Re: Mersenne: Fw: numeric hazards of high performance CPU design =Pentium 4 - constant speed problem
I just felt I had to say, that I am very disturbed by this. The idea of my CPU simply shutting down when it overheats is a sensible idea. This is much more dodgy, espicaly as there doesn't seem to be any way of finding out, short of lots of benchmarks, if your processor is doing this... :-( It also raises problems for prime95, as it looks like running prime95 will reduce your PC's speed by half. I am going to recieve a pentium 4 shortly, and although I shall try to send it back for an AMD processor, if I can't I shall run tests with prime95. However if these figures are true then it won't be searching for primes :-( Chris -- Chris Jefferson, Girton College, Cambridge, CB3 0JG --- http://mrjeff.webjump.com Don't bother, it's not worth looking at. On Sat, 19 May 2001, Roger Gariépy wrote: I came about this information on degrading calculations after about 10 minutes of usage. I think it can help explain stange behavour on your test of Prime 95 for P4. Don't be confuse by the web page title. Roger Gariépy :-) - :-( [EMAIL PROTECTED] - Original Message - From: validlab [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Thursday, May 17, 2001 5:20 PM Subject: numeric hazards of high performance CPU design http://www.inqst.com/articles/athlon4/0516main.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
Re: Mersenne: missing exponents?
You should use another MailClient as Microsoft Outlook Express 4.72.3110.1 8) Didn't you read all the bad things about Mailwurms etc? Sorry, I just felt the urge to say this. There is nothing particualarily bad about Outlook Express, these various viruses require you to excute attachments, and you can do that in any mail client.. If any other mail client gets as popular as OE, then it will start to have viruses aimed at it's address book too! Chris regards, Mohk _ 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: missing exponents?
Checking the status page, we seem to be stuck on 26 exponents between 6,325,000 and 6,972,593 - that haven't had one LL test. I've been double checking exponents in this range for months (and getting them done at the rate of more than 1 per month). I've been double checking because that is work makes the most sense, but does it make sense to double check this range when there are untested ones? If these 26 were actually being tested, they would be knocked off at the rate of at least one per day, and it has been a while since one has been finished. Haven't we had enough discussions about taking bnumbers people are takingf a long time to test / not chexcking uin very often? :) Chris ++ | Jud McCranie | || | former temporary part-time adjunct | | instructor of a minor university | ++ _ 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: Check This Out! Just got a new email at THEMAIL.COM
Just so everyone knows, I have reported this person and his account will be canceled with the day. Chris Jefferson, Girton College, Cambridge, CB3 0JG --- Disclaimer: Please do not read any hidden messages from my e-mails, as anything that looks like it is is simply my bad English. If I want to say something I will :-) On Thu, 31 Aug 2000 [EMAIL PROTECTED] wrote: Dear [EMAIL PROTECTED], qing he wanted us to inform you that THEMAIL.COM is now giving out a powerful free email service. Best of all, I get paid for reading email! - Check it out for yourself at: http://www.themail.com/ref.htm?ref=1243269 TheMail.com PostMaster _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt
Re: Mersenne: The recent popularity of Single-Checking
Nathan Russell wrote: There is a user, "sd70045", who has almost 100 single-checking assignments out on a single machine ID In any case, these exponents will expire in 16 days. As a result, I'm not concerned about it. Within 3 weeks they'll be re-circulated among other users. The only thing that would cause concern, is if the user intentionally updates these exponents in the next two weeks... xactly! Last time I checked there was an infinate number of possible mersenne candidates and using the current version of prime95/NT/whatever, we are umlikely to run out any time soon,so unless things get REALLY serious, surely with things like this it's best to just wait till they expire and let the automatted system deal with it? Chris Eric _ 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: GIMPZ
On Mon, 28 Feb 2000 [EMAIL PROTECTED] wrote: Jukka Santala wrote: First of all, I take offence at the use of the term "hacker" here. I would have thought most people following this list are knowledgeable enough to make the distinction - what GIMPS for example does is hacking Thanks for clearing me up on that - I was under the (apparently misguided) impression that GIMPS was about recreational mathematics. My sincerest apologies. I shall begin to recode all my software, er, I mean to say, warez, immediately. -Ernst And this is the reason why 'hackers' get such bad press. hackers are not interested in "warez", "crackz" , or anything similar. The people who wrote Linux were hackers, as were the people who originally wrote DOS (big bill never was. =\ ) We are hackers here, we are trying to combine together to power of many computers to see what happens and what interesting results we might create.. Chris _ 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?
