Re: Mersenne: Factoring
Thanks for the factor.exe citation. At 01:40 AM 6/16/00 -0700, Jim Howell wrote: [Wed 14 Jun 2000, Paul Leyland writes] Today I found this number 3756482676803749223044867243823 with ECM and B1=10,000. It has two factors, each of 16 digits, which could *not* have been found by trial division in any reasonable time. - I use a program called "factor.exe", which uses several factoring methods. It factors the above number within several seconds. (For this number, the factors are found with the P-1 method.) In case anyone is interested, the factors are 1483398061194277 and 2532349728015299. This program runs on Windows, and can be downloaded from Chris Caldwell's main page, at: http://www.utm.edu/research/primes Go down to section 4, (Software), and look for "factor.exe", described as a DOS program, but it actually runs in a Command Window on Windows 95 and later, and (probably) not under actual DOS. I find "factor.exe" quite useful for factoring small numbers (it will accept numbers up to about 130 digits). --Jim !DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN" HTMLHEAD META content="text/html; charset=iso-8859-1" http-equiv=Content-Type META content="MSHTML 5.00.2314.1000" name=GENERATOR STYLE/STYLE /HEAD BODY bgColor=#ff DIVFONT face=Arial size=2[Wed 14 Jun 2000, Paul Leyland writes]/FONT/DIV DIVFONT face=Arial size=2BRToday I found this number 3756482676803749223044867243823 with ECM andBRB1=10,000.nbsp; It has two factors, each of 16 digits, which could *not* haveBRbeen found by trial division in any reasonable time./FONT/DIV DIVFONT face=Arial size=2/FONTnbsp;/DIV DIVFONT face=Arial size=2-/FONT/DIV DIVFONT face=Arial size=2/FONTnbsp;/DIV DIVFONT face=Arial size=2I use a program called "factor.exe", which uses several factoring methods.nbsp; It factors the above numbernbsp;within several seconds.nbsp; (For this number, the factors are found with the P-1 method.)nbsp; In case anyone is interested, the factors arenbsp; 1483398061194277 and 2532349728015299.BR/FONT/DIV DIVFONT face=Arial size=2This program runs on Windows, and can be downloaded from Chris Caldwell's main page, at:/FONT/DIV DIVFONT face=Arial size=2/FONTnbsp;/DIV DIVFONT face=Arial size=2A href="http://www.utm.edu/research/primes"http://www.utm.edu/research/prime s/A/FONT/DIV DIVFONT face=Arial size=2/FONTnbsp;/DIV DIVFONT face=Arial size=2Go down to section 4, (Software), and look for "factor.exe", described as a DOS program, but it actually runs in a Command Window on Windows 95 and later, and (probably) not under actual DOS.nbsp; I find "factor.exe" quite useful for factoring small numbers (it will accept numbers up to about 130 digits)./FONT/DIV DIVFONT face=Arial size=2--Jim/FONT/DIV DIVFONT face=Arial size=2nbsp;/DIV/FONT/BODY/HTML _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Yikes !! Restart?
I was testing 9,028,373 from a worktodo.ini file that said Test=9028373,63 That is all the worktodo.ini file said. I use manual prime retrieval and asked for, and got from George, three new numbers as 9,028,373 was my only number. The worktodo.ini file was changed to Test=9028373,63 Test=new number 1,60 Test=new number 2,60 Test=new number 3,60 There are line feeds at the end of the ,63 and ,60 so there are no extra blanks anywhere in the worktodo.ini file. The changes were made while 9,028,373 was running with notepad or one of the other simple MicroSoft utilities. The changes were tehn saved and the worktodo.ini file has the four numbers. Suddenly, 9028373, which was at 14% done, disappeared!! In its place,.the P-III (450 MHz) was factoring new number 1 (pass 1 of 16). There is nothing, nada, zilch, zippo, about the loss of 9028373 in the results file. Why? It is true that I briefly shut down as I often do to clear Java files, but I invariably go to the LL test screen, click for STOP and then click for EXIT. At startup, the LL testing starts up again automatically (thanks to some one who gave me fine explicit instructions as to how to do this). I believe the STOP and then EXIT saves the latest p and q files so I lose only a few minutes, not up to 1/2 hour or whenever the last p and q files were saved. I have often used Norton Utilities to (a) system check for errors and there is a persistant error that crops up from playing Java based chess (after 15 or so games; it takes that many to win just once) and to (b) speed disk, (another Norton Utilities feature), i.e., reorganize the C drive. But I have been doing this for MONTHS AND MONTHS while running LL tests (more than 250 done over the years) and have never had an ill effect. I will have to restart 9028373 but then, why did it stop? Is this a microsoft feature (i.e. a bug that in an undocumented yet powerful add on)? Also, should I just stop the factoring passes and restart so that I am back again on prime 9028373? The MERSENNE directory where I have all the files and programs has a p9028373 file, a q9028373 file and a p file for the new number. I'd like to resume on the p and q files for 9028373, obviously. Anybody can respond. Ask for more info if you need it. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Replies to Yikes !! Restart?
