Mersenne Digest Sunday, February 13 2000 Volume 01 : Number 693 ---------------------------------------------------------------------- Date: Thu, 10 Feb 2000 23:33:21 -0500 From: Pierre Abbat <[EMAIL PROTECTED]> Subject: Re: Mersenne: "How Many Angels, How Many Pins?" Or PrimeNet's Assignment Strategy On Thu, 10 Feb 2000, Stefan Struiker wrote: >Team M: > >Is it better to have 10 pins at 500MHz with one or two angels dancing, >or one 5GHz behemoth looking for luck, given the way PrimeNet >assigns exponents? Only ten pins?? Even a 64K microcontroller has forty! phma _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 14:49:27 +0100 From: Paul Landon <[EMAIL PROTECTED]> Subject: Mersenne: Can I reserve the poaching thread? ;-) May I exclusively reserve the topic of "poaching"? >;-) I will release it in 60 days. (unless it is completed by someone else before then). Paul Landon _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 09:17:38 -0500 From: Pierre Abbat <[EMAIL PROTECTED]> Subject: Re: Mersenne: Can I reserve the poaching thread? ;-) On Fri, 11 Feb 2000, Paul Landon wrote: >May I exclusively reserve the topic of "poaching"? >;-) >I will release it in 60 days. (unless it is completed by >someone else before then). I think we should forge ahead. The hunter poached eggs and the blacksmith forged checks. phma _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 10:46:05 -0600 From: [EMAIL PROTECTED] Subject: Re: Mersenne: pi At 10:50 AM 2/9/00 -0500, Jeff Woods wrote: >You're bumping up against the Fundamental Theorem of Calculus here. Pi >DOES have a precisely defined value, but you cannot express it in decimal >form. You can express it as an infinite expansion, however. Infinite to me means never ending. A precisely defined value to me is a finite value. A never ending value is not finite. >Just as you can never get to the end of pi, though its value is known, you >can never PRECISELY note the area of a circle -- you can only express it >more and more accurately, depending on how accurate the value of PI you use is. I have a circle with a area of 5 square inches drawn on my pad. 5 inches is precise. Dan > _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 09:06:01 -0800 From: Paul Leyland <[EMAIL PROTECTED]> Subject: RE: Mersenne: pi > At 10:50 AM 2/9/00 -0500, Jeff Woods wrote: > >You're bumping up against the Fundamental Theorem of Calculus here. Pi > >DOES have a precisely defined value, but you cannot express it in decimal > >form. You can express it as an infinite expansion, however. > > Infinite to me means never ending. A precisely defined value to me is a > finite value. > A never ending value is not finite. Ah, OK. Enlightenment dawns. You're using the words in a way which is completely different from the mainstream mathematical usage. While you're entirely free to do so, please don't be surprised if people misunderstand you. The conventional meaning of "infinite", at least in mathematical usage, is something like "greater than any specified quantity, no matter how large". A quantity such as e (2.718281828459045...), pi (3.14159265358979...) or 1/7 (0.142857142857...) may each require an infinite number of digits to represent their values *exactly* in the decimal representation, but they are most assuredly not infinite themselves. To see this, note that not one of them is greater than 4. Paul _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 12:23:26 -0600 From: Jeremy Blosser <[EMAIL PROTECTED]> 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 == 1110000 + 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 ------------------------------ Date: Fri, 11 Feb 2000 13:14:28 -0600 From: "Kyle Evans" <[EMAIL PROTECTED]> Subject: RE: Mersenne: pi > I have a circle with a area of 5 square inches drawn on my pad. 5 inches is > precise. You do?? How did you do that? Did you set your compass so that the points were exactly sqrt (5/pi) inches apart? What you probably have really is a circle that approximates 5 sq inches enough to suit YOU. Kyle Evans. _________________________________________________________________ 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, 