Mersenne Digest Thursday, October 21 1999 Volume 01 : Number 649 ---------------------------------------------------------------------- Date: Wed, 20 Oct 1999 21:37:38 +0100 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: The Mysterious Ways of Mersenne primes On 19 Oct 99, at 1:01, Steinar H. Gunderson wrote: > >you can compare this to something like the value of Pi, relation of the > >radius to the circumference, which human mind tries to instantly > >rationalize as a "real" number, demonstrated clearly by the actual attempt > >to _legalize_ Pi as 3. I thought the legal value of pi was 4, in Indiana. Actually the timber trade still calculates the volume of logs in an absurd way which implies that pi = 4. > >In fact, ask anyone what Pi is, and majority of > >them will instantly reply to you "3.14". In my experience, most of them will think of something sitting on a plate, probably stuffed with apple & destined to be served "schlagobers". > > >The square of two is another good > >example of how "irrational" and counter-intuitive mathemathics really is. > > You made a slight typo there -- you did mean the square _root_ of two, did > you? In base phi, 2^2 seems to be irrational ;-) > >To really claim that primes are either "random" or "non-random" > >in nature would give you a ranom chance of being right ;) Prime numbers clearly _aren't_ random in themselves, since they can be constructed in a wholly deterministic way. Their distribution may approximate to some defined trend with apparently random deviations from that trend, but that's a different assertion altogether. > > But then, define random! If I toss a (`fair') coin, I'd say that it's > random. However, a very quick viewer (or a computer) might see the moment > before the coin hits the ground (and stays there), what it will turn up > as. In other words, then the randomness is _not present_ at that time. > Now, if you go backwards, you can probably calculate (if you're VERY > quick -- remember this is all theoretical) this earlier on, perhaps all > the way back to when the coin leaves your hand. Who knows, perhaps even > further? :-) I used to know someone who could shuffle a deck of cards so accurately that he still knew what order they are in with about 95% accuracy, even after eight or nine runs through. Needless to say, it wasn't wise to play for money against him too often! The point about the coin tossing is that I would expect that it's _very_ rare for a human to have sufficiently accurate control to consciously remove the "randomness" from the act of tossing a fair coin. I wouldn't bet on the outcome of a coin tossed by a robot, though. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 20 Oct 1999 21:37:38 +0100 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: My prime is bigger than yours (Was: something else) On 20 Oct 99, at 0:39, Lucas Wiman wrote: > After a certain point, the LL test would become profitable again, if I understand > correctly. That crossover point is 2^31-1 for Mersenne numbers (It would certainly > be possible to prove the next mersenne prime be trial division, though the LL test > would be *much* faster). Quantum computer might raise this crossover point into the > billions of digits, but I believe that trial division would still be O(sqrt(n)), > (with a very small constant, but it still increases with the sqrt), whereas > the LL test is O(lg(n)) (it would also be sped up by quantum computing). > Unless I'm missing something about quantum computing (and I probably am). The thing which people tend to forget about quantum computing is that, before you can read the result you're interested in, you need to be able to read the state of the system. That implies that you need as much physical memory in the system as there are possible states in the quantum field you're computing. Though this doesn't rule out quantum computing as a potential major advance, the physical universe (or, at least, the fraction of the universe occupied by a computer's memory) does still restrict the size of the computation you can do in one "cycle". So the order of the algorithm still does matter - once the solution space is too big to fit into physical memory - which will happen rather easily with number theoretic (and combinatorial) calculations. > (please forgive any typos, this telnet app doesn't allow backspace charactors > on my shell account. Does anyone know of a good telnet app for windows?) > (I would think that it wouldn't be hard to make one, but apparently it is). Try QVT/Term. Unfortunately not freeware, but it does do a good job. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 20 Oct 1999 21:37:38 +0100 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: My prime is bigger than yours (Was: something else) On 19 Oct 99, at 20:17, [EMAIL PROTECTED] wrote: > [ ... snip ...] > (2) Among the Proths, the fact there are so many possible kinds of > candidates dilutes the effort, i.e. makes it vastly more time-consuming > to test all the candidates up below any reasonably-sized threshold. Ah, but I could write down an immensely long list of Proth numbers, all of which are _exactly_ 10 million digits long. If I work systematically through this list, sooner or later I'll strike gold. Meanwhile, if you're working through the Mersennes (even with a program four times as efficient), you might be unlucky and not find one until you're looking at numbers longer than 20 million digits. That evens the odds out a bit - by then, we'll be eliminating candidates at the same rate, but mine (being smaller) will be more likely to be prime than yours. Having said that, I agree that it's very likely that the biggest prime number known will be almost always be a Mersenne prime. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 20 Oct 1999 17:39:46 -0400 (EDT) From: Chip Lynch <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: The Mysterious Ways of Mersenne primes On Wed, 20 Oct 1999, Brian J. Beesley wrote: > I thought the legal value of pi was 4, in Indiana. Actually the > timber trade still calculates the volume of logs in an absurd way > which implies that pi = 4. I've seen this discussion before... if I recall, their estimation of PI was better for their purposes... the absurdity would be assuming that trees are perfect cylinders. ;-) > > But then, define random! If I toss a (`fair') coin, I'd say that it's > > random. However, a very quick viewer (or a computer) might see the moment > > before the coin hits the ground (and stays there), what it will turn up > > as. In other words, then the randomness is _not present_ at that time. > > Now, if you go backwards, you can probably calculate (if you're VERY > > quick -- remember this is all theoretical) this earlier on, perhaps all > > the way back to when the coin leaves your hand. Who knows, perhaps even > > further? :-) Ah, this has the ring of Schroedinger to it... The apparatus required to measure the flip of a coin that precisely early on may just have to interfere with the results. ?? Air density, air flow, speed, direction, and position in three dimensions... Brings a tear to one's eye. - ---Chip \\ ^ // (o o) ---oOO--(_)--OOo------------------------------------ | Chip Lynch | Computer Guru | | [EMAIL PROTECTED] | | | (703) 465-4176 (w) | (202) 362-7978 (h) | ---------------------------------------------------- _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 20 Oct 1999 17:59:57 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: The Mysterious Ways of Mersenne primes > >What else is pi then > >1+1/3+1/5+1/7+1/9 and so on ... ? > > Ermmm. Isn't that value closer to 2, actually? :-) > This value diverges to +infinity. > I thought (without checking) that the value of pi was something like: > > 4/1+4/3-4/5+4/7-4/9+4/11-4/13... > > At least it involved 4 in some way, and alternate pluses and minuses. > Anybody with a little more experience, please step in and clarify :-) Ok,here it is: pi/4=1-1/3+1/5-1/7+...+(-1)^k/(2*k+1)... this is based on the expansion of arctan into an infinite series, since arctan(1)=pi/4, the rest is history... - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 20 Oct 1999 18:07:16 -0400 (EDT) From: Darxus <[EMAIL PROTECTED]> Subject: Mersenne: estimating mersenne primes Okay, so I got my line of log base 2 of the exponents of the 1st 37 mersenne primes. I took those numbers & did a linear extrapolation, and did a 2^n to the resulting extrapolated numbers. I then went back and did my exponential extrapolation to the exponents of the 1st 37 primes. I was pretty surprised that the extrapolations for M38-M42 (all that I did) were *exactly* the same for both methods of extrapolations, based on 2 different fitted lines (one exponential based on the exponents, and one linear, based on the log base 2 of the exponents). If you care, M38-M42 came out as: #38 5014947.208 #39 7414614.414 #40 10962529.54 #41 16208132.64 #42 23963772.48 The (linear) line fitted to the log base 2 of the exponents was y = 0.5641x + 0.8206 with R2 = 0.9925 The (exponential) line fitted to the exponents was y = 1.7661e^(0.391x) with R2 = 0.9925 Hmm... R2's match. So they are of equal use. I still wanna know why extrapolating off of the number of digits, instead of the actual exponents, gave me a number closer to 6972593 (38th discovered mersenne prime). I dunno, coulda just been a coincidence. I'm trying to find out what exactly the lines are that are conjectured to fit this data.. like on http://www.utm.edu/research/primes/notes/faq/NextMersenne.html -- gives the slope, but I haven't found the offset. I want to see how reliably that can be used to predict these numbers (like, taking off the 37th, & predicting w/ 1-36). __________________________________________________________________ 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: Wed, 20 Oct 1999 15:14:25 -0700 From: Bob Margulies <[EMAIL PROTECTED]> Subject: Mersenne: Preda's slowly diverging series. > > Date: Wed, 20 Oct 1999 12:19:06 +0000 > From: "Steinar H . Gunderson" <[EMAIL PROTECTED]> > Subject: Re: Mersenne: Re: The Mysterious Ways of Mersenne primes > > On Wed, Oct 20, 1999 at 10:53:56AM +0200, Preda Mihailescu wrote: > >What else is pi then > >1+1/3+1/5+1/7+1/9 and so on ... ? > > Ermmm. Isn't that value closer to 2, actually? :-) > > Anybody with a little more experience, please step in and clarify :-) > > /* Steinar */ Actually, Steinar, it's a little closer to infinity. Preda's series diverges. He wrote that on one of those days when he hadn't washed his glasses. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 20 Oct 1999 18:37:13 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: estimating mersenne primes At 06:07 PM 10/20/99 -0400, Darxus wrote: >Okay, so I got my line of log base 2 of the exponents of the 1st 37 >mersenne primes. I took those numbers & did a linear extrapolation, and >did a 2^n to the resulting extrapolated numbers. > >I then went back and did my exponential extrapolation to the exponents of >the 1st 37 primes. > > >I was pretty surprised that the extrapolations for M38-M42 (all that I >did) were *exactly* the same for both methods of extrapolations, Your two methods are equivalent. > I still wanna know why extrapolating off of the number of digits, instead >of the actual exponents, gave me a number closer to 6972593 (38th >discovered mersenne prime). I dunno, coulda just been a coincidence. Probably so. If you use the number of digits in one method and the actual exponents in another, the predictions will differ slightly. One of them will be closer to the true value. +---------------------------------------------------------+ | 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: Wed, 20 Oct 1999 19:53:36 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Reciting Mersennes... <<Noone could call their full decimal name in a life time, allthough it is finite in length.>> If I remember correctly, someone once recited millions of digits of Pi from memory in three days. Heh. S.T.L. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 20 Oct 1999 20:02:29 -0400 (EDT) From: Darxus <[EMAIL PROTECTED]> Subject: Re: Mersenne: estimating mersenne primes On Wed, 20 Oct 1999, Jud McCranie wrote: > At 06:07 PM 10/20/99 -0400, Darxus wrote: > > >I was pretty surprised that the extrapolations for M38-M42 (all that I > >did) were *exactly* the same for both methods of extrapolations, > > Your two methods are equivalent. I know, but I thought the algorhythms for fitting linear & exponential lines would differ enough to result in at least a small difference in results. > > I still wanna know why extrapolating off of the number of digits, instead > >of the actual exponents, gave me a number closer to 6972593 (38th > >discovered mersenne prime). I dunno, coulda just been a coincidence. > > Probably so. If you use the number of digits in one method and the actual > exponents in another, the predictions will differ slightly. One of them > will be closer to the true value. Right. Using the actual exponents (instead of the # of digits) should, usually, yield more accurate results, right ? Of course, using the expanded prime would give the best accuracy, but I'm not prepaired to deal w/ numbers millions of digits long yet :) __________________________________________________________________ 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: Wed, 20 Oct 1999 20:49:40 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: estimating mersenne primes At 08:02 PM 10/20/99 -0400, Darxus wrote: >I know, but I thought the algorhythms for fitting linear & exponential >lines would differ enough to result in at least a small difference in >results. The method of fitting an exponential that I use basically takes the log of both sides and does a linear least squares on that. > Right. Using the actual exponents (instead of the # of digits) should, >usually, yield more accurate results, right ? It should. Of course, the number of digits is very close to 0.30103 * the exponent, so there shouldn't be much difference. +---------------------------------------------------------+ | 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: Wed, 20 Oct 1999 20:50:06 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Reciting Mersennes... > <<Noone could call their full decimal > name in a life time, allthough it is finite in length.>> > > If I remember correctly, someone once recited millions of digits of Pi from > memory in three days. Heh. You probably don't :). I believe the world record was around 40,000 digits. I find it highly unlikely that a human brain could hold that many digits. Even assuming reciting 3 digits per second, that would take 3.85 days, no sleep. I agree with Preda that these numbers are "abstract". They are completely unimaginable in terms of size, yet completely handlable thanks to mathematics. This is probably why people find them so fascinating. - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 20 Oct 1999 18:50:57 -0600 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Re: The Mysterious Ways of Mersenne primes > I thought the legal value of pi was 4, in Indiana. Actually the > timber trade still calculates the volume of logs in an absurd way > which implies that pi = 4. Maybe it has to do with the volume of stacked logs and the fact that there are still gaps between the logs. If only logs were hexagonal, we wouldn't have that problem! > > >In fact, ask anyone what Pi is, and majority of > > >them will instantly reply to you "3.14". > > In my experience, most of them will think of something sitting on a > plate, probably stuffed with apple & destined to be served > "schlagobers". Good point. In regards to my legal situation, I had lots of people asking me what a prime number was, and those folks aren't likely to understand pi any more either. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 20 Oct 1999 20:56:07 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: estimating mersenne primes > > >I was pretty surprised that the extrapolations for M38-M42 (all that I > > >did) were *exactly* the same for both methods of extrapolations, > > > > Your two methods are equivalent. > > I know, but I thought the algorhythms for fitting linear & exponential > lines would differ enough to result in at least a small difference in > results. I believe the first thing to do in finding an exponential curve fit is to take the log of the data, then apply a linear fit. (?) That is how I would do it anyway. This would produce identical results to the accuracy of the logarithm. - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 03:33:37 +0200 (CEST) From: Henrik Olsen <[EMAIL PROTECTED]> Subject: Re: Mersenne: Reciting Mersennes... On Wed, 20 Oct 1999 [EMAIL PROTECTED] wrote: > Date: Wed, 20 Oct 1999 19:53:36 EDT > From: [EMAIL PROTECTED] > To: [EMAIL PROTECTED] > Subject: Mersenne: Reciting Mersennes... > > <<Noone could call their full decimal > name in a life time, allthough it is finite in length.>> > > If I remember correctly, someone once recited millions of digits of Pi from > memory in three days. Heh. 4+ digits per second for three days? This fails even the simplest sanity check:) > > S.T.L. > _________________________________________________________________ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers > - -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ Animal behaviour is best described by the four F's Feed, Fight, Flee and Reproduce _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 07:39:59 +0200 From: Philippe Trottier <[EMAIL PROTECTED]> Subject: Mersenne: RE: PI and other periods HI, Again if you look from a human eye, we can see (imagine) a nearly possible period in that number ..., again that's human brain doing overtime... But again MAYBE, there is a real period to that number... and this number also start to have a considerable amount of known digits (We would have to share multiple generation just to say it) Philippe At 12:09 20.10.1999 +0100, you wrote: >Value of pi is the product of the infinite series ... > >pi = 4 (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 -1/15 + 1/17.........) > >Hope this helps.. > >Regards, >Ian McLoughlin, Chematek U.K. > >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 ------------------------------ Date: Thu, 21 Oct 1999 01:27:46 EDT From: [EMAIL PROTECTED] Subject: Mersenne: If I Remember Correctly... (hah) <<I believe the world record was around 40,000 digits.