The consensus, as I read the messages, is that all is O.K. Soon I will have Test=9028373,63 Test=999,63 Test=999,63 Test=999,63 and LL factoring will resume on 9028373. I hope this is right as I will be away for a week starting Tuesday, June 6, 2000. All in all, there is and has not been any lost time as the factoring was going to be done anyway. I am running Version 19. The improvements to version 20 seem slight. At 06:23 AM 6/4/00 -0400, you wrote: I was testing 9,028,373 from a worktodo.ini file that said Test=9028373,63 That is all the worktodo.ini file said. I use manual prime retrieval and asked for, and got from George, three new numbers as 9,028,373 was my only number. The worktodo.ini file was changed to Test=9028373,63 Test=new number 1,60 Test=new number 2,60 Test=new number 3,60 There are line feeds at the end of the ,63 and ,60 so there are no extra blanks anywhere in the worktodo.ini file. The changes were made while 9,028,373 was running with notepad or one of the other simple MicroSoft utilities. The changes were tehn saved and the worktodo.ini file has the four numbers. Suddenly, 9028373, which was at 14% done, disappeared!! In its place,.the P-III (450 MHz) was factoring new number 1 (pass 1 of 16). There is nothing, nada, zilch, zippo, about the loss of 9028373 in the results file. Why? It is true that I briefly shut down as I often do to clear Java files, but I invariably go to the LL test screen, click for STOP and then click for EXIT. At startup, the LL testing starts up again automatically (thanks to some one who gave me fine explicit instructions as to how to do this). I believe the STOP and then EXIT saves the latest p and q files so I lose only a few minutes, not up to 1/2 hour or whenever the last p and q files were saved. I have often used Norton Utilities to (a) system check for errors and there is a persistant error that crops up from playing Java based chess (after 15 or so games; it takes that many to win just once) and to (b) speed disk, (another Norton Utilities feature), i.e., reorganize the C drive. But I have been doing this for MONTHS AND MONTHS while running LL tests (more than 250 done over the years) and have never had an ill effect. I will have to restart 9028373 but then, why did it stop? Is this a microsoft feature (i.e. a bug that in an undocumented yet powerful add on)? Also, should I just stop the factoring passes and restart so that I am back again on prime 9028373? The MERSENNE directory where I have all the files and programs has a p9028373 file, a q9028373 file and a p file for the new number. I'd like to resume on the p and q files for 9028373, obviously. Anybody can respond. Ask for more info if you need it. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: The recent popularity of Single-Checking
Cheers to you Mikus. I second you wholeheartedly. At 11:51 AM 5/24/00 -0500, Mikus Grinbergs wrote: ... some snipping Since when has this project become a competitive event ? This mailing list has gotten several messages like the one above, which I interpret as comparing ANOTHER USER to standards set by the writer, rather than acknowledging that *all* users are contributors to the project. Will it mean the end of the world if that other user had mis-stated the resources available to him ? I think it is intrusive to publicly comment about ANOTHER USER when the writer spots something that does not meet his own expectations. Can't we please let each participant remain responsible for his own performance? _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: pi
Quoting from Dan: "Logic seems to indicate that pi would have to be a finite exact value since the area in the circle is finite. So, either the figure for pi is in error (not likely) or pi has a end." No, this might be called one of the pathologies of mathematics. What seems to be so isn't. It is certain that Pi is a "never ending series" as you put it. Perhaps this will help. Sum 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... to infinity as the fractions become smaller and smaller (1/(2^n) as n increases without limit). The sum is 2. Can you Dan accept that a never ending sum of smaller and smaller terms has a precise finite value? It is an integer at that. Plus we never get to add all the terms -- there is always just one more and it would take infinite time to add the infinity of terms. Now look at 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ... to infinity as the fractions become smaller and smaller. The sum is infinity, that is, it never stops increasing. Can you Dan accept that this sum of smaller and smaller terms has no precise value as it slowly and endlessly grows larger (hence infinity)? And there is a neat or "pathological" property of this infinitely large sum. Let's say we get larger than integer N after a million billion billion terms. So now we are adding 1/(million billion billion + 1), then 1/(million billion billion + 2), then 1/(million billion billion + 3), then + 4 etc. As the sum crawls toward N + 1, we are less than .000 000 000 000 000 000 000 001 away from N + 1 eventually (an American billion being 9 zeros). The sum never "lands on" exactly N + 1 and skips landing on all integers (and there are an infinity of those). In fact, to get as close as one wants, say .000 (million more zeros) 01, to an integer, another N' is needed where N' is N (N' is much larger than N). The partial sum can be made as close to an integer as we like. But the partial sum is never exactly an integer. In other words, for all integer M, the fixed sum 1 + 1/2 + 1/3 + 1/4 + + 1/M (a fixed sum because M is the last one in a finite summation) is never an integer even though the infinite series (as M grows to infinity) passes through all integers. The better mathematicians in this group (that is, all other mathematicians :-) may give a better explanation. At 12:06 AM 2/9/00 -0600, Dan wrote: Hi, I have been considering the possible role pi might play in the progression of mersennes. It is generally accepted that the value of pi is a never ending series. But when I look at the circle, the formula for the area of a circle with a radius of 6 inches is: A=pi*r^2 = 3.1416 * (6)^2 = 113.0976. We did not, however, use the full and correct expansion of pi in the calculation. Pi has been figured out to over a billion (not sure of the exact figure) digits with no apparent end or pattern. But when I look at a circle I see a finite area within the circle with no means of growing or escape. Logic seems to indicate that pi would have to be a finite exact value since the area in the circle is finite. So, either the figure for pi is in error (not likely) or pi has a end. The end. What say ye? Dan _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: The return of poaching?