On Fri, 4 Feb 2000, John R Pierce wrote: ... I think the 10 intervals might be a bit too draconian... I agree, 30 days should be considered a minimum. I don't know it if could be put into the primenet server, but could a 'trust' setting be put in? Maybe for the first 15 days a new person has an exponent, they should be limited to a max of 30 days with it. This could be set into the software, just so any people who join then immediatly quit don't chug up the system. Also, maybe the smallest components could be given to people with a high 'trust' rating, so we think they will get done. Obviously, anyone could fiddle their trust rating, I don't think it is worth getting too advanced, just stick in the first started date in the .ini file, don't put too much into it... Chris _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Factoring Mersenne
Hello! I was fiddling around with Mersenne factors the other day and came across an interesting result. I'm not sure if it is of any use, but I think if anyone can extend it just a little further, then it would cut down the numbers we would have to try to factor by a HUGE amount... Anyway, any mersenne's factor can be written as 2kp+1 So any persenne number 2^p - 1 (here on written as P) can be written as (2ap+1)(2bp+1) = P i.f.f. it is not a prime Now define x = p(a+b)+1, y=p(a-b) Then x+y=2ap+1, x-y=2bp+1 so P=(x-y)(x+y) x^2 - y^2 = P Now write n=a+b, m=a-b so x=pn+1 , y=pm Then (pn)^2 + 2pn + 1 + (pm)^2 = P taking this mod p^2 and rearranging a little 2pn = P-1 mod p^2 this means 2pn = (P-1) + pZ for some integer Z so (P-1) must have a factor of p, which we can cancel (we also know this directly). Call (P-1)/p = Q Then 2n = Q mod p n = Q/2 mod p which is well defined Therefore we can find the sun of the two factors mod p. I have tried (and failed so far) to get a similar relationship for y (or a or b) If we could get such a relationship for y, and we assumed we were looking for the smallest factor, then we could work out something about that factor (hopefully it's value mod p) which would cut down on factoring requirements. Any ideas? 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: Re: splitting up 10m digit primes
On Sat, 16 Oct 1999, Jukka Santala wrote: "Brian J. Beesley" wrote: On 14 Oct 99, at 18:15, Chris Jefferson wrote: Surely this isn't really an issue. PrimeNet would surely recognise a result submitted by a "poacher" as such either disqualify it automatically, or credit the actual owner of the assignment instead of the "poacher". Except that PrimeNet doesn't control the prize. This is the error everybody is doing. EFF is adminstrating the competition and prize, given by anonymous donaters to advance distributed computing / mathemathical algorithms on computers. PrimeNet is just one of the organizations (With largest changes known!) to get that prize, but it doesn't decide upon who gets it. The first person to present a prime filling the requirements will - and that's why result-files "few iterations short" will be worth more than their weight in gold. Yes, but the licence for Prim95/NT specifies that anyone who uses this program must obey it's licence. Someone using a partly completed file would also be liable under this. However, proving that they has used the interim file generated by this particular program might be difficult... _ 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: Re: splitting up 10m digit primes
Also one would have to ask what would be the incencitive for someone to act as a backup server... or prevent them from "stealing the work" as it were, by using high-speed computers to finish the test a month before the main person does in hopes of getting the prize. I think that the new licence could stop people from doing this, or could quickly be altered to say so, as I assume that a new version would need to be bought out to support it possibly... or at least make it easier... 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. Although it would mean working at the slowest speed, it might be a good idea to, along with backing up, get the to cmpare exponents at the same time. This would fix the problem of one of them quitting, another could be 'bought in', and also would allow double=checking as the check went along. However, I suspect the programming would be quite difficult. Chris -Donwulff _ 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: Front-end design
Sorry, I've deleted the mail. QWhere can I get the most recent Prime95 source code from, and what should I compile it with? I'd like to at least try to make a front-end, and I'm sure at least the base of a screen saver would take all of 30 minutes. I know that we'd perfer people to use prime95 all the time, but a screen saver would be useful for people who refuse to... 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
Mersenne: A slight divergence...
