40:48 -0500 Subject: Mersenne: [Mersenne]: Milstein At 10:45 AM 3/10/99 +0100, Peter Tichy wrote: >I ran a search using Copernic, and this is what came out of it; > >http://www.aero.org/news/current/topAwards.html The award came from the president of his COMPANY, not the president of his COUNTRY, as was claimed. A big difference! Anyhow, there is information about him there. He doesn't seem qualified to evaluate a number theory algorithm, however. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Gordon Spence <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 15:26:41 +0000 Subject: Mersenne: Odds of finding a Mersenne prime >From: [EMAIL PROTECTED] >Date: Sun, 7 Mar 1999 16:12:07 -0000 >Subject: Re: Mersenne: Category 1,2 or 3 ? > >Gordon Spence writes: > >>>>What bothers me most I guess is that the ordinary humble joe in the street >>>>being realistic has no chance whatever of finding the next mersenne prime. > >This is a slight exaggeration. If you're running LL tests or double-checks at all, >you've more chance than if you're not. True if I buy just one ticket I have a chance, but if you have 10,000 tickets me thinks you have a greatly improved chance (though still statistically improbable) [snip] > Therefore there is about 1 >chance in 100 that another Mersenne prime less than Spence's Number remains to be >found. I never actually worked out the figures, but something must have sunk in at some level of (un)consciousness, I have stopped doing any factoring work now (hardly get any 'credit' for doing it) and have turned over 6 machines to double checking leaving just 4 at LL testing. [snip] >1. Does anyone know where the estimate of an exponent yielding a Mersenne prime >that Prime95 outputs in its status pop-up comes from? (George, I can see & >understand th e source code, what I would like to know is the source of the >algorithm) Very good question, I often wondered that. BTW I am testing M20295673 at home. Apparent I have odds of about 161,000 to 1 that it is prime. > >2. Does our continued effort in eliminating possible Mersenne primes change that >estimate in any way? Since I joined the project 10 months ago, we have found no >new Mersenne primes (any day now?) but eliminated a great many exponents, >nevertheless the formula doesn't seem to have changed, which it probably should >have done if it's (even partly) based on empirical data. Intuition says that it should. But is this a variation on the old coin-tossing problem that is counter intuitive? regards G Gordon Spence, Nokia IP Telephony Applications Engineer Grove House, Waltham Way, [EMAIL PROTECTED] White Waltham, Maidenhead, http://www.nokiaiptel.com/ Berkshire, SL6 3TN, UK. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Joth Tupper <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 13:27:45 -0500 Subject: Mersenne: AMD CPU Message text written by "George Strohschein" > My new AMD CPU reported a sum check error while double checking. I suppose you would change to Intel while it's still possible? Anybody comment? George< George, Please try to include more details in a hardware question. You appear to be wondering about switching from one CPU to another, but this is no longer trivial. I have an AMD K-6 300, an AMD K6-2 400 and a P-II 266 all running prime95. I have had Cyrix PR166, AMD 486DX-4 and Intel P-166MMX and Intel P-133. The upgrade to the K6-2 was about $300 cheaper than to a P-II (and I am still using my old AT case). For most of what I do, it is ok that the K6-2 flops on FLOPs. Switching to an Intel processor need not be the answer. Among Pentium class processors, perhaps it would be a good idea -- the $I premium is pretty low for P5's and prime95 does lots of float so you can get much better throughput. The question is very different for K6, K6-2 and Intel P-II class processors. Unless you plan to swap a new computer within the free look period, I do not know if I would swap. [For one thing, I think you need different CPU sockets or slots for each of K6, P-II/Celeron and Celeron-370. This means a different main board.] The K6 gets double checking and the other two are running first pass LL's. The K6 is the oldest and longest running processor of these three. For a sum check error, I would want to distinguish between some sort of accident or transient and an underlying hardware problem. Maybe you have a bad fan or unreliable line voltages. I have had wierd problems from main boards (bit flipping back in 486DX-33 days on many boards -- made copying unreliable), errors from RAM that got cooked (perhaps from a CPU fan failing so that the P5-133 ran hot). So far, I have not had a CPU fail on me. Can you run any tests (perhaps the prime95 torture test) to bang away on CPU, RAM and HDD? Has the error occurred again? If running Win9X/, do you get the infamous Blue Screens? Good luck! Joth ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Joth Tupper <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 13:52:43 -0500 Subject: Re: Mersenne: Milstein Thanks for sharing the bib search results. There seems to be about a 10 year gap between the 2 sets of papers as well as some shift in field. The linear algebra papers would have to have some pretty heavy-duty simplifications before I would be inclined to pay any attention to Milstein's opinion on primality testing. About 20 years ago, I took a couple of courses from John Rhodes at UC Berkeley on finite state machines (Rhodes called it Automata Theory). Basically, any finite state machine can be decomposed as a semi-direct product of finite groups and (perhaps several copies of) one very elementary semi-group U3, three elements 1,x,y: 1 is the identity and xy = y and yx = x. (Forgets left argument.) Now, from back in the 60's, any finite group can be represented in