A good sensible posting. I concur and thank Jeff Woods for writing it. At 11:12 AM 2/4/00 -0500, you wrote: I hate to open a can of worms here, but feel I must However, I am not a poacher myself, nor do I advocate it. I only write this to tell you why I don't feel sorry for folks who queue up WAY too much work and then gripe about it when someone else calls them on the carpet about it by poaching them. I write this in the hopes that you'll see the error of your ways, and work not just for yourself, but for the good of the group. My conclusion at the end of this message is for George's consideration, and the rest of this message defends this conclusion: George: v20, *and* the PrimeNet server, ought not allow any one machine to keep more than ten times its average communication frequency in exponents queued, and no more than 60 days no matter what -- requests for additional exponents when the server knows that that machine already has two months' work ought to be denied. If a machine reports in every 3 days, let it keep no more than 30 days. If it reports in daily, let it keep ten days. By stopping exponent hogs from locking up hundreds of exponents just because they like the small ones, GIMPS will reach its goals (milestones, proving M37, etc), much faster. -- Dave has at least 80 exponents reserved between 2.4M and 3.99M. Eighty. Almost all are less than suspected M37. It is a certainty that without poaching, we will have to wait until late 2000 or later to prove M37, because Dave is trying to do all the double-checking singlehandedly. I cannot stress this part enough: This is why we have thousands of participants in GIMPS! It is our PRIMARY raison d'etre! To spread around the workload to get things done faster! By trying to take 80 of the 280 or so exponents left for doublechecking up to M37 (nearly 30% to ONE participant!), Dave is intentionally thwarting the very purpose of GIMPS: distributed mathematical research. DISTRIBUTED computing is key! Each of Dave's 80 exponents will take a P-II/400 0.09 seconds per iteration. If the average exponent is closer to 2.8M, here's how much time Dave has set aside: 2.8M x 80 x 0.09 = 20,160,000 seconds DIV 86,400 = 233 days. That's if Dave uses P-II 400's, on PRIMARY tests. Double-checks use a different LL code, and take longer. I doubt Dave is using P-II's for this purpose, too. If it's P-90's, that's 233 x 4.5 (times slower) x 1.2 (times slower to double check, a guess), or 1574 days of work queued up for Dave. I can only find six named machines of Dave's in the work list. 1574 days of work over 6 machines is an AVERAGE of 262 days of work queued up per machine. What a PIG. Why does ANYONE need nine months of work queued up, especially for machines that seem to report back to GIMPS on a daily basis? Many of us want to see results -- we want milestones, we want to see "All exponents less than 3,000,000 have been double checked." We want to see "Double checking proves 3021377 is the 37th Mersenne Prime". Most of Dave's assignments have gone untouched for 30 - 90 days. We don't want to wait a YEAR for this milestone, just because you and a handful of others want to test all the little exponents. Your machines are useful to us, don't get me wrong. Nobody here wants you and Dave (and other exponent hogs) to quit GIMPS. We just want you to reserve a reasonable number of exponents, and take what comes to you. These machines will be equally useful to us whether double-checking 2916117 or 4717123 and we'll get where we're going faster that way! Dave's machines are permanently connected (or frequently connected) -- they have reported progress nearly daily -- slow, steady progress, but they report. Thus, IMO, Dave should not have his clients set to queue up more than TWO DAYS of work. I set mine at ONE day, so that I don't even get a new assignment until the machine is less than a day away from finishing its exponent and being left with NO work. And that's the way it ought to be -- nobody ought to even be ABLE to hold up the progress of the group in reaching milestones for this long. When your machine is ALMOST out of work, THAT is the time to request the smallest available exponent OF THAT MOMENT. So, to your paragraph below, there's nothing wrong with seeking out the smallest available exponents but there *is* something wrong with seeking out nine months' worth of them, and holding up the very purpose of the group. If Dave gets poached, I won't shed a tear. I'd have done a similar analysis on your assignments, but didn't know your ID. You're probably not as heinous as Dave is, since he appears to be the worst of the lot on cursory inspection, but ANYONE holding more work than necessary is on the list of "won't cry for you, Argentina" folks. MOST folks understand this. There are 26,600 machines
Mersenne: Icon
I am using WIN 98. How do I set up an icon on the desktop to kick off PRIME95 (as I needed to do twice today when the dang computer crashed)? _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Icon
I did all that, following your instructions. Prime95 disappears when I minimize it. It used to be on the taskbar (right word?) at the bottom of the WIN98 screen. Can't there be an icon on the desktop, as I originally asked? Also, is there a FAQ about this? At 10:34 PM 2/2/00 +, you wrote: On Wed, Feb 02, 2000 at 03:56:01PM -0500, Vincent J. Mooney Jr. wrote: I am using WIN 98. How do I set up an icon on the desktop to kick off PRIME95 (as I needed to do twice today when the dang computer crashed)? The right thing would be putting it either in the Startup folder (on the start menu), or by following this procedure: 1. Open the Prime95 window. 2. Select Advanced/Password, and enter 9876. (I'm not sure if you need to do this.) Click OK. 3. Select Options/Windows 95/98 service. 4. Select Options/Tray Icon. If you set Prime95 up this way, it will run even if you're not logged in, and automatically on system startup. /* Steinar */ -- Homepage: http://members.xoom.com/sneeze/ _ 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: The Second Mersennium Behind Us, How Now For Myriad The Third?
