Mersenne Digest Sunday, February 27 2000 Volume 01 : Number 698 ---------------------------------------------------------------------- Date: Thu, 24 Feb 2000 20:04:21 EST From: [EMAIL PROTECTED] Subject: Mersenne: Re: Into the shadow of Death Valley rode the P100 John Pierce wrote: >I've retired that >processor now as its time per exponent is just too >high (besides its running linux now and I've never >bothered to figure out the linux client). I had a similar frustration with my trusty old P120 laptop once first-time LL tests exponents started getting around 7M and more. I adopted the "amphetamine drip" solution: removed the keyboard from the laptop, slapped an extra heatsink and 12VDC cooling fan on top of the alu. plate sitting atop the CPU, fiddled with the clock multiplier jumper settings, and since then it's been running stably at 180MHz. It isn't exactly pretty, but I've found a separate full-sized PS/2 keyboard easier to use anyway, and being able to do a 9M-range exponent in 3.5 months rather than 5 is nice. If i do need to go mobile (which is infrequent, it takes only a few minutes to restore the original configuration and turn the clock back down to 120MHz. Of course, it's running Win95, so I don't have to deal with the Linux client, although others seem to have done so without too much pain. - -Ernst _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 24 Feb 2000 17:57:49 -0800 From: "John R Pierce" <[EMAIL PROTECTED]> Subject: Mersenne: Re: Into the shadow of Death Valley rode the P100 > >I've retired that > >processor now as its time per exponent is just too > >high (besides its running linux now and I've never > >bothered to figure out the linux client). > > I had a similar frustration with my trusty old P120 laptop once > first-time LL tests exponents started getting around 7M and more. ... well, said former p100 now running linux is actually my home firewall/gateway/web/mail/ftp server so I'd rather not be running primexx on it anyways. - -jrp _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 24 Feb 2000 21:17:48 -0500 From: "Rick Pali" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Re: Into the shadow of Death Valley rode the P100 From: John R Pierce > well, said former p100 now running linux is actually > my home firewall/gateway/web/mail/ftp server so I'd > rather not be running primexx on it anyways. Just curious, but why? Would mprime compromise the security of that system in any way? Rick. - -+--- [EMAIL PROTECTED] http://www.alienshore.com/ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 25 Feb 2000 13:45:31 +1100 From: Simon Burge <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: Into the shadow of Death Valley rode the P100 "John R Pierce" wrote: > well, said former p100 now running linux is actually my home > firewall/gateway/web/mail/ftp server so I'd rather not be > running primexx on it anyways. If it's a low-traffic firewall there'll be truck loads of spare CPU cycles :-) Simon. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 24 Feb 2000 21:12:07 -0800 From: "John R Pierce" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: Into the shadow of Death Valley rode the P100 > > well, said former p100 now running linux is actually > > my home firewall/gateway/web/mail/ftp server so I'd > > rather not be running primexx on it anyways. > > Just curious, but why? Would mprime compromise the security of that system > in any way? its memory limited and I don't want any more swapping than absolutely necessary, my internet connect is a brisk 768k SDSL. Anyways, a pentium 100 is hardly gonna matter anymores, I'm cranking nearly 600 P90 CPU hours per day as it is on other much faster machines (mostly p2-400s and better) - -jrp _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 5 Mar 1999 20:07:26 +0100 From: Attila Megyeri <[EMAIL PROTECTED]> Subject: Mersenne: Specific exponent reservation Hi, Is it possible to reserve a specific exponent through Primenet? I would like to test an exponent that is not randomly assigned to me but don't want to loose the credit for it on my Primenet account. Thanks, Attila _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 25 Feb 2000 08:26:48 -0500 From: "Nayan Hajratwala" <[EMAIL PROTECTED]> Subject: Mersenne: (2^2^n) + 1 Hi Folks... can anyone help Ryan out? - -----Original Message----- From: RL Penter [mailto:[EMAIL PROTECTED]] Sent: Thursday, February 24, 2000 7:07 PM To: [EMAIL PROTECTED] Subject: Hey, my name is Ryan Penter and I am currently studying Maths at Loughborough University in England. I was wondering if you could help me with a problem; I need to find the largest known prime of the form: (2^2^n)+1 congratulations by the way on finding the largest Mersenne prime!!! any help would be amazing, thanx for your time, Ryan _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 25 Feb 2000 14:56:31 +0000 From: Alexander Kruppa <[EMAIL PROTECTED]> Subject: Re: Mersenne: (2^2^n) + 1 Nayan Hajratwala wrote: > > problem; I need to find the largest known prime of the form: > (2^2^n)+1 > congratulations by the way on finding the largest Mersenne prime!!! These are Fermat numbers, Fermat conjectured that all numbers of this form would be prime and proved it for F_0=3, F_1=5, F_2=17, F_3=257,F4=65537. However, not a single prime beyond those 5 has been found so far, all 4 < n <31, and many >31, are proved composite. It is commonly believed that indeed there is not a single Fermat prime except the first five. Find another one and you'll be famous! See http://www.perfsci.com/prizes.html for a Fermat factoring contest, www.mersenne.org/ecmg.htm for current ECM factoring limits on Fermat numbers, and http://vamri.xray.ufl.edu/proths/fermat.html for overall status of Fermat numbers (prime, genuine composites, some factors known, completely factored) Ciao, Alex. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 25 Feb 2000 14:58:36 +0000 From: Alexander Kruppa <[EMAIL PROTECTED]> Subject: Re: Mersenne: (2^2^n) + 1 >www.mersenne.org/ecmg.htm for current ECM factoring limits on Fermat numbers, Oops, should read: ecmf.htm Ciao, Alex. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 25 Feb 2000 15:23:17 +0100 From: Reto Keiser <[EMAIL PROTECTED]> Subject: Mersenne: p-1 and trial factoring hi all parallel use of p-1 and trial factoring - --------------------------------------- george suggested to run a p-1 test and trial factoring test before ll-testing an exponent in version 20. The possible factors are approximately logarithmic distributed, that means there are about as many 66, 67 and 68 bit factors in the same range. But the calculating time increases exponentially. So a computer spends about the same time in finding 68 bit factors than factoring up to 67 bits. So it makes sense to factor up that length, where P[finding a factor with n bits] = n-bit-factoring-time / ll-testtime. So testing up to 68 factors should not take more time than (1/34) of an ll-test. Most of the factors are found in the first part of the test. using the p-1 factoring we have the same situation: Using a B1 value of 50000 finds more factors than continuing from 50000 to 100000. Why can't we do first first the factorization up to n-2 bits (1/4) of the trial factoring time, then start the P-1 factoring up to 1/3 of the B1 value, after this, we can complete the trial factoring process and at the end we complete the P-1 (using the save file od intermediate file). (the parameters can be optimized) If one person runs the whole test, it is also possible that the computer performs the stage 2 during the night when the computer is not in use and Prime95 can use most of the memory. no 68 bit factors - ----------------- until now >210 factors are found for 10megadiginumbers and more than 280 exponents were factored up to 68 bits. Some (about 7) 67 digit factors were found but none with 68 bits. The value in the cleared exponent list is rounded to the next digit round(log2(factor)) so that only factors >67.5 bits are declared as 68 bits and factors from 66.5 up to 67.5 bits as 67 bit factors. But there should be about two or three 68 factors? organization of p-1 factoring - ----------------------------- A lot of factors of exponents between 10000 and 1000000 were found using the new P-1 method. Is there a database which contains which exponent were tested using which B1 and maybe a database od the save files? reto _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 25 Feb 2000 20:17:31 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: p-1 and trial factoring <color><param>0100,0100,0100</param>On 25 Feb 00, at 15:23, Reto Keiser wrote: <color><param>7F00,0000,0000</param>> Why can't we do first first the factorization up to n-2 bits (1/4) of the > trial factoring time, then start the P-1 factoring up to 1/3 of the B1 > value, after this, we can complete the trial factoring process and at the > end we complete the P-1 (using the save file od intermediate file). (the > parameters can be optimized) </color>This sounds fairly sensible. However, this entails splitting the factoring part into fairly small sub-assignments, which may cause unneccessary complications with the server. Also, trial factoring and P-1 are quite different from the point of view of system requirements - - trial factoring uses very little memory (in practice it runs almost entirely in the L1 cache) whereas P-1 is actually more of a memory hog than LL testing. So I suspect we want some bias towards early trial factoring rather than P-1. <color><param>7F00,0000,0000</param>> until now >210 factors are found for 10megadiginumbers and more than 280 > exponents were factored up to 68 bits. Some (about 7) 67 digit factors > were found but none with 68 bits. </color>This is likely to be a statistical anomoly. A sample size of 7 is a bit small to condemn the data as biased. <color><param>7F00,0000,0000</param>> A