>> Right you are. My trusty 1994 Guiness Book of World Records puts it at exactly 40k, by Hideaki Tomoyori, in 17hr 21min (including 4hr 15min of breaks). S. "I'm so old, my memory's failing me already" L. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 01:40:18 +0200 From: Harald Tveit Alvestrand <[EMAIL PROTECTED]> Subject: Re: Mersenne: platform-independent savefile format (Was: ...) At 21:37 20.10.99 +0100, Brian J. Beesley wrote: >But I can write an entire array of any >size with one call from a high-level language, whereas writing it >byte by byte takes as many calls as there are bytes in the array. >Given that the system call is likely to involve a processor context >save & restore and a switch from user to kernel privelege & back >again, I rather suspect that the single call method may be more >efficient. Only if you use unbuffered I/O, which is highly unusual, and dead slow. On some C libraries, if you do byte-at-a-time output, you'll output a thousand bytes before you even get the overhead of doing a routine call - and almost always a whole data block (1K or 8K, depending) before you do a system call. Certain problems have been solved by others..... Harald A - -- Harald Tveit Alvestrand, Maxware, Norway [EMAIL PROTECTED] _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 09:23:52 +0200 From: Philippe Trottier <[EMAIL PROTECTED]> Subject: Mersenne: Getting back in maths ... HI, The way we see prime number is like this usually X is prime if only X and 1 can divide without modulo ("reste" in french) but what if we write it like this ? X is non prime if belong to this group P*Y P= all Prime # Y= all value from I* (Integer positive greater than 0) so all the rest should be prime ... now if someone could revers this, then we could have all prime numbers for us ... (I would like to express this in the real math symbols) Philippe _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 09:34:57 +0200 From: Philippe Trottier <[EMAIL PROTECTED]> Subject: Re: Mersenne: If I Remember Correctly... (hah) HI, In my old work we had to transfer between two media (paper and computer) many numbers of about 40 digits long every day... after a while we were reading them walking a 20 meter distance and telling it to the secretary without error (she was psyched because of that) ... the secret was singing them.. try it it will probably work if you are auditiv type. Philippe At 01:27 21.10.1999 EDT, [EMAIL PROTECTED] wrote: ><<I believe the world record was around 40,000 digits.>> > >Right you are. My trusty 1994 Guiness Book of World Records puts it at >exactly 40k, by Hideaki Tomoyori, in 17hr 21min (including 4hr 15min of >breaks). > >S. "I'm so old, my memory's failing me already" L. >_________________________________________________________________ >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, 21 Oct 1999 09:41:18 +0200 From: Philippe Trottier <[EMAIL PROTECTED]> Subject: Mersenne: Getting back in maths ... >> Y= all value from I* (Integer positive greater than 0) oups Y is >1 ... that's a better My mistake, Philippe _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 17:32:48 +1000 From: Simon Burge <[EMAIL PROTECTED]> Subject: Re: Mersenne: platform-independent savefile format (Was: ...) Harald Tveit Alvestrand wrote: > At 21:37 20.10.99 +0100, Brian J. Beesley wrote: > > >But I can write an entire array of any > >size with one call from a high-level language, whereas writing it > >byte by byte takes as many calls as there are bytes in the array. > >Given that the system call is likely to involve a processor context > >save & restore and a switch from user to kernel privelege & back > >again, I rather suspect that the single call method may be more > >efficient. > > Only if you use unbuffered I/O, which is highly unusual, and dead slow. > On some C libraries, if you do byte-at-a-time output, you'll output a > thousand bytes before you even get the overhead of doing a routine call - > and almost always a whole data block (1K or 8K, depending) before you do a > system call. You