Mersenne: Reference Machine
Anyone consider using a Cray as our benchmark? Also Anyone considering renaming prime95 considering it is 2002? Thanks Frank. _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: most powerful machine
http://www.msnbc.com/news/783667.asp?0na=x2202490w#BODY
Mersenne: m(127) by machine
Does anyone know which parts of the ll test are due to lucas and which to Lehmer? Specifically was the MODing at the end of the function known to Lucas, or was it an addition of Lehmer's. I am trying to design a ball machine that will prove m(127) prime using technology no more advanced than that which Lucas would have had. Type of machine I mean is found here http://www.database.com/~lemur/rb-rolling-ball.html I envision a machine with one track per place value. I would square 194 by adding 194 4 times, shifting adding 1940 9 times then adding 19400. When the number was large enough to MOD base N, I would append zeros to N until it was the largest without going over and subtract that number, then remove a zero and repeat. 8567 mod 2 subtract 2000 as many times as possible then do it for 200 the 20 then 2. The subtract 2 would be easy. Once the MOD was complete. I would send it back to the multiplying section, removing a ball from a counter to keep track of how many cycles I was going through. If the number is prime the final tray will be empty. if not, it will contain the final MOD. Thanks, Frank Anzalone
Mersenne: quicker multiplying ?
6 is -2 mod 8 6*6 = 36 36 = -4 mod 8 2^2 = 4 if the mod of the represented as a negative is much less than the positive, could we square the negative and save some time ? Thanks Frank Anzalone
Mersenne: Quicker Multiplying ?
6 is -2 mod 8 6*6 = 36 36 = -4 mod 8 2^2 = 4 if the mod of the represented as a negative is much less than the positive, could we square the negative and save some time ? Thanks Frank Anzalone
Re: Mersenne: 2000 - first calender year without a Mersenne
- Original Message - From: "Frank_A_L_I_N_Y" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Sunday, December 31, 2000 7:59 PM Subject: Re: Mersenne: 2000 - first calender year without a Mersenne > Sorry, I replied to Mr Russell before reading Mr Montgomery's reply. > Mr M said it much better than I. > > Reagards Frank > - Original Message - > From: <[EMAIL PROTECTED]> > To: <[EMAIL PROTECTED]> > Sent: Sunday, December 31, 2000 6:46 PM > Subject: Re: Mersenne: 2000 - first calender year without a Mersenne > > > > > > Nathan Russell observes: > > > Well, unless there is an announcement within the next few hours, 2000 > > > will be the first calender year in the history of GIMPS without a > > > Mersenne prime. > > > > > > Is the number of searchers, and the power of their hardware, increasing > > > enough to keep up with the increased runtimes and (slightly) decreased > > > chance of a given exponent being prime? Or can we expect only one prime > > > every several years, as was the case before the start of the GIMPS > > > effort? > > > > The chance that a given Mp is prime is O(1/log(Mp)) = O(1/p). > > The LL test for Mp needs O(p) iterations. > > The time per iteration (using an FFT) is about O(p*log(p)). > > So the estimated time per LL test is O(p^2 * log(p)) > > whereas the chance of success on one LL test is O(1/p). > > > > We need a few adjustments to the formula since (for example) > > the time to trial divide by primes < N is approximately > > O(log(p) /p) for fixed N. [We test O(N/p) divisors below N, > > with a cost of O(log(p)) per divisor.] This trial division > > time decreases with p, whereas LL time increases, which > > affects our strategy. > > > > Nonetheless, to test all O(2^b / b) primes with b bits, > > we estimate O(2^b / b) * O(2^(2b) * b) = O(8^b) operations > > with O(1) expected successes. Doing all 24-bit p's > > takes about eight times as long as doing all 23-bit p's. > > Even with more contributors and faster hardware, > > we soon get diminishing returns. > > > >Peter Montgomery > > > > > > _ > > 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: 2000 - first calender year without a Mersenne
- Original Message - From: "Frank_A_L_I_N_Y" <[EMAIL PROTECTED]> To: "Nathan Russell" <[EMAIL PROTECTED]> Sent: Sunday, December 31, 2000 7:53 PM Subject: Re: Mersenne: 2000 - first calender year without a Mersenne > Even with hardware twice as fast, any current two year exponent would still > take a year at that time. > I don't think the rate of double the speed every two years can hold out for > ever. > Even if the next hardware can get through these exponents faster, the longer > exponents would come down the pipe sooner, requiring the next hardware jump > that much sooner. > > Regards Frank > - Original Message - > From: "Nathan Russell" <[EMAIL PROTECTED]> > To: <[EMAIL PROTECTED]> > Sent: Sunday, December 31, 2000 7:01 PM > Subject: Mersenne: 2000 - first calender year without a Mersenne > > > > Well, unless there is an announcement within the next few hours, 2000 > > will be the first calender year in the history of GIMPS without a > > Mersenne prime. > > > > Is the number of searchers, and the power of their hardware, increasing > > enough to keep up with the increased runtimes and (slightly) decreased > > chance of a given exponent being prime? Or can we expect only one prime > > every several years, as was the case before the start of the GIMPS > > effort? > > > > This might be a good discussion, since the list is fairly quiet now. > > > > Nathan > > _ > > 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
We could let prime95 decide the next election . Give everybody a different prime number. Multiply the primes for candidate A together, likewise for B. If the factorization of the composite is not square free then we know that 1) Someone voted twice for the same candidate, and 2) We know who that is. If the 2 composites contain the same factor, then we know that 1) Someone voted for both candidates and 2) Again we know who. No lawsuits, no recounts, no chads. Frank
Re: Mersenne: Prime Time: L-L Test Doesn't Exist?
