Re: Mersenne: Mprime in dual cpu setup?
On 14 Oct 99, at 18:14, St. Dee wrote: I'm running mprime (v19) on a dual-processor box (RH 6.0, very basic, no graphical interface at installed) and am curious about the hit others take when moving from using one to two processors. (People running duals under NT are also welcomed to respond!) I'm running two dual systems, both running NT WS 4.0 SP5. One has 2 x PII-350 and one has 2 x PIII-450. If I run a single instance of mprime, I get LL iteration times on exponents near 8,200,000 of about .220. If I run two instances of mprime, each gets iteration times of around .245. I expected some hit, but I have no idea if that is too big of a hit or not. Sounds about right. The performance hit gets bigger with bigger clock multipliers. The problem is that having 2 processors accessing 1 memory bus tends to cause memory bus congestion. Curiously, I did notice that when the box was doing some factoring to 64 bits, it didn't seem to make any difference in the factoring times whether I had one or two processors crunching. Yes. Trial factoring will run from the processor cache (even on a Celeron) so doesn't hit the memory bus. Ideally you want to be running something different on the processors of a dual system; a mix of ECM on small exponents LL testing also works well. In case it matters, the box contains 2 Celeron 466 processors on an Abit BP6 board. Anyone looking for a big speed bump at low cost, try out a combo like this! I have it on good authority that Intel are trying hard to prevent people constructing dual Celeron systems - because of the potential damage to the PIII market. Be warned, you might buy the bits it might not work 8-( Regards Brian Beesley _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: DOSville
On 14 Oct 99, at 17:29, Lucas Wiman wrote: I'm most definitely _not_ Bill Gates's biggest fan, but I have to say that Windows NT _does_ multi-task pretty well. In fact, in a SMP environment, it's actually rather _more_ effective than linux, you can (but don't have to) force particular threads to run on a given processor. With luck, provided there aren't _too_ many threads in the "need CPU cycles" queue, this can give you a significant performance boost, since the data you're working on might well be still available in the CPU cache, even if you've been timesliced or interrupted out since you fetched it - whereas pre-fetched data sitting in the cache of another processor is useless to you. Linux is smarter -- it automaticaly gives preference for the last CPU used, without any special settings. Sometimes, however, if for some reason the kernel or other threads need that specific CPU, Linux will move the process. You win. Have you noticed what happens when you on Windows NT run one instence of Prime95 on idle priority with affinity to one CPU and start a new CPU-hogging program with normal priority and no processor affinity? The other program will be on the first CPU 50% of the time and on the other CPU the other 50% of the time. 25% of the time one CPU (the one Prime95 isn't using) will be idle, while the other program is using the CPU which Prime95's processor affinity is set to. That's how smart the processor affinity of Windows NT is! I agree that it should be possible to set the automatic "glue" stronger on Linux for certain processes like mprime (without recompiling the kernel) but I think Linux have a much better approach to this than NT. -- Sturle URL: http://www.stud.ifi.uio.no/~sturles/ Er det m}ndag i dag? ~~ MMF: http://www.alladvantage.com/go.asp?refid=BUP399 - St. URLe _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: types of work to request - 10m digit prime vs. nextprime
-- Date: Thu, 14 Oct 1999 20:44:16 -0400 (EDT) From: Darxus [EMAIL PROTECTED] Subject: Mersenne: types of work to request - 10m digit prime vs. next prime As soon as I heard that there was a $100,000 prize available for finding a prime, I decided to switch to the 10m digit test, even though my chances of finding it were extreemly small. I mean, the tiny chance of winning that cash is better than leaving your idle CPU time idle, right ? Unfortunately, this cash prize had clouded my thoughts, as I fortunately realized when my girlfriend told me she opted not to switch to the 10m digit tests, because she was more interested in getting her name in the history books than getting $100,000, and there was is a significantly greater chance of finding the next prime than there is of finding the 1st 10m digit prime. I too am more interested in fame than fortune (and incidentally don't put much stock in the Islands) and to this end I've been latching on to smallish