could even do the buffering yourself if you can spare an array of size n*sizeof(int). In pseudo-ish code: int *intarray; intarray = malloc(n * sizeof(int)); for (i = 0; i < n; i++) intarray[i] = (int)round(realarray[i]); write(output, intarray, n * sizeof(int)); free(intarray); Obviously you wouldn't malloc/free the array for each save, but you get the picture. One drawback is that you have n round() calls per save, but this probably doesn't add up to much in the grand scheme of things. Does the Windows and/or Mac C compilers have a unixish stdio library that has buffered I/O with things like fwrite() and friends? If so, this all becomes a moot point... As Harald said: > Certain problems have been solved by others Simon. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 12:09:02 +0000 From: "Steinar H . Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: RE: PI and other periods On Thu, Oct 21, 1999 at 07:39:59AM +0200, Philippe Trottier wrote: > Again if you look from a human eye, we can see (imagine) a nearly possible >period in that number ..., again that's human brain doing overtime... But >again MAYBE, there is a real period to that number... No. As far as I know, there is a proof saying that pi has no periods. /* Steinar */ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 07:33:39 -0700 From: "Joth Tupper" <[EMAIL PROTECTED]> Subject: Re: Mersenne: RE: PI and other periods Anyone remember Louisville numbers? The simplest I recall is .110001000000000000000001000000... = sum of 0.1^(n!) for n=1,2,3,... Many such numbers and constructions exist which share strange properties: 1) the digit patterns exist and are well-defined 2) the numbers, like pi, are transcendental [i.e., cannot be roots of any polynomial in one variable with integer coefficients]. [Recall that the rational number p/q is a root of the "polynomial" qX - p = 0.] Showing pi transcendental takes a lot of effort. Showing the Louiville numbers transcendental takes a lot less effort (but maybe a lot more memory than I seem to have!). Joth - ----- Original Message ----- From: Philippe Trottier <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, October 20, 1999 10:39 PM Subject: Mersenne: RE: PI and other periods > HI, > > Again if you look from a human eye, we can see (imagine) a nearly possible > period in that number ..., again that's human brain doing overtime... But > again MAYBE, there is a real period to that number... and this number also > start to have a considerable amount of known digits (We would have to share > multiple generation just to say it) > > Philippe > > At 12:09 20.10.1999 +0100, you wrote: > >Value of pi is the product of the infinite series ... > > > >pi = 4 (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 -1/15 + 1/17.........) > > > >Hope this helps.. > > > >Regards, > >Ian McLoughlin, Chematek U.K. > > > >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 > _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 16:55:25 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Mersenne: Re: If I Remember Correctly... (hah) On Thu, Oct 21, 1999 at 09:34:57AM +0200, Philippe Trottier wrote: >HI, > In my old work we had to transfer between two media (paper and computer) >many numbers of about 40 digits long every day... after a while we were >reading them walking a 20 meter distance and telling it to the secretary >without error (she was psyched because of that) ... the secret was singing >them.. try it it will probably work if you are auditiv type. But then (going back to pi), the record never said anything about the values being _memorized_? /* 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 ------------------------------ Date: Thu, 21 Oct 1999 11:14:06 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: RE: PI and other periods At 12:09 PM 10/21/99 +0000, Steinar H . Gunderson wrote: overtime... But > >again MAYBE, there is a real period to that number... > >No. > >As far as I know, there is a proof saying that pi has no periods. If pi was periodic it would be rational, but pi is irrational. +---------------------------------------------------------+ | 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, 21 Oct 1999 17:16:52 +0200 From: "Grieken, Paul van" <[EMAIL PROTECTED]> Subject: Mersenne: difference between LL and double check Why is there a difference in iteration time between the LL test and a double test. The double test took about 0.115sec and a LL test 0.254sec for the same amount of iterations. bye, Paul