I am not sure I can trust the author of the article. If you look closely, he states that i is the square root of 1. i is the square root of -1 - Original Message - From: "Nathan Russell" <[EMAIL PROTECTED]> To: "xqrpa" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Sunday, November 12, 2000 8:54 PM Subject: Re: Mersenne: Prime Time: L-L Test Doesn't Exist? > To be fair, the quote says that it is difficult to determine the > primarlity of 'a given large number'. Only an infentesimal fraction of > arbitrary large numbers are Mersenne, or other special forms like > 'Proth' primes. > > Nathan > > > xqrpa wrote: > > > > To All: > > > > In case you missed the article "Prime Time" in New Scientist, the URL > > is: > > > > https://www.newscientist.com/features/features.jsp?id=ns226444 > > > > The author goes on to write: > > > > > > "Even so, it is mathematics that will gain the most. "Right now, when > > we tackle problems without knowing the truth of the Riemann > > hypothesis, it's as if we have a screwdriver," says Sarnak. "But when > > we have it, it'll be more like a bulldozer." For example, it should > > lead to an efficient way of deciding whether a given large number is > > prime. No existing algorithms designed to do this are guaranteed to > > terminate in a finite number of steps. " > > > > Well, the L-L Test seems to be just such an algorithm. > > > > Best Wishes, > > > > Stefanovic > > > > > > > > > > > > > _ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt
Re: Mersenne: Hello?
I think part of the problem is the current length of time for one LL test to complete. It would help if we could parallel process the mega virtual machine on one suspect at a time. Any math majors out there ? If Transmeta takesoff, anyone with an internet appliance or cell phone with web access could run prime95. www.transmeta.com - Original Message - From: <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, September 25, 2000 8:39 PM Subject: Mersenne: Hello? > Oh, Hi,.., so there is still someone here! > For a week there I thought the world had ended. I haven't recieved a > mersenne email for a week now. > > Well, happy hunting all. > > Dan > > > > _ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt
Mersenne: dupes
what's with all the duplicate messages ? is someone trying to pull a denial of service? _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: GIMPS in Science News
what aobut the fact that our tests will take longer and longer as the exponents get larger Frank -Original Message- From: Stefan Struiker <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Cc: James Escamilla <[EMAIL PROTECTED]>; [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: Thursday, March 30, 2000 1:48 PM Subject: Re: Mersenne: GIMPS in Science News >TeamM: > >I will be more detailed later, once I collect and refine my thoughts, but at >this point let me say that I think it is the group attracted to SETI, and the >Area 51, uh, "enthusiasts," who need some work, not the MPrime interface. > >More to come, > >Regards, >Stefanovic > >Geoffrey Faivre-Malloy wrote: > >> > The main reason Ive heard for people liking the Seti project is >> > because the screen saver looks pretty. >> >> I've been thinking about this for about a month now and I really think it's >> time for Prime95 to get a facelift. Now, I was thinking just along the >> lines of having a better GUI. I.E. Have a percentage complete bar instead >> of showing that in text. Maybe a log window for those who want it. Things >> like that. >> >> However, for those who wanted something pretty, we could probably do that >> without using up a lot of CPU time. >> >> At the very least though, IMHO, Prime95 needs a facelift. Comments? >> >> G-Man >> >> P.S. George - do you use the same codebase for win31 or is Prime95 really >> meant only for 32 bit operating systems? What compiler do you use? >> >> _ >> 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 _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: Smooth and hairy numbers
I would be more worried about a more exact definition of the word small. -Original Message- From: Robert G. Wilson v <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Cc: [EMAIL PROTECTED] <[EMAIL PROTECTED]>; [EMAIL PROTECTED] <[EMAIL PROTECTED]>; [EMAIL PROTECTED] <[EMAIL PROTECTED]>; [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: Monday, February 14, 2000 1:14 PM Subject: Re: Mersenne: Re: Smooth and hairy numbers >I would think that 2^727 -1 would qualify as hairy. > >[EMAIL PROTECTED] wrote: > >> If smooth numbers are ones whose prime factors are all small, >> what then are hairy numbers? Is there an official definition? >> >> "And Jacob said to Rebekah his mother, Behold, Esau my >> brother is a hairy man, and I am a smooth man:" (Gen. 27:11) >> >> George 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 _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Where's the flaw in my thinking?