exponents. Speaking of fortune - for a few short weeks in April and May, joining GIMPS really was a positive-expectation bet. I could test one exponent in the 4-5M range a week for a 1-in-35000-more-or-less shot at the prize, for roughly $1 electricity per exponent (less than 2 KWH/day at 8c each, with the monitor off when I wasn't at the keyboard). Of course that meant it was more a lottery than research, and it was bound to end within a couple months. [snip] It was what, half a million dollars total ? I think it would havebeen much better to award $25k per new prime discovered for the next 20 primes. The purpose of the EFF awards was not to help GIMPS; it was to inspire people to find better ways to find big primes, and, more generally, encourage fresh mathematical thought. Conjecture time: The prime number earning the $150K prize will not be a Mersenne. Why do I say that? Even with processor speeds increasing, we have a good idea how long it'll take to find big primes by Lucas-Lehmer. Even for the 10M-digit prime it'll be a damn long time the way we are doing it now. Finding the monsters requires an intellectual leap by someone - possibly in processor design, more likely in number theory. Admittedly this leap may well be a better version of L-L in which case Mersennes will still be the record primes for a long while to come. But my hunch is that there is a better chance of finding some new way to either construct primes, or to test some other special-form number, than there is of dramatically improving on Lucas-Lehmer. Just a hunch. I might be wrong. I hope I live long enough to see all of the EFF prizes awarded, whether to Mersennes or not. Gordon Bower PS - On an unrelated note --- what is the smallest natural number that is not known whether it is prime or composite? Surely *someone* out there is trying to work from the bottom up and factor every number. (I don't know the answer. I am guessing the it is a smallish number of maybe 15 or so decimal digits?) _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: problem with prme95 - spl file - ME TOO !
I am also having the same problem, but only on one machine, I have 9 others that are fine, all are using the same version of v19 beta 4 I click on Test | PrimeNet... then tick the box "Send new completion dates to PrimeNet" Click ok, then go to Advanced | Manual Communication and click ok. It connects to the server, updates the information on the server then says Done communicating with the server, just as normal. This computer has not been updated on the primenet server since the 3rd Oct so it's happened a few times and I had not realised till today. I have checked that before I do the Manual Communication to see if the prime.spl was there... it was not ! Sorry, Need help having tried to overwrite version 18 with 19-on an LL test(Win98).Have All the files and managed to run the test from my last save file pxxx -Also have q xxx It initially restarted it.from scratch...irksome...and downloaded about 10 factorization exponents, when I just wanted to update and continue..my initial LL test .I have lost (I think the spl. file )- having been resigned to dragging and dropping files into the old folder. and deleting old versions... My computer will not update progress to the primeserver...just keeps sending computer update and user info...no update on my numerical test..? Any ideas please?! Confused...spl files??? how can I create one? 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 Mike, -- ATLAS CELESTE - Bevis Star Atlas - "The CD-ROM" http://www.u-net.com/ph/mas/bevis/ Astronomy in the UKhttp://www.u-net.com/ph/ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: estimating primes (was: Re: Mersenne: Islands of Truth)
I'd also guess that the skipped prime may have been pretty close to 2^5014947-1, and have a number of digits close to 1408773. ... Hmm... I just changed my worktodo.ini to Test=5014947,63 (where's the 63 come from ? it was used for the last number I was assigned). It's saying "Error: Work-to-do file contained composite exponent: 5014947" I suppose that means it's already been tested found to be non-prime ? (composite = non-prime, right?) That's because the exponent itself needs to be prime, and 5014947 is not. Divides by 3 in fact. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: pre-LL factoring
Hi, At 06:47 AM 10/15/99 +0200, Shot wrote: The question is: why didn't Prime95 factor the older one from 63 to 64? No good reason. The program doesn't do any trial factoring once an LL test has begun. Regards, George _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: problem with prme95 - spl file - ME TOO !