I read a few days ago that the patent office is considering withdrawing the patent. It was stupid to grant it in the first place, but what is the effect if patents granted can be withdrawn (as has happened in a few other cases)? At 12:52 AM 1/12/00 -0700, you wrote: " Dickens applied for the patent in October 1996 " I was using windowing in 1987, so his patent is invalid (prior invention). The problem now becomes, will these companies choose to challenge the patent in court, spending millions of dollars, or will each company alone figure it's cheaper to pay this guy than to pay their lawyers. Apparently, that's been the tactic for many other similar "patent" cases lately. What the article termed "submarine patents" for their stealth. Sad...isn't it? Let's all be thankful that neither Lucas nor Lehmer decided to patent their formula! :-) _ 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: Why 2K?
At 03:48 PM 1/12/00 EST, Ernst wrote: Jud McCranie wrote: This is getting off topic, but: The criteria for something to be patentable is that the average practitioner in the field wouldn't think of it. So it boils down to whether the average programmer would think of windowing, given the problem. Well, that's the major criterion (non-obviousness) if no one has explicitly demonstrated or patented a similar thing previously... " Dickens applied for the patent in October 1996 " I was using windowing in 1987, so his patent is invalid (prior invention). ...in that case windowing is considered "prior art," and the patent is invalid on its face. Jud, assuming you have reasonable supporting documentation for your use of windowing prior to 1996, you should consider sending it to the U.S. patent and trademark office, http://www.uspto.gov (even if you have no desire to attempt to patent it - clearly, showing that you merely thought of it before 1996 in order to invalidate Joe Schmoe's patent is much easier than proving that you thought of it before anyone else did and seeking a patent yourself). Note that prior art is most easily established via publication, public use or sale - if you only wrote a windowing script for your own use, it may be more difficult to prove. From a programming perspective, my own top "why 2K" question is this this: even given that the person(s) who first used a mere 2 characters to store the year had good reason (e.g. severely limited computer memory) to do so, why didn't they use those 2 precious bytes as a 2-byte integer? Had they done so, we'd be talking instead about the "Y32K" or "Y64K" bug, and even Microsoft might have had sufficient time to fix their software by then. :) -Ernst It wasn't so much the computer memory, Ernst, as it was the disk storage space. An insurance application record would have perhaps 6 dates within 100 bytes: date of applicant's birth, date application for insurance was taken, date of proposed enrollment, date the first premium was due, date the premium was received/recorded in the system, date of expiration if the payments stopped, and probably more. Saving the "century" field 6 times was 12 bytes saved in COBOL PIC 99 mode. Clever was the use of COBOL PIC XX as a COMPUTATIONAL field to store a date in 16 bits (which was the length of PIX XX). 7 bits for year since 2^7 = 128 so a year value up to 99 was stored there; 5 bits for day since 2^5 = 32 so a day value was stored there and 4 bits for month as 2^4 = 16 so a month value was stored there. Two bytes for a YEAR-MONTH-DAY value was great. Adding century was a bummer to this idea. The programmer had to have a REDEFINED PIC 99 COMP-4 of the PIC XX and then use a routine to extract three fields. As some may recall, the packed-digits format (COMP-3) was also used to store disk space on the file's record. IBM created/used this format to allow space savings. But the bottom line was that in the 1960's and 1970's, disk store space was expensive and saving it was worth the effort spent in more programming (people were cheaper that computers, in a way). Yes, memory was expensive and limited, but it was not the cause of the Y2K issue. No one in the late 1980's EVER believed that the PC would be as powerful as it is now, that disk storage would be as cheap, and that all these improvement would be in the home !! Only the 1.44 MB diskette of ten years ago remains the same. And I am delighted that MERSENNE.ORG lets me hunt for giant primes even if I never find one. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Zip Codes
Also since the list is quite quiet, my old zip code of 21701 is a Mersenne prime. Are there any other zip codes that are Mersenne primes? I don't know how to look up 02203 or 02281 for example. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Zip Codes
Thanks, Joth. 1. 2Not good 2. 3Not good 3. 5Not good 4. 7Not good 5. 00013Not good 6. 00017Not good 7. 00019Not good 8. 00031Not good 9. 00061Not good 10. 00089Not good 11. 00107Not good 12. 00127Not good 13. 00521Not good 14. 00607Not good 15. 01279Not good 16. 02203A valid zip code 17. 02281Not good 18. 03217 A valid zip code 19. 04253 A valid zip code 20. 04423 A valid zip code 21. 09689Not good 22. 09941Not good 23. 11213 A valid zip code 24. 19937Not good 25. 21701 A valid zip code 26. 23209Not good 27. 44497Not good 28. 86243Not good 29 and higher are 6 digits. At 06:13 PM 12/17/99 -0800, Joth Tupper wrote: You might check www.usps.com. - Original Message - From: Vincent J. Mooney Jr. [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, December 17, 1999 2:48 PM Subject: Mersenne: Zip Codes Also since the list is quite quiet, my old zip code of 21701 is a Mersenne prime. Are there any other zip codes that are Mersenne primes? I don't know how to look up 02203 or 02281 for example. _ 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: Atanasoff