van Grieken Alcatel telecom Nederland Afd: TTAC Netwerk Elementen Tel: 070-3079353 email: [EMAIL PROTECTED] marklin collector _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 09:07:04 -0700 (PDT) From: poke <[EMAIL PROTECTED]> Subject: Re: Mersenne: difference between LL and double check The exponent you are using to LL test is probably significantly larger than the exponent your are using to double test. It's doing the same operation on both but on the LL test it is using a larger FFT (AFIK). Larger FFT requires more memory. More memory requires more time to juggle all of that data. - -Chuck On Thu, 21 Oct 1999, Grieken, Paul van wrote: > Why is there a difference in iteration time between the LL test and a > double test. > The double test took about 0.115sec and a LL test 0.254sec for the same > amount of iterations. > bye, > > Paul van Grieken > Alcatel telecom Nederland > Afd: TTAC Netwerk Elementen > Tel: 070-3079353 > email: [EMAIL PROTECTED] > > marklin collector > > _________________________________________________________________ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers > -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : WWW: http://www.silverlink.net/poke : : E-Mail: [EMAIL PROTECTED] : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : Ask Mike! Aviation's response to Dear : : Abby. http://www.avstarair.com : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 12:14:51 -0400 (EDT) From: Darxus <[EMAIL PROTECTED]> Subject: Re: Mersenne: RE: PI and other periods On Thu, 21 Oct 1999, Philippe Trottier wrote: > HI, > > Again if you look from a human eye, we can see (imagine) a nearly possible > period in that number ..., again that's human brain doing overtime... But > again MAYBE, there is a real period to that number... and this number also > start to have a considerable amount of known digits (We would have to share > multiple generation just to say it) I have some intrest in the number Pi -- I know 50-some digits, and have been looking into getting a few million digits hardbound. But while watching the movie Pi, it occurred to me that since the number Pi has *nothing* to do with base 10, there would be no repitition in the digits in any approximation of it in base 10 (or any other integer base, for that matter). The sequence of digits *should* be completely random, and it's goofy for people to try to look for patterns. I mean hey, if it's what you gotta do, go for it, but I think time would be better spent on other things. __________________________________________________________________ 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: Thu, 21 Oct 1999 19:14:17 +0200 From: Philippe Trottier <[EMAIL PROTECTED]> Subject: Re: Mersenne: RE: PI and other periods At 11:14 21.10.1999 -0400, Jud McCranie wrote: >At 12:09 PM 10/21/99 +0000, Steinar H . Gunderson wrote: >overtime... But >> >again MAYBE, there is a real period to that number... >> >>No. >> >>As far as I know, there is a proof saying that pi has no periods. > >If pi was periodic it would be rational, but pi is irrations Yes, I have learned math in French and its very far away. And my english start to get rusted in Finland. sorry for the confusion, I know that PI is irrational, but like the mersenne grouping , if you look at pi your brain might force you to see some period or bunch of digits that seems to be repeating... Philippe _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 21 Oct 1999 18:39:43 +0200 From: Preda Mihailescu <[EMAIL PROTECTED]> Subject: Re: Mersenne: RE: PI and other periods > > I have some intrest in the number Pi -- I know 50-some digits, and have > been looking into getting a few million digits hardbound. > > But while watching the movie Pi, it occurred to me that since the number > Pi has *nothing* to do with base 10, there would be no repitition in the > digits in any approximation of it in base 10 (or any other integer base, > for that matter). The sequence of digits *should* be completely random, Some digits of the development of pi in base 10 was used by Rivest in the hash mechanism MD2 as a random source .... Preda > and it's goofy for people to try to look for patterns. I mean hey, if > it's what you gotta do, go for it, but I think time would be better spent > on other things. > > __________________________________________________________________ > 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 ------------------------------ End of Mersenne Digest V1 #649 ******************************