On Fri, 15 Oct 1999, Michael Oates wrote: I have checked that before I do the Manual Communication to see if the prime.spl was there... it was not ! prime.spl only ever exists when there is something to send to the server and it hasn't been sent yet. If it's not present, there is no communication spooled. -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ Thomas Daggert to Lucifer: I have my soul, and I have my faith. What do you have... angel? The Prophecy _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: DOSville
Linux is smarter -- it automaticaly gives preference for the last CPU used, without any special settings. Sometimes, however, if for some reason the kernel or other threads need that specific CPU, Linux will move the process. You win. Actually, NT does the same thing. Nope. You set the affinity to CPU 0, 1, etc. The process will then _only_ run on that specific CPU. ... have you actually tested this? Start Prime95 at idle priority with CPU affinity set to one of the CPUs. Start the "Tast Manager", choose "Performance" and look at the graphs. One should be at 100%, the other close to 0%. Then start another process at normal priority and see how the load of that process divides between the CPUs, leaving one 50% idle while Prime95 stays on the single CPU it has set affinity to (the other). I tried this on a Windows NT 4.00.1381 Service Pack 3 Terminal Server. -- Sturle URL: http://www.stud.ifi.uio.no/~sturles/ Er det m}ndag i dag? ~~ - St. URLe _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: problem with prme95 - spl file - ME TOO !
On 15 Oct 99, at 13:16, Michael Oates wrote: I am also having the same problem, but only on one machine, I have 9 others that are fine, all are using the same version of v19 beta 4 What's different? Must be _something_ ... I click on Test | PrimeNet... then tick the box "Send new completion dates to PrimeNet" Click ok, then go to Advanced | Manual Communication and click ok. It connects to the server, updates the information on the server then says Done communicating with the server, just as normal. This computer has not been updated on the primenet server since the 3rd Oct so it's happened a few times and I had not realised till today. I have checked that before I do the Manual Communication to see if the prime.spl was there... it was not ! I thought this behaviour was normal since about V19 beta 2, when I queried it I was told it had been modified as a result of a request from Scott Kurowski to update the computer information every time the client contacts PrimeNet, for whatever reason. Even if you force a connection without there being a need to communicate results or update completion dates. There will not be a prime.spl file in this case (nor if the system realises during a forced connection that it would like to fetch another assignment from the server). Confused...spl files??? how can I create one? Select "Send new completion dates" in the Test/Primenet menu. Or simply wait for an assignment to finish, or long enough for the system to want to update the completion dates automatically (Options/Preferences/Days between, default 28 days) Regards Brian Beesley _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Modular arthimatic..
Hi! Just something I was pondering a couple of days ago... Consider a general number (odd) number c which can be factored into ab=c W.L.O.G. assume b is greater than a then let x=(a+b)/2 , y=(b-a)/2 then (x+y)(x-y)=c x^2 - y^2 = c x^2 = c + y^2 So if we can find if this equation has any integer solutions, we've found our factors... Ways of doing this: The difference of two squares is always an arthimetic progression of odd numbers. Here is an example.. 2^2 - 1^2 = 3 3^2 - 2^2 = 5 4^2 - 3^2 = 7 and so on... So look at general sum of an arthimetic series S(n) = (n/2)(2a + (n-1)d) In this case d=2 and a is odd, so need to try to solve c = na + n(n-1)/2 for integers n,a Also, try to solve x^2 - y^2 = 0 mod c As if this is solvable, then (x-y)(x+y)=nc, for integer n, so must be able to cancel out all factors of n in either (x-y) or (x+y) to get back to a solution of equation.. Alternativly, could try to find out by some kind of set notation what the size of the group of solns. is... This is where I come unstuck. I believe this is an example of an eliptic curve, and I want the c'th term in it's L-series. Could we transform it into a modular form and then quickly work out this term. I could well be in cloud-cockoo land now, as I aren't even totally sure what a modular form is, but I know that the L-series of modular forms, and some series related to modular forms are the same, and this proof lead the the solution of Fermat's Last Thereom Anyway, if anyone could just vaguely point me in the right direction, or tell me if I am talking rubbish before I go and start reading up on all this... Thanks! Chris Jefferson, Girton College, Cambridge, [EMAIL PROTECTED] Someone may have beaten me to Fermat's Last Theorem, but I've done Riemann's general equation. However it won't fit in my signature file... _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Modular arthimatic..
At 06:25 PM 10/15/99 +0100, Chris Jefferson wrote: Consider a general number (odd) number c which can be factored into ab=c W.L.O.G. assume b is greater than a then let x=(a+b)/2 , y=(b-a)/2 then (x+y)(x-y)=c x^2 - y^2 = c x^2 = c + y^2 So if we can find if this equation has any integer solutions, we've found our factors... Good idea, but this is Fermat's factoring method. It works pretty well if a and b are close. +-+ | 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
Re: Mersenne: Modular arthimatic..