The Burks's book mentions Konrad Zuse and his programmable, floating-point binary Z-3, George Stibitz and the Bell Labs Model II - V; also Mark I of IBM and others. These are labeled electro-mechanical computers and the Burks say that they were well established by the mid-1930's when Atanasoff was doing his work. The Burks then go on to declare Atanasoff used the continuous electronic technology of the times; they distinguish between analog and digital mode; they declare that Atanasoff was part of chain of development with electro-mechanical computing technology first and the electronic computer technology being Atanasoff's contribution. Chapter 5 called Atanasoff Place in History covers these points and more. The Burks state that the ENIAC was not the first electronic computer. They write that it was Atanasoff who started the computer revolution. My own judgement is that Atanasoff gets 5 stars out of 5; other maybe are deserving too. I wish he were still around so I could tell him about GIMPS (Dr. Atanasoff was a PC user, not a MAC user). I also give Atanasoff 5 stars for NOT PATENTING anything. Cripes, can you image where we'd be if we had to ask permission to improve someone else's patent? At 10:11 PM 11/28/99 -0500, Jud McCranie wrote: At 07:31 PM 11/28/99 -0500, Vincent J. Mooney Jr. wrote: Pleasse tell us what there is to disagree with. This is off-topic, but there was prior work on the Mark I, in Germany by Zuse, and in England on the code breaking project. There is no clear inventor of the computer in the eyes of most historians. Much of the controversy is covered in chapter 8 of "ENIAC" by Scott McCartney and other books such as ""Portraits in Silicon". Iowa State University seems overzealous in promoting Atanasoff. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Atanasoff
At 06:32 PM 11/28/99 -0500, Jud McCranie wrote: At 01:57 AM 11/25/99 -0500, Vincent J. Mooney Jr. wrote: There seems to some interest in the first computer. I refer you to the book "The First Electronic Computer : The Atanasoff Story" by Alice R. Burks, Arthur W. Burks still available on amazon.com. That book is controversial, and most people in-the-know don't agree with it. Pleasse tell us what there is to disagree with. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: (2^p-1)/p == 0 (mod 3) ?
5 is an odd prime. 2^5 = 32 and minus one, is 31. 31 is not divisible by 3. At 07:50 PM 10/26/99 +0200, you wrote: Hello all, a simple Number Theory question. Is always (2^p-1) / p ,odd prime p, divisible by 3 ? Then 2^p == 1 (mod 3p) would also hold, can this be used to improve the efficiency of a Rabin-Miller probable prime test? Ciao, Alex. _ 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: ReCache for Windoze (was: mprime startup at boot-time)
I have 256 MB of memory (about 30 gig of hard drive space). Will this process assist me? At 07:23 PM 10/25/99 +0100, you wrote: On 24 Oct 99, at 18:23, Bruce A Metcalf wrote: Hello, I must have missed the discussion of ReCache the last time around. Would someone be willing to explain where this can be obtained, how to install, and the likely benefits to Prime95? Brian Beesley responded: ftp://lettuce.edsc.ulst.ac.uk/gimps/software/ReCache.zip To install: Unzip the file place the executable in a directory referenced in the search path. [Or in the same directory as Prime95] Read the other file. To run: from DOS command prompt: change directory to the folder containing Prime95 then issue the command "ReCache nn Prime95.exe" where nn is the amount of physical memory in the system in megabytes. Can easily be set up as a Windows shortcut. Benefits: the ReCache program forces unused DLLs out to swap space causes a general "tidy up" of the whole Windows memory space. This makes any compute-intensive program launched using it operate a little more efficiently. Speed up of 1% or 2% is usual. I'd also be particularly interested in an automatic routine, as my Windoze box crashes 3 or 4 times a day. (Yes, I know -- but I've only read through chapter 3 in "Linus for Dummies" so far.) Place a shortcut to Prime95 (or to launch Prime95 using ReCache) in your startup folder, using "Start/Settings/Taskbar/Start Menu/Add" But you probably should find out why windoze crashes so often. If you're on a busy LAN, it does help to have a full set of LAN security patches installed! Regards Brian Beesley _ 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: ECM Factoring
When this is cleared up, it will make a good FAQ. Who maintains the FAQ list? Do you agree the answer here is a good FAQ? At 01:10 PM 10/2/99 -0700, you wrote: Hi, I need some help. I would like to look for a factor of a mersenne prime in a specific area. For example, for a mersenne exponent of say 40,000,000. I want to use the Prime95b program, (v19 I guess), to search for a factor in a specific range from, say, 2^40 to 2^50. I do not understand the ECM factoring instuctions included with Prime95. You can also edit the worktodo.ini file directly. For example: ECM=751,300,0,100,0,0,0,24 The first value is the exponent. The second value is bound #1. The third value is bound #2 - leave it as zero. The fourth value is the number of curves to test. The fifth value is the number of curves completed. The sixth value is the specific curve to test - it is only used in debugging. The seventh value is 0 for 2^N-1 factoring, 1 for 2^N+1 factoring. The eighth value is the MB of memory the program should use. I don't understand how to set the ECM= paramaters to accomplish my goal. It is my understanding that one can use ECM or 2^p-1 factoring with V19. Any help would be appreciated. Thanks Dan _ 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: graphical interface for gimps
Neat Idea !!