It is well known that n is prime if for all prime factors of n-1, a^(n-1) = 1 mod n and a^((n-1)/q) is not 1 mod n. For example, take a=2, and 2^p+1 (p is prime, yes, that IS a plus) Then we need to check if 2^(2^p)=1 mod (2^p -1) and 2^((2^p)/2) is not 1. Now, we know that 2^p = 1 mod (2^p - 1) so, 2^n = 2^n*2^p mod (2^p - 1) It is a simple extension to say that (2^n = 2^(n mod p) ) mod 2^p-1 So 2^(2^p) = 2^(2^p mod p) mod (2^p - 1) (Still following?) So to check primality of 2^p+1, only need to check value of 2^p and 2^(p-1) (which is obviously (2^p)/2). The main reason I am asking this is that I know that to check whether a number is a factor of a mersenne prime involves checking 2^p - 1 mod n for a number n and I was wondering if anyone's factoring code would go that high and wether it would be quicker to check this than the traditional 2^p - 1. 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
Mersenne: Factoring
I was just wondering, could anyone give me any info on how factoring is done, is there a preliminary factoring before numbers send out, how high we factor, what possible factors are, etc. and also, I would really like to see the maths behind it as well. I need something to study over summmer vac :) 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
Re: Mersenne: Serious problems with v.18
If what you say is true, then whoever designed version 17 acted in a completely unconscionably rash manner by releasing it without thoroughly testing it for problems as serious as that. And has therefore shot the whole GIMPS effort in the foot by setting it back many weeks. Hopefully, realization of the impact on GIMPS is punishment enough to make sure this won't happen again... On the other hand, it is often difficult to find out when trying to squeeze speed out of programs if you've gone too far, and the only way to test the program is the do entire LL tests in both this and another program we are sure works.. Doing it for more than a couple of exponents is VERY slow... Although I do agree, I hope that it doesn't happen again.. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Back to the maths of primes for a sec....
Sorry, just a quick question! In various places, I have read that the generalized Riemann hypothesis is true, then there is a very simple test for primeness, namely if n is an a-SPRP for all integers a2(log n)^2, then n is prime. From a computation viewpoint, is this actually of any use, as it will show if numbers are composite and if it is quick, then primes could be checked using it, then double checked via another means, also giving the opportunity to disprove a major hypothesis of maths... Chris Jefferson, Girton College, Cambridge, [EMAIL PROTECTED] I have a proof that x^n+y^n=z^n never has integer solutions for n2. However, it won't fit into my signature file Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Stoopid Bureaucracies!
I tried at my company too (A very large Aerospace company based in Washington) and my boss said that it didn't add any value to the company so she couldn't approve it. I gotta find a way to show it does have value... -Chuck If you find one... 1) £50,000 2) Lots of free publicity Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: I am curious
---QUOTE--- I was being a little sarcastic. I think that the original poster who was wanting to team up with other people running at least 10 machines is not in the spirit of the adventure. I think it is fine to make a team if everyone on the team has regular physical access to each machine, but I don't like the idea of teaming up with unknown people. That's why I said "why not make everyone a big team", with a little sarcasm that was probably too subtle. ---QUOTE--- Yes, I would have to agree here. Trying to create groups to get nice big numbers of CPU years I do agree with, but not for the money. By the way, aren't we forgetting something? I hope if anyone DOES win, they will give a reasonable portion to the people who wrote the very highly optimised software to do it, and the people who made sure they weren't re-checking an exponent that hadn't been checked a hundred times before Just out of interest, can I have someone demand I give them a share of the money / stop being in GIMPS if they really wanted to (not that I should think they would...) Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: PrimeNT
Hi! I'm sure this is asked time and time agai, but I'm new, so could someone point me in the right directio to install and maintain NTPrime over a large number of computers from an NT Server. Is it possible? if not, what is the best way to go about setting it up on a large number of machines (That have to be secure..)? Chris Jefferson, Girton College, Cambridge, [EMAIL PROTECTED] I have a proof that x^n+y^n=z^n never has integer solutions for n2. However, it won't fit into my signature file Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