11 Feb 2000 13:35:36 -0600 From: David Underbakke <[EMAIL PROTECTED]> Subject: Re: Mersenne: Where's the flaw in my thinking? At 12:23 PM 2/11/00 -0600, you wrote: >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 == 1110000 + >1110 << 2 == 0111000 + >1110 << 1 == 0011100 + > == 11000100 which is 196 > In other words you are saying 14*14 = 14*(8 + 4 + 2) = 14*8 + 14*4 + 14*2 or in base 10 14*14 = 14*(10 + 4) = 14*10 + 14*4 Your logic appears correct, but it appears to be a computer base 2 implementation of what we do longhand in base 10. You are just taking advantage of the fact that multiplying by 2 is base 2 is a position shift, just like it is real easy in base 10 for us to take 1234 * 100 = 123400 _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 18:58:16 -0000 From: Alex Phillips <[EMAIL PROTECTED]> Subject: Mersenne: NTPrime and Prime9x simultaneously ? Dear All, Can anyone tell me if it is possible to have both the NT Prime service (under NT) and Prime95 (Under Win98), both installed in the same directory, and sharing files on a dual boot machine (NT for work and 98 for games). Because I can't seem to get the NT setup program to report on it's status. So I don't know if it's working ? Any Ideas ? Kind Regards, Alex Phillips. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 15:01:04 -0500 From: Pierre Abbat <[EMAIL PROTECTED]> Subject: Re: Mersenne: Where's the flaw in my thinking? >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 == 1110000 + >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? It is not stupid, it is in fact the normal way of squaring a small number. The reason humongous numbers are squared with FFT is that shift-and-add takes O(n^2) bit operations, where n is the number of bits in the number being squared, whereas FFT takes O(n*ln(n)*ln(ln(n))), which is a lot faster. The FFT of n floats takes log_2(n) stages, each of which runs through the array once which takes n operations; the ln(ln(n)) term (please correct me if this term is wrong) is because the more bits there are in the number you are squaring, the more precisely you need to compute the floats in the FFT. phma _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 14:26:06 -0600 From: [EMAIL PROTECTED] Subject: Re: Mersenne: pi At 11:39 AM 2/11/00 -0600, you wrote: > > >On Fri, 11 Feb 2000 [EMAIL PROTECTED] wrote: > >> Infinite to me means never ending. A precisely defined value to me is a >> finite value. > > Your definition of infinite is not correct. Just glanced at my Websters Dictionary. infinite: 1. lacking limits; endless. Endless and never ending seem synonymous to me. What dictionary are you using? >> A never ending value is not finite. > > Pi is greater than 3 and less than 4, therefore it is finite. > > Question to you. How much greater is pi to 3 or less than 4. If you cannot give me a answer then I will help you. Subtract 3 from your "finite" value of pi, or subtract your "finite" value of pi from 4. No approximations. Please give the answer in finite terms. Disclaimer: All email I have sent to the [EMAIL PROTECTED] list since 2-9-00 assumed that all on the list had read my post "Re: more info on pi" in which I explained that "I am not a mathematician." . However: that post seems to have disapeared. Then I changed the title to "Re: pi and 4" and re-sent again at 9:38 A.m. Central time 2-11-00 (this morning). cc'ing to [EMAIL PROTECTED] as per his offer to help in tracking it. This email will give all a very good understanding of my observations if it should ever be delivered. I am contemplating re-sending it again. I am not sure why? Remember; I am not a mathematician. It is a hobby. I am a cabinetmaker. And also, you know what happens when you assume? Well, perhaps, I have made one out of you and me. :) smile Good natured.. thats me. Really. Thanks for bearing up under my verse. Dan- _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 15:31:39 -0500 From: "Rick Pali" <[EMAIL PROTECTED]> Subject: RE: Mersenne: NTPrime and Prime9x simultaneously ? From: Alex Phillips > Can anyone tell me if it is possible to have both > the NT Prime service (under NT) and Prime95 (Under > Win98), both installed in the same directory, and > sharing files on a dual boot machine (NT for work > and 98 for games). That's a definite 'yes' Alex. Just make sure that you use the same versions of both programs and upgrade them at the same time when the time comes. I did that for a long time and both programs co-exist in the same directory and use the same data and ini files with no trouble at all. 