On 15 Oct 99, at 18:25, Chris Jefferson wrote: Just something I was pondering a couple of days ago... Consider a general number (odd) number c which can be factored into ab=c W.L.O.G. assume b is greater than a then let x=(a+b)/2 , y=(b-a)/2 then (x+y)(x-y)=c x^2 - y^2 = c x^2 = c + y^2 So if we can find if this equation has any integer solutions, we've found our factors... Ways of doing this: The difference of two squares is always an arthimetic progression of odd numbers. Here is an example.. 2^2 - 1^2 = 3 3^2 - 2^2 = 5 4^2 - 3^2 = 7 and so on... So look at general sum of an arthimetic series S(n) = (n/2)(2a + (n-1)d) In this case d=2 and a is odd, so need to try to solve c = na + n(n-1)/2 for integers n,a Also, try to solve x^2 - y^2 = 0 mod c Are we not back to Fermat's Method for factorization (again)? If we're dead lucky and pick a value c such that a and b are very similar in magnitude, this method works a treat (hence it's very unwise to pick a public key which factorizes into two nearly equal numbers. You make the job of cracking your key a lot harder if you pick the product of two numbers which differ in length by a couple of bits.) There is still a gap between the largest factors which can be found (practically, not theoretically) by techniques suited to "small" factors, like trial factoring, P-1 and even ECM, and Fermat's Method which is practical only for "small" values of b-a. (Fermat is just plain _awful_ at factorizing 3*p for large prime p!) Probably the continued fractions method is the best line of attack on numbers which resist "reasonable" efforts with other methods. Regards Brian Beesley _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: splitting up 10m digit primes
On Thu, Oct 14, 1999 at 06:15:52PM +0100, Chris Jefferson wrote: In my personal opinion, the best way of doing this would be to set up 3 computers in a 'loop' all doing the same exponent. Then they could communicate at regular intervals. We are already doing this manually, although only with 2 computers (if the residues match, you don't need the 3rd one). We're taking residues every one million iterations, and mail them to each other. So far, they've matched :-) And if one machine is faster than the other -- well, then it goes on to another exponent. No waiting needed. /* 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
Mersenne: The Mysterious Ways of S.T.L.
Hello, everybody. As usual I'm quoting different people. Disturbingly, I noticed a weird HTML tag on my last E-mail. I can assure you I didn't put it there, and don't know why my software's acting up on me (because I've never seen that jibberish before). HTML mail is evil, only second to MIME. Long live ASCII! Please excuse my delay in sending this message. Also, if this extrapolation of the number of digits is accurate, there is another prime between the 37th 38th(p=6972593) discovered primes. Unfortunately, the extrapolation of P just didn't go well. Actually, the extrapolated 39th mersenne prime is 6.34% off of 2^6972593-2. I suppose that's not so bad. That would also mean one was skipped. So it is currently my fairly strong opinion that a mersenne prime was skipped between the 37th 38th discovered primes. I reserve the right to change my mind at any instant. I'd also guess that the skipped prime may have been pretty close to 2^5014947-1, and have a number of digits close to 1408773. This is similar to the conjecture I made oh-so-long ago. 6.9M was confirmed, but at the same time I had to predict a missing one (which I said was probably in the 4M range, but that's far less certain). [EMAIL PROTECTED]: I'm really looking forward to hearing how you made your estimates. How did you make this estimate ? Fit an exponential curve to the known primes, and extrapolate the 1st one that should have at least 1m digits? Who knows the mysterious ways of STL? I usually just go by S.T.L. (my initials). At some point I had a vague recollection that STL had believed there was a number missing, and I was quite happy to see that it basically matched what I got. And rounded, my estimate for #39 equals his. Your estimates are close to what I have. I haven't the slightest idea how one establishes priority for a discovery, but here I go. I think I've improved on the conjecture of Wagstaff, Gillies, Lenstra, Pomerance, et al. (At the very least, it's another conjecture.) Some time before I E-mailed the list with my 3 conjectures I had made the main one. I had not told the list of it because I planned to use it in a ridiculously important paper for school. But it seems that my method is being rediscovered and I may as well announce what I've seen. Here it is, and what led me to it. I had picked up _Unsolved Problems in Number Theory, Second Edition_ by Richard K. Guy, and was reading it. In section A3 (which contains a humorous typo), I found the following: Suppose M(x) is the number of primes p = x for which 2^p - 1 is prime Lenstra, Pomerance, and Wagstaff all believe this [an early conjecture by Gillies] and in fact suggest that ?? M(x) ~ e^gamma log x ?? where the log is to base 2. So I started investigating this. Armed with a copy of all Mersenne primes (I have a bad habit of saying this when I really mean exponents for which the Mersenne number is prime) from 2 to 3021377, a loyal TI-92+, and a newly gained knowledge of basic statistics, I started computing some things. First, I made a list of numbers 1-37. And I had the list of exponents, sorted by size. (I called it mersenne.) Then I plotted points with the 1-37 values for X and log[2] (Mersenne) for y. I got an astoundingly linear graph, as others have. Then, I plotted e^gamma log[2] (mersenne) versus the list of 1-37. Alongside this I graphed y=x. This is because the y=x line represents the Wagstaff conjecture. (If all exponents for which the corresponding Mersenne number is prime followed the Wagstaff conjecture exactly, e^gamma log[2] (mersenne) would equal 1, 2, 3, 4, 5, for each exponent in turn.) This was a rough measure of how well the Wagstaff conjecture applies to the actual set of Mersenne prime exponents. This graph seemed a little strange. So, I graphed e^gamma log [2] (mersenne) - (1, 2, 3, 4, etc). This represents how far off the Wagstaff conjecture is when applied to the data. (The Wagstaff conjecture *should* say that M(3021377) = 37, but it doesn't. This is why I graph this jibberish). This graph was INCREDIBLY disturbing. Save for one Mersenne prime, all these "errors" were above 0, and often big. Ech! So, I used my TI-92+ to take a linear regession line of this data (because I had recently learned how to do regression lines and correlation coefficients). This line was Y = .004769x + 1.4615. See what's happening here? It seems that there's a consistent error (1.4615) in the Wagstaff conjecture that doesn't change as the Mersenne primes grow (the .004769). So I went back and applied this correction to the graph "that seemed a little strange" and it fit y=x much better. Hence, my new conjecture: ?? M(x) ~ e^gamma log[2] (x) + C ?? Of course, I used 1.4615 to make my 3 conjectures to the Mersenne mailing list. In reality, I'm guessing it might be 1.5, or even 2^(1/e^gamma)! (In fact, I'd rather go with 2^(1/e^gamma), as Erhardt chose 1.5 for the e^gamma in the
Re: Mersenne: types of work to request - 10m digit prime vs. next prime
Conjecture time: The prime number earning the $150K prize will not be a Mersenne. This isn't so much a conjecture as a prediction (there is a difference). A conjecture is a very specialized prediction. Why do I say that? Even with processor speeds increasing, we have a good idea how long it'll take to find big primes by Lucas-Lehmer. Even for the 10M-digit prime it'll be a damn long time the way we are doing it now. Finding the monsters requires an intellectual leap by someone - possibly in processor design, more likely in number theory. Admittedly this leap may well be a better version of L-L in which case Mersennes will still be the record primes for a long while to come. But my hunch is that there is a better chance of finding some new way to either construct primes, or to test some other special-form number, than there is of dramatically improving on Lucas-Lehmer. Just a hunch. I might be wrong. I hope I live long enough to see all of the EFF prizes awarded, whether to Mersennes or not. Ok, it seems doubtful that we will ever be able to find a test more efficient than the LL test. The LL test involves p multiplications mod Mp, which is pretty impressive. However, I agree with your prediction because there are much more targeted types of numbers with similar running times (e.g. Proth numbers). As Chris Nash pointed out, a Proth test would have taken 1/4th the time of the LL test on the Mersenne found in June on a number of precisely 1,000,000 digits. You may be right about the construction of prime numbers. Also if someone were to find a faster way to multiply than an FFT convolution, that would dramatically improve primality testing. PS - On an unrelated note --- what is the smallest natural number that is not known whether it is prime or composite? Surely *someone* out there is trying to work from the bottom up and factor every number. (I don't know the answer. I am guessing the it is a smallish number of maybe 15 or so decimal digits?) Probably the one right after the largest sieved interval. But I have to ask the question: Who cares? Unless the larger sieved limit is showcasing a new sieving algorithm, then why does it matter? To verify the primality of numbers up to a hundred digits is a simple matter. Just my $0.00 worth. (the FSF's motto) -Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: The Mysterious Ways of S.T.L.