lot of factors of exponents between 10000 and 1000000 were found using > the new P-1 method. Is there a database which contains which exponent were > tested using which B1 and maybe a database od the save files? </color>Yes - I think we need this database - with or without savefiles, it's a waste of effort to inadvertently duplicate work done before. Since P-1 is deterministic (like trial factoring, but unlike Pollard's rho or ECM) you should get the same result every if you use the same limits on the same exponent. If anyone has any data to contribute, I'd be willing to assemble & publish the database. I also have adequate storage space on my anon ftp server for save files. <nofill> Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 25 Feb 2000 16:52:43 -0500 From: George Woltman <[EMAIL PROTECTED]> Subject: Re: Mersenne: p-1 and trial factoring Hi, At 03:23 PM 2/25/00 +0100, Reto Keiser wrote: >parallel use of p-1 and trial factoring >--------------------------------------- > >Why can't we do first first the factorization up to n-2 bits (1/4) of >the trial factoring time, then start the P-1 factoring up to 1/3 of the >B1 value, after this, we can complete the trial factoring process and at >the end we complete the P-1 (using the save file od intermediate file). >(the parameters can be optimized) I can't see any flaws in your reasoning, although it would be a bit unwieldy to implement. >no 68 bit factors >----------------- > >until now >210 factors are found for 10megadiginumbers and more than 280 >exponents were factored up to 68 bits. >Some (about 7) 67 digit factors were found but none with 68 bits. My database has: 33219661 73867482830512390441 33223387 83006905661336745889 33221387 123317319076102495049 33235409 128314644111933147703 33238463 131707491089550166169 33230671 139408728702078150121 33224957 193425473534465274127 That's 6 67-bit factors and 1 68-bit factor. Not the expected distribution, but nothing to be concerned about yet either. >organization of p-1 factoring >----------------------------- > >A lot of factors of exponents between 10000 and 1000000 were found using >the new P-1 method. Is there a database which contains which exponent >were tested using which B1 and maybe a database od the save files? All exponents from 20000 to 110000 were done with B1=1M and B2=40M Exponents from 110000 to 600000 (still in progress) were done with B1=100K and B2=4M. I still have the save files for exponents below 110000. I think Alex has the save files for the larger exponents. However, it must be pointed out that at some point you are better off switching to ECM rather than expanding the P-1 bounds. I'm not sure what that point is. Regards, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 25 Feb 2000 15:27:09 -0800 From: "Simon J Rubinstein-Salzedo" <[EMAIL PROTECTED]> Subject: Mersenne: Perfect numbers Can someone please outline a proof as to why (2^p-1)(2(p-1)) is a perfect number if 2^p-1 is prime? 2^6972593 - 1 is prime. e^(i*pi) + 1 = 0. This is the e-mail address of Simon Rubinstein-Salzedo. When you read this e-mail, Simon will probably be at a math contest. Don't forget to check Simon's website at http://www.albanyconsort.com/simon Thanks SJRS _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 26 Feb 2000 02:35:15 +0100 From: =?iso-8859-1?Q?Ignacio_Larrosa_Ca=F1estro?= <[EMAIL PROTECTED]> Subject: RE: Mersenne: Perfect numbers A number N is perfect if an only if sigma(N)=2N, where the sigma function is the sum of alldivisors of N, including 1 and N. The sigma function verify: i) sigma(p)=p+1, if p is prime ii) sigma(p^n)=1+p+p^2+...+p^n=(p^(n+1)-p)/(p-1), if p is prime iii) sigma(a�b)=sigma(a)�sigma(b), if gcd(a,b)=1 (it's a multiplicative function) Then, if N=2^(p-1)(2^p-1), with 2^p-1 prime 8a Mersenne prime), we have sigma(N)=sigma(2^(p-1)(2^p-1))=sigma(2^(p-1))sigma(2^p-1)=((2^p-1)/(2-1))(2^ p-1+1)= (2^p-1)2^p=2(2^(p-1))(2^p-1))=2N. There is a partial converse: If N is perfect AND EVEN, then N=2^(p-1)(2^p-1), with 2^p-1 prime. It is not proved the inexistence of perfect odd numbers, althought the minimum cote is very high. Un saludo, Ignacio Larrosa Ca�estro A Coru�a (Espa�a) [EMAIL PROTECTED] - ----- Original Message ----- From: Simon J Rubinstein-Salzedo <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Saturday, February 26, 2000 12:27 AM Subject: Mersenne: Perfect numbers > Can someone please outline a proof as to why (2^p-1)(2(p-1)) is a perfect > number if 2^p-1 is prime? > > 2^6972593 - 1 is prime. > e^(i*pi) + 1 = 0. > This is the e-mail address of Simon Rubinstein-Salzedo. > When you read this e-mail, Simon will probably be at a math contest. > Don't forget to check Simon's website at http://www.albanyconsort.com/simon > Thanks > SJRS > > _________________________________________________________________ > 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: Fri, 25 Feb 2000 21:01:59 EST From: [EMAIL PROTECTED] Subject: Mersenne: Prime95... what else:? Someone's sending mail to the list that makes its background appear red again (in AOL 3.0). Hrm. <<1)To be sure PRIME 95 saves it's work when I need to reboot Windoze 98, I bring PRIME 95 to the surface, hit Escape, and wait till the program resonds [Execution Halted]. Does re-booting from this point without closing PRIME95 save up-to-the-second work that has been done to a file which is continued next time PRIME 95 loads? >> Just shut down your computer normally. Win95 or Win98 sends a signal to all programs that a shutdown is occuring, and Prime95 automatically saves everything. Set it up as a Win95 service, no icon, and you can "set it and forget it". <<2) Given the same "P-90 Computer Years" as the next three Top Producers and comparing my COMPONENTS TESTED (third column below) why is it my computer turns up as such a slacker? ...This isn't golf. >> Pro'lly because you turn your computer off. An efficient person who works two hours a day will get less done than a slacker who works 18 hours a day. That is, unless the slacker is REALLY lazy, or non-Intel. :-P Heh heh. Stephan "Property of Bill and Andy" Lavavej _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 26 Feb 2000 00:33:49 EST From: "Nathan Russell" <[EMAIL PROTECTED]> Subject: Mersenne: A couple quick questions I just joined GIMPS (now 6% done testing a number with exponent just short of 10M if it makes a difference) and I have been looking into the theory behind Mersenne primes. Can anyone show me or at least point me to a webpage with the proof that the exponent of a Mersenne prime must be prime? How about a proof that the LL test works? I have had math through DiffEq I. It is intuitively obvious to me that every Mersenne number with even composite exponent will be found by the formula M(p) = 4M(p-2)+3. Since M(2)=3 is a multiple of 3, all these numbers will also be multiples, and therefore composite. However, I can't understand why this is true of numbers whose exponents have higher This is particularly easy to see when the numbers are written in binary. Since it is difficult to hand-compute the factors of Mersenne composites much above 1023, I cannot easily search for patterns in higher Mersenne numbers with composite exponent that has no factor of 2. A completely unrelated question: Why, on the PrimeNet stats summery page, are far more numbers listed as "finished LL" than as "available for doublecheck"? Does this simply mean that some numbers do not require doublechecking because they were turned in by a proven computer? Or have they been already double-checked and turned in since the page was last updated? ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 26 Feb 2000 10:33:35 +0100 From: "Hans-Martin Anger" <[EMAIL PROTECTED]> Subject: Re: Mersenne: A couple quick questions let m=2^(a*b)-1. then 2^a-1 is a divisor of m. example: 2^35-1=(2^5-1)*(2^30+2^25+2^20+2^15+2^10+2^5+1) general: 2^(a*b)-1 = (2^a-1)*(2^((b-1)*a)+2^((b-2)*a)+...+2^(1*a)+1) regards Martin - -----Urspr�ngliche Nachricht----- Von: Nathan Russell <[EMAIL PROTECTED]> An: <[EMAIL PROTECTED]> Gesendet: Samstag, 26. Februar 2000 06:33 Betreff: Mersenne: A couple quick questions > I just joined GIMPS (now 6% done testing a number with exponent just > short of 10M if it makes a difference) and I have been looking into the > theory behind Mersenne primes. > Can anyone show me or at least point me to a webpage with the proof that > the exponent of a Mersenne prime must be prime. >============ snip =================== _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 27 Feb 2000 02:55:21 -0800 From: Paul Leyland <[EMAIL PROTECTED]> Subject: RE: Mersenne: p-1 and trial factoring BJB wrote: > Yes - I think we need this database - with or without savefiles, > it's a waste of effort to inadvertently duplicate work done before. > Since P-1 is deterministic (like trial factoring, but unlike > Pollard's rho or ECM) you should get the same result every if you use > the same limits on the same exponent. If your implementations of rho and ECM are not deterministic, I suggest that you reimplement and/or get a working machine. Running rho with the same iterated function and starting value on the same exponent should give the same result every time. Running ecm with the same limits and the same curve on the same exponent should likewise give you the same result every time. Indeed, rerunning a new implementation with the same parameters as an old and (presumably) working implementation is one of the important ways of debugging and tuning the new version. The degree of freedom in choosing an elliptic curve for ECM is probably what you're hinting at. I'd suggest that a database of number of curves at run each B1/B2 limit is still useful. George keeps such a database for small exponents. Paul _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ End of Mersenne Digest V1 #698 ******************************