This is not stupid. I am an electronic technician by training (not by trade it's a hobby now). Put number "a" into a shift register. Do the same with number "b". Set a b pointer to look at the right most bit of b loop start If b pointer points to a zero do nothing If b pointer points to a one add a to the accumulator If b pointer does not point to the left most bit shift b pointer and "a" left and go to loop start If b pointer points to the left most bit read the accumulator If a=3 and b=5 then a=11 b=101 first loop a=3 b will add 3 to the accumulator (because of the right hand one) second loop a=6 b will not add 6 to the accumulator (because of the zero) third loop a=12 b will add 12 to the accumulator (because of the left hand one) the accumulator has 3+12 which equals 15 which equals 3*5. You just took the specific case of a=b -Original Message- From: Jeremy Blosser <[EMAIL PROTECTED]> To: Mesenne Mailing List (E-mail) <[EMAIL PROTECTED]> Date: Friday, February 11, 2000 1:42 PM Subject: Mersenne: Where's the flaw in my thinking? >Okay, I was sitting there the other day thinking about a non-FFT squaring >algorithm... > >Say we have 14, which in binary is 1110... > >If we left shift this by the position of the 1, for each 1 in the binary >representation, and add them together, we should get the square... So to >square 14, we do this: >1110 << 3 == 111 + >1110 << 2 == 0111000 + >1110 << 1 == 0011100 + > == 11000100 which is 196 > >So for each squaring, we have x left shifts and adds, where x is no larger >that p. > >In any case... is this just me being dumb and missing that this is just a >stupid way of squaring a number? >_ >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: pi
>Can we say the same to the case of 10 divide by 3 , The result is 3 1/3 but >as a decimal way of writing you never end. Almost, but the difference is 10 / 3 is expressable as one number divided by another. to my kowledge there is no a and b where a/b=pi. Someone correct me if I am wrong. -Original Message- From: Grieken, Paul van <[EMAIL PROTECTED]> To: 'Jud McCranie' <[EMAIL PROTECTED]> Cc: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: Wednesday, February 09, 2000 11:53 AM Subject: RE: Mersenne: pi >I am not a math man but I follow this discussion. >Can we say the same to the case of 10 divide by 3 , The result is 3 1/3 but >as a decimal way of writing you never end. > >Maybe I just miss the whole thing, in that case I am sorry, and will >continue just reading this kind of topics. > >Bye, >Paul van Grieken > >> -Original Message- >> From: Jud McCranie [SMTP:[EMAIL PROTECTED]] >> Sent: Wednesday, February 09, 2000 3:22 PM >> To: [EMAIL PROTECTED] >> Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] >> Subject: Re: Mersenne: pi >> >> At 12:06 AM 2/9/00 -0600, [EMAIL PROTECTED] wrote: >> >> >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. >> >> No, pi is irrational, which means that the digits go on forever without >> repeating. >> >> >> >So, either the figure for pi is in error (not likely) or pi has a end. >> >> The calculated value of pi is never exact, since it is calculated to a >> finite precision. >> >> >> ++ >> | Jud McCranie | >> || >> | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| >> | 137*2^224879+1 is prime! (67,687 digits, 1/00)| >> ++ >> >> _ >> 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 _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: my disk needed a reload
I had to reload my hard drive. Lost my exponent, exe, worktodo file I was 2 weeks in Would like to "give back" the number so we don't waste 6 weeks of the 2 month time limit. How do I do this. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: P III took a 10 count
I Just fried my 550 p III. My exponent was due dec 26. Sending this e-mail via my 166mhz P I. P III will be fixed by 12/15/1999. Will this change my exponent run in any way. My news reader does not have a spell checker. I will have to use the spell checker that doubles as a fly swatter Why is the word dictionary in the dictionary? If you need the spelling, it's on the cover. If you need the definition, you wouldn't know were to go to get the word defined. eye epologize N ad Vance fore N E spelin Miss steaks. (8>)> _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: sorry
cant belive i spelled school sshool _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: questions
why is f(0) in an ll test = 4 also when i went to sshool (i'm 34) 7 mod 8 == 7 i have seen 7 mod 8 == -1 is -1 == 7 mod 8 which is more correct _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