matrices - -- lots of ways. If U3 can be represented by linear algebra (exercise for the reader), this seems to complete the case for finite state machines -- in very vague terms. Again, I hope there is something a wee bit deeper than fleshing out this general approach, then I remain unimpressed. What would impress me? Something along the lines of Rapheal Robinson's results on spheres: the Bolzano-Tarski theorem proved (what, back in the 1920's?) that you could cut a solid 3D sphere into finitely many chunks, then rearrange the chunks to make another solid (no holes or gaps) 3D sphere with _twice_ the volume. Pretty spooky, I always felt. Robinson first proved that 9 chunks would do it. Then he found a way with 5 (maybe it is 4) and I think he showed that this was the minimum. The linear representations of finite state machines is at first blush a "fairly" straightforward application of linear representations of finite groups and the decomposition theorem for finite state machines. Is there some real content? Message text written by INTERNET:[EMAIL PROTECTED] >* Moeller TL, Milstein J Generalized algebraic structures for the representation of discrete systems LINEAR ALGEBRA APPL 274: 161-191 APR 15 1998 * Moeller TL, Milstein J Algebraic representations for finite-state machines .2. Module formulation LINEAR ALGEBRA APPL 247: 133-150 NOV 1 1996 * Moeller TL, Milstein J Algebraic representations for finite-state machines .1. Monoid-ring formulation LINEAR ALGEBRA APPL 239: 109-126 MAY 1996 < ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: "Herr, Stephen" <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 12:07:24 -0700 Subject: Mersenne: VME claim >lrwiman wrote on Tuesday, March 09, 1999 2:44 PM: > >In a letter sent by Henk Stokhorst, he rellayed grand claims made by meganet >about a primetest in polynomial time. They are being way to secretive about >this. If they are afraid of anyone but clients using it, then patent it, but as >it stands this reeks of a scam. The other thing that can happen is non-discloser type agreements where one enters into a contract not to sell or profit from the knowledge of the formulae. The other thing about all of this is that the Esteemed Professor Jaime Milstein said it had errors. That is not being noticed at on in these discussions. He said it seemed like it was valid math, yet there were some minor corrections necessary. He also stated he had not done any type of rigorous proof of the claim, just that he had "recast it ...within a sound mathmatical framework" ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: The thrill of minimalism <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 13:16:22 -0600 Subject: Mersenne: Milstein and Aliens, both > >http://www.aero.org/news/current/topAwards.html This page contains the following: ... an analysis team that quantified the effects of phenomenology on Space-Based Infrared System performance. Is this project not alluded to by the SF film "Darkstar?" ________________________________________________________________________ David Nicol 816.235.1187 UMKC Network Operations [EMAIL PROTECTED] ++++ stop the execution of Mumia Abu-Jamal ++++ ++++ more info: http://www.xs4all.nl/~tank/spg-l/sigaction.htm ++++ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Kevin Sexton <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 12:24:53 -0800 Subject: Re: Mersenne: VME claim > Professor Jaime Milstein is a top ranking government mathematician, who > won > a medal from the president last year for his achievements for the country. > > He have published many articles in different publications, such as "Linear > > Algebra and its applications" published by Moshe Goldberg. > They say "the president" and "achievements for the country" this seems to imply, since it seems to be a United States address that they mean President Bill Clinton, and achievements for the United States. but if it is a company president and "achievements for the company" this changes the meaning considerably. Maybe a conflict of interest as an independent researcher, if he is an employee of the same company with the algorithm. > > Professor Jaime Milstein have reviewed the method, described the work as > novel and intriguing, and highly recommends its implementation. This seems to me that they are saying it hasn't even been implemented and tested yet. It might be impractical to implement. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Dennis E Okon <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 15:52:07 -0500 Subject: Re: Mersenne: *P*M3021377 in base 62 >> On second thought, maybe it is good to use base 62 Using the gaintint code from Perfectly Scientific (www.perfsci.com) for the most of the math, I converted M3021377 to bases 26, 36, and 62. They can be found at: http://web.mit.edu/dokon/www/Mersenne/ For base 26, the characters are a - z For base 36, 0 - 9 and a - z For base 62 0 - 9, a - z, and A - Z I'm still working on *P*M3021377. If you find any mistakes, let me know. :) - -Dennis Okon [EMAIL PROTECTED] ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Jud McCranie <[EMAIL PROTECTED]> Date: Wed, 10 Mar 1999 16:02:48 -0500 Subject: Mersenne: [Mersenne] Celeron How does the current Celeron stack up against a P-II for this work? +----------------------------------------------------------+ | Jud McCranie [EMAIL PROTECTED] | | | | Where a calculator on the ENIAC is equipped with 19,000 | | vacuum tubes and weighs 30 tons, computers in the future | | may have only 1,000 vacuum tubes and perhaps only weigh | | 1.5 tons. -- Popular Mechanics, March 1949. | +----------------------------------------------------------+ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ End of Mersenne Digest V1 #527 ******************************