At 08:22 PM 9/28/99 -0700, you wrote:
Instead of a boring status bar, how about a graphic of a
caterpillar gnawing away on a leaf? It starts out as a full
leaf and disappears as the little beastie devours his sustenance.
Have an outline of the original leaf for size comparison.
That would be cool: have it turn into a butterfly at the end.
Or if the exponent is prime, have it turn into a pile of gold
or something. {8^D spike
_
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Re: Mersenne: Linux mprime and glibc 2.1
Get the Western Digital 18.5 Gig hard drives at 7200 RPM for under $ 300 each. My system has two. Now I have to fill 30 + Gig of hard drive space. At 07:15 PM 8/16/99 -0400, you wrote: preallocates 16MB memory, even if it doesn't use it all. This will cause the program to fail badly if the memory's not available. The cure was to add enough swap to appease the initial allocation, which is then never used, so the swap space isn't really used. I think I used 10MB swap:) Bleah. That's probably it. Who wants to send me a free harddrive? :) TomG who won't be running mprime until he upgrades his harddiskdrive(s) _ 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: Factoring and Databases
I may be a little obtuse here (and spelling, expression of ideas may be inadequate) but A Mersenne number's prime divisors are unique to that number. Letting a and b be primes, 2^a - 1 and 2^b - 1 have completely different factors. So we can make a table (database) with p1 divides M(q1) p2 divides M(q2) p3 cannot divide any Mersenne number p4 divides M(q3) p5 cannot divide any Mersenne number p6 divides M(q2) etc. where p1 = 3, p2 = 5 and so on for all the primes in sequence. The q1, q2 will also be primes but not necessarily in sequence and may occur several times (as it does for p6). I will use the language that "pn belongs to qm" to mean that the nth prime is a divisor of the Mersenne number q sub-m (2^qm - 1). I can then say that pn (the nth prime) either fits condition A (it divides M(qm) where qm is known) or that pn fits condition B (it cannot divide any Mersenne number). ALERT: Am I right about conditions A and B or does condition B work for specific Mersenne numbers only? I suspect that if someone looked at the primes up to p200, the 200th prime, all have an associated Mersenne number M(qm) (M of q sub-m). Lucas Wiman, for example, states that he has found 1868 new factors in the range of Brian's 10,000,000+ digits, which I take to mean that 1,868 new primes are known to belong to a specific qm. Why test factor for primes in the range 2^1 to 2^10? If someone made the table I described, it is possible that all primes less than 2^10 are in the table I have described because they are known divisors of a Mersenne number OR are not candidates for dividing any Mersenne number by other conditions (subject to the ALERT above). Therefore factoring could start at 2^10 + 1 and continue up to 2^x (where x is a suitable integer that GIMPS choses). Eventually, all primes in the range 2^10 to 2^11 will be covered (not a candidate for a divisor of a Mersenne number or the prime is known to belong to qm for some m). Then 2^11 from 2^12 will be covered, etc. There is a key idea here, that each pn will eventually belong to some qm, and that the smallest pn without a qm will rise over time due to the effort of factorers such as Lucas Wiman. Would we be able to try brute force factoring at some point for the Mersenne number M(s) where s 10,000,000 since there are so many primes taken out of the potential list? ALERT: I said "each pn will eventually belong to some qm". Is it possible that p1234 (the 1,234th prime) is never a divisor of a Mersenne number? O.K. Ken, Luke, Brian and you other smarter-than-me guys and good mathematicians, fix this up, shoot it down, use it or whatever else is possible. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Mersenne Cryptosystem
Try this: Nelson H. F. Beebe [EMAIL PROTECTED] Center for Scientific Computing University of Utah Department of Mathematics, 322 INSCC 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Publication began with volume 1, number 1, in January 1977, when I began my subscription, and the journal currently appears quarterly, in January, April, July, and October. Volume 9, number 3, appeared in June, instead of July, 1985. My subscription lapsed some years ago. Originally it was published and/or edited at Rose-Hulman Institute of Technology, Terre Haute, IN 47803, USA, and then moved in July 1995 to the Department of Mathematical Sciences, United States Military Academy, West Point NY 10996-9902, USA. Cryptologia is a laymen's publication, in the main, but has some heavy math. Mr. David Kahn, author of CODEBREAKERS (an excellent book just from the point of history), writes for it and other notable persons in the field did also. This journal is unusual in that volumes are numbered with roman, rather than arabic, numbers. For convenience of bibliography tools like bibsort, this bibliography uses the equivalent arabic form. If Mersenne primes have been used in cryptology, these people will know. See the web site http://liinwww.ira.uka.de/bibliography/Misc/cryptologia.html for some info and the journal has a World-Wide Web site at http://www.dean.usma.edu/math/resource/pubs/cryptolo/index.htm At 08:10 PM 3/11/99 -0800, Terry wrote: If I remember right there was mention a while back of a cryptographic algorithm based on Mersenne primes. Can anyone give a pointer to information on this cryptographic algorithm? Terry Terry S. Arnold 2975 B Street San Diego, CA 92102 USA [EMAIL PROTECTED] (619) 235-8181 (voice) (619) 235-0016 (fax) Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: Link from Knuth's Home Page