Suppose M(x) is the number of primes p = x for which 2^p - 1 is prime Lenstra, Pomerance, and Wagstaff all believe this [an early conjecture by Gillies] and in fact suggest that ?? M(x) ~ e^gamma log x ?? where the log is to base 2. Hence, my new conjecture: ?? M(x) ~ e^gamma log[2] (x) + C ?? Of course, I used 1.4615 to make my 3 conjectures to the Mersenne mailing list. In reality, I'm guessing it might be 1.5, or even 2^(1/e^gamma)! (In fact, I'd rather go with 2^(1/e^gamma), as Erhardt chose 1.5 for the e^gamma in the conjecture and now several mathematicians call the Erhardt Conjecture I'm afraid that if you are correct, so is Wagstaff. The symbol "~", at least in mathematics means that if f(x)~g(x) then f(x)/g(x)=1 as x-infinity. Your conjecture seems like it would yeild a better aproximation than Wagstaff's (you could certainly argue that 2 is a special case, since it's corresponding Mersenne is the next bloody prime, and there is 1 of the 1.4615 right there). -Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Approximate!
I'm afraid that if you are correct, so is Wagstaff. The symbol "~", at least in mathematics means that if f(x)~g(x) then f(x)/g(x)=1 as x-infinity. So constants don't matter, of course. Your conjecture seems like it would yeild a better aproximation than Wagstaff's Nod, that's what I was aiming for. I wasn't trying to prove Wagstaff wrong - just find a closer way to estimate M(x). At least the ~ means that adding a constant doesn't change f(x)/g(x) = 1 as x - infinity... right? (See, if something turns out to be faulty in the way I made my conjecture, that paper I mentioned will be a lot weaker.) S. "Glad he kept a scribbed piece of notebook paper so he could remember how he made his conjecture in the first place" L. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: splitting up 10m digit primes
Personally, I think the big problem with regards to this is not people quitting so much as the possibility of major hard-drive failure etc. on the testers. I doubt many of them keep good backups NO EXCUSE! A Zip drive or a CD-R is inexpensive and effective; one will service many networked systems, they don't all have to be running the same OS. True, also Pkzip 2.04g (I don't know about WinZip) had the ability to span a zip archive across floppy disks. Even on a LL test of 33mil would take up under 3 floppies. (This wouldn't be reasonable for large networks, but it would be easily achievable for the home user...) -Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: DOSville
Linux is smarter -- it automaticaly gives preference for the last CPU
used, without any special settings. Sometimes, however, if for some
reason the kernel or other threads need that specific CPU, Linux will
move the process. You win.
Actually, NT does the same thing.
Nope. You set the affinity to CPU 0, 1, etc. The process will then
_only_ run on that specific CPU.
Right. But if you DON"T specify affinity, it does something very much like
what you described linux as doing.
...
have you actually tested this?
Start Prime95 at idle priority with CPU affinity set to one of the CPUs.
Start the "Tast Manager", choose "Performance" and look at the graphs.
One should be at 100%, the other close to 0%. Then start another process
at normal priority and see how the load of that process divides between
the CPUs, leaving one 50% idle while Prime95 stays on the single CPU it
has set affinity to (the other). I tried this on a Windows NT 4.00.1381
Service Pack 3 Terminal Server.
well, on a regular (non-TSE) NT 4 Server (service pack 4) dual PPro-200, I
ran two instances of prime95, and gave one explicit affinity, and the other
I left default ('run on any CPU'). Guess what? Both CPU's remained 100%
busy, and both instances of prime95 got 49-50% of the total (per the process
monitor in taskmgr.exe). This implies to me that it is clever enough to
ALWAYS run the 'floating' process on the free CPU and leave the affined CPU
to the affined process. Maybe TSE (Terminal Server Edition) has way
different heuristics, I dunno.