Yes. The Romans used the word "fasces" to decribe a bundle of sticks bound together to hold an axe at one end (a picture would be worth a lot but I don't have one). The cord was wrapped around the bundle. The axe was used in war as well as construction. Benito Mussolini and the Italians knew about this, being well steeped in Italian, i.e., Roman history. Beniti coined fascist from "fasces" telling the Italians that they were strong if bound together. History lesson for the day. At 02:09 PM 2/17/99 +, you wrote: Note that the Fascist party in Italy was called this because its symbol had a bundle of something (wheat? twigs?) in the middle, and the Italian for bundle is "fascio". -- Adam Atkinson ([EMAIL PROTECTED]) It is a sobering thought, for example, that when Mozart was my age, he had been dead for two years. (T. Lehrer) Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Rankings
What is up with http://project.vobis.de/gimps/ I just get faliled to open configuration file: "/usr/local/Counter/conf/count.cfg" (where faliled is failed, I presume)
Re: Mersenne: Galois
I posted the original book review because someone was discussing Galois transforms on the list. I simply though that those people might like to know of the book. At 09:35 PM 12/27/98 +0100, [EMAIL PROTECTED] wrote: From the London Times of December 17, 1998 THE FRENCH MATHEMATICIAN By Tom Petsinis Penguin, £7.99 (Fiction) ISBN 0 140 26472 8 . The book attempts to end the mystery of a difficult loner who, in a twist to gladden the hearts of any plodding schoolboy, was rejected by the now-forgotten mathematical sages Hmmm ... Fourier and Liouville who were between the rejecters cannot really be regarded as now-forgotten either. PM of the time on the grounds that he was a no-hoper with silly ideas. It is great subject matter, although newcomers to Galois may get a little lost between fact and fiction, detail and dreams. For while Petsinis creates a lively and convincing portrait, he peppers Galois's life with lengthy and obscure hallucinations, as well as a peculiar habit of talking to his biographer. After reading this version of the life of Galois, one can imagine all too well why the teenage genius had few friends and fewer patrons. Reviewed by HELEN RUMBELOW for the London Times
Mersenne: Galois
(I qm assuming this is not too far off topic.) From the London Times of December 17, 1998 THE FRENCH MATHEMATICIAN By Tom Petsinis Penguin, £7.99 (Fiction) ISBN 0 140 26472 8 Evariste Galois is the mathematicians' pin-up: he single-handedly rescued their chalky art from eternal dullness and propelled himself into the realms of glamorous notoriety. He lived fast and died young. By the time he was shot in a mysterious duel at the age of 20, Galois had already been imprisoned for threatening to kill the King in post-revolutionary France and had invented "Group Theory", an astounding discovery that unifies geometry and algebra. One hundred and sixty years on, it is now a fundamental part of modern maths that extends to nuclear physics and genetic engineering. Few mourned Galois's death. In The French Mathematician, Tom Petsinis creates a fictional Galois to narrate a novel that tries to explain why the prodigy was so misunderstood; why as E.T. Bell put it: "In all the history of science there is no completer example of the triumph of crass stupidity over untameable genius than is afforded by the all-too-brief life of Evariste Galois." Of course, there has to be much fiction in a biography that uses the Romantic concept of allowing its subject to speak his own mind. From the little known of Galois between his school reports of "original and queer" to the desperate last night of his life, when he scribbled to a friend as much as he could of his insights into mathematics, adding in the margins "I have not the time", Petsinis has created a Galois who was as brash as he was brilliant. He rejected anything that did not interest him, including his mother, women, his schoolwork and, most bravely for the time, God and King. With the algebraic symbol of "x" Galois writes that mathematicians have both a cross on which to suffer and angel's wings on which to soar. The book attempts to end the mystery of a difficult loner who, in a twist to gladden the hearts of any plodding schoolboy, was rejected by the now-forgotten mathematical sages of the time on the grounds that he was a no-hoper with silly ideas. It is great subject matter, although newcomers to Galois may get a little lost between fact and fiction, detail and dreams. For while Petsinis creates a lively and convincing portrait, he peppers Galois's life with lengthy and obscure hallucinations, as well as a peculiar habit of talking to his biographer. After reading this version of the life of Galois, one can imagine all too well why the teenage genius had few friends and fewer patrons. Reviewed by HELEN RUMBELOW for the London Times
Mersenne: Banners