-jrp
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Mersenne: Re: Reliability (was Re: splitting up 10m digit primes) + Possible Wish List item
Joth Tupper wrote: The size of the files is an issue. With interim result files in the 7MB to 10MB range, some ISPs just cannot handle the size. We're talking about "the program" here, there's no reason to stick with e-mail - and in fact it's just an encumbrance. (Well, beyond that being simpler and more easily avilable, but still...;). As for your bandwidth-concerns in general, this is (among other obivious things!) why I said the option to act as backup should be one more selection in the config. If you can afford the bandwidth and storage space, you can check the box. I guess now you'd have to add another box to select between e-mail and "direct" connect, which would be far more efficient and straightforward, but require both clients online at the same time and no firewalls. Then people with ADSL or T-1 could offer their storage-space for the project. People uploading even 10 megs over 56k modem once in a world wouldn't be too much for many people (Myself included, even though I need to pay for time online) to know their work is secure. So I guess I should get into work coding this ;) -Donwulff _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne Digest V1 #644
Mersenne DigestFriday, October 15 1999Volume 01 : Number 644 -- Date: Thu, 14 Oct 1999 21:39:15 -0500 From: Ken Kriesel [EMAIL PROTECTED] Subject: Re: Mersenne: # of digits in 2^p-1 Look it up in the FAQ listed at the bottom of every mailing list message, is best in my opinion. Ken At 09:15 PM 1999/10/14 -0400, Darxus wrote: What's the best way of finding the number of decimal digits for the number 2^p-1 ? __ 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 _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Thu, 14 Oct 1999 22:49:17 -0400 From: Jud McCranie [EMAIL PROTECTED] Subject: Re: Mersenne: # of digits in 2^p-1 At 09:15 PM 10/14/99 -0400, Darxus wrote: What's the best way of finding the number of decimal digits for the number 2^p-1 ? p * log10(2) and round up to the next integer. log10(2) = 0.301029996. +-+ | 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, 14 Oct 1999 23:02:01 -0400 (EDT) From: Darxus [EMAIL PROTECTED] Subject: Re: estimating primes (was: Re: Mersenne: Islands of Truth) On Thu, 14 Oct 1999, Darxus wrote: On Thu, 14 Oct 1999, Darxus wrote: On Thu, 14 Oct 1999 [EMAIL PROTECTED] wrote: conjectures. (#1: That there's a prime around the 4M range that we're missing. #2: That the discovered M38, which all we knew about was that it was in the 6M range, was actually around 6.9M, which I was correct about, and #3: Pdigits #38 5,014,947 1,408,773 #39 7,414,614 2,070,471 Wow... I recalculated my estimates of P as # of digits * 3.321928094887 -- based on #5.6 from the faq (I really must read that whole thing some time so I stop asking stuff in it). They came out as: #38 4679842.61 #39 6877955.78 At some point I had a vague recollection that STL had believed there was a number missing, and I was quite happy to see that it basically matched what I got. And rounded, my estimate for #39 equals his. So now I'd estimate we're missing a prime near 2^4679842-1.. but of course when I try to do that manually, I'm getting told it's composite. __ 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: Fri, 15 Oct 1999 06:47:18 +0200 From: "Shot" [EMAIL PROTECTED] Subject: Mersenne: pre-LL factoring Hi all, I have a simple question: In between of a LL-test I downloaded v19. Soon came the time to request additional work and I got second exponent to stand in the queue. Prime95 switched to factoring the newer one from 63 to 64 - no factor. So far so good - I remember reading somewhere that v19 now factors up to 64 before attempting the LL-test. But then Prime95 switched back to continue the LL-test of the older exponent... The question is: why didn't Prime95 factor the older one from 63 to 64 (I checked - it is factored up to 63)? It would take an additional day, but it could save two weeks that it will take to complete the older one's LL-test... Thanks for your time, - -- Shot __ c"? Shot - [EMAIL PROTECTED] hobbies: Star Wars, Pterry, GIMPS, ASCII `-' [EMAIL PROTECTED] join the GIMPS @ http://www.mersenne.org Science Explained (by Kids): Some oxygen molecules help fires burn while others help make water, so sometimes it's brother against brother. _ Unsubscribe list info --