Excellent work. I am curious - who do you contact for the $1,500 prize? One banner did not get through -- they are not numbers so I cany point to it. There are two GIMPS/Primenet. Ffor the glory of mathematics and one GIMPS/Primenet. Join 7000+ fellow computer users belows bd At 01:16 AM 12/13/98 EST, you wrote: I've completely remade all of my GIMPS Banners, and added a couple new ones. They're located at http://mersenne.cjb.net/ , and there's about 60 of them (30 of one font, 30 of another.) These are the very same ones Scott Kurowski uses on the PrimeNet page. *grin* Thanks, Mr. Kurowski! Feel free to use them as much as you like. :-D If you have a web page, please, please use them, as GIMPS needs mucho publicity. They're 40x400, 256 color GIFs that are about 8K apiece. You can copy them or just link to them in my FTP directory. Directions are on the page. If you could, E-mail me and tell me which slogan you like the best. Feedback is god, good :-D Thanks! STL137
Re: Mersenne: Re: 128-bit CPU
To the exact cent? I guess you have not heard the news that the Euro dollar is causing. The calculations must be correct to the 10th of a mil for the conversion factors. Thus one needs E,EEE,EEE,EEE,EEE.c (yes, 5 decimals to round up.) It is known in Europe as maybe worse than the Y2K issue. In Italy, they don't have decimals at all for the Lira so adding any decimals at all is a headache. P.S. All these side notes being passed around are very interesting, even if off the topic somewhat. At 01:48 PM 10/28/98 -0800, you wrote: With regard to the need for 128-bit cpus: Another area that will inevitably demand such data types is the financial industry. If you use packed BCD (very popular with the "exact" calculations that CPAs demand) and you want to represent anything under $100 trillion to the exact cent, you already need 64 bits for the significant digits, which means the sign nibble pushes you over the 64-bit limit. Budgets (especially national ones) are only going to get bigger and things like the Euro and conversions between currencies will make it necessary for the international financial types to go to such data sizes. Truett Lee Smith San Francisco, CA E-mail: [EMAIL PROTECTED]
Re: Mersenne: A short gdunken on Aaron B's situation
As the one who started all this, I commend Seth L. Chazanoff's comments below. I realize this is for some an intriguing issue, hard to resolve. One person resolved it by a personal, and uncalled for, criticism of me; others have also called this uncalled for. As several have mentioned, I was indeed recalling the rejection of the "scientific work" by so-called "scientists" of Germany and Japan during WWII. These results were tossed out by the Western powers. The case here is not as serious, not as offensive, and is a good one for a different and lower level of ethics discussion. Aaron is not to be compared to the WWII "scientists". He is also very likely to be a really nice person as well. (Footnote: I seem to recall that the use of penicillan as very beneficial was give to Germany after 1939). My vote is to disallow the results when 1) The air is clear on what happened and if 2) Aaron cannot convince GIMPS he had ALL needed permissions. I emphasize ALL needed permissions. Like many of you, I too work in an environment where there are scads of idle cycles at night and on the weekends. But the company only lent me one machine for my use, not the whole network. Getting the network would be impossible, as it should be. A) Someone wants or needs to work at night or on the weekend. B) The GIMPS program is is on their machine and who is to maintain it? C) What about the firewall that the company has? A major problem is that of the appearance of a "hacker" in the unsophisticated minds of too many people running the network, running the company, or people otherwise involved (purchasing did not buy computers for GIMPS). I don't think that Aaron is even up to the level of a "hacker" yet I worry that the perception will be advanced by the unsophisticated (which includes uninformed newspaper writers who know far to little to write on this subject, probably using a laptop.) Maybe some of the unsophisticated are likening the event to the danger of spam. Of couse it isn't equal to that or even like that, but perceptions are important. It may well be true that Aaron Blosser caused no damage to anything or anyone. Yet that cannot be the sole deciding issue. Surely Seth L. Chazanoff's method of expression, improper use of comany resources, should also be used. This is where getting ALL NEEDED permissions comes in. Also we need to respect the secretary who says "don't put that thing on my machine" because the secretary does not know _anything_ about computers beyond the keyboard (but viruses are a worry). Again, ALL NEEDED permissions raises its head. Well, we could argue this for a long time. I vote for discarding the results and asking GIMPS to warn its participants to never do this again. GIMPS should not credit Aaron for the work. At 09:38 PM 9/17/98 -0700, you wrote: We have been having quite a bit of discussion on what to do with Aaron's results, given that U.S. West claims that he didn't have permission to use the machines in question. Let's try this: Assume that I am your supervisor, and you come to me and and make your pitch for permission to put a program on all of the department's computers. I like it and I tell you go ahead. Someone else (an auditor? a P.Oed co-worker) comes along, discovers this program on the computers, escalates a complaint to a "pointy haired" someone who will listen to the complaint of the improper use of company resources, and shows you the door for "stealing" the company's valuable excess CPU cycles. Did you have permission? If not: Did you act in good faith? Should we throw out your results? Should we not credit you for your work? Vincent J. Mooney Jr. [EMAIL PROTECTED]