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, 11 Feb 2000 14:34:23 -0600 From: [EMAIL PROTECTED] Subject: Re: Mersenne: Pi and Greek >Date: Fri, 11 Feb 2000 14:32:48 -0600 >To: "Vincent J. Mooney Jr." <[EMAIL PROTECTED]> >From: [EMAIL PROTECTED] >Subject: Re: Mersenne: Pi and Greek >In-Reply-To: <[EMAIL PROTECTED]> > >Disclaimer: I am not a mathematician. It is a hobby. I am a cabinetmaker. > >I was not necessarily speaking in a factual, but a Biblical, metaphysical manner. >Dan- > >At 10:56 PM 2/10/00 -0500, you wrote: >>Not so. Read up on why pi was selected, by whom and when. >> >>History of Pi by Peter Beckmann is one source. >> >>At 02:58 PM 2/10/00 -0600, Dan wrote: >>>I just found out that pi is the 16th letter of the Greek Alphabet. So this >>>is more evidence for the theory that the numbers 4 and 16 are important in >>>regards to pi and also to mersenne primes. >>>Dan >> > _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 14:40:50 -0600 From: [EMAIL PROTECTED] Subject: RE: Mersenne: pi At 01:14 PM 2/11/00 -0600, Kyle Evans wrote: > >> I have a circle with a area of 5 square inches drawn on my pad. 5 inches >is >> precise. > >You do?? How did you do that? Did you set your compass so that the points >were exactly sqrt (5/pi) inches apart? > >What you probably have really is a circle that approximates 5 sq inches >enough to suit YOU. > >Kyle Evans. > I just drew a circle. Then wrote inside the circle: "The area is precisely 5 square inches". Dan _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 15:42:03 EST From: [EMAIL PROTECTED] Subject: Mersenne: Re: irrational bases George Sassoon ([EMAIL PROTECTED]) wrote (regarding base-e arithmetic): >Maybe pi could be expressed exactly in such a >system. After all, e^(pi*i) = -1. Indeed, it follows that pi=-i*log(-1). But now one has the problem that one has defined one transcendental number in terms of another, and is thus no closer to writing pi in closed form in terms of whole numbers. I prefer to use base i, i.e. to no longer restrict oneself to the reals. In the complex (x,y) plane (i.e. every complex number x + i*y is viewed as the point (x,y) in a Cartesian-style coordinate system), one has that i = (0,1), which involves just integers. One also has the nifty identity i^i = -pi/2 i.e. the imaginary number i, raised to itself, gives - voila!- a real result involving pi in a simple way. (Proof: log(i^i) = i*log(i). But in complex polar form, i = e^(i*pi/2), so log(i) = i*pi/2, from which the result quickly follows.) Thus, pi=-2*i^i. >This led to a discussion as to whether or not it is possible to have a number >system based on a non-integer base. Your example with base e shows that indeed, one can. On the other hand, i (as in my example) is not an eligible base for a number system, since it has complex modulus one (i.e. one can raise i to any power one likes but never get off the unit circle.) But one can simply use, say, b = 2*i as the base, and then one has the identity pi = -2*(b/2)^(b/2). And now, at this point of our seemingly off-topic foray into the wonders of pi, e and the complex numbers, we suddenly are back on-topic. Here's why: Richard Crandall, who devised DWT algorithm at the heart of the Mersenne testing codes all of use in one form or another, refers to it, in words, as the "irrational-base discrete weighted transform" (IBDWT). I've quibbled with him about his choice of wording here, since it seems to cause much confusion among folks who have not actually implemented such an algorithm computationally. The source of the confusion is that, even though representing a prime-exponent Mersenne number 2^p-1 using N binary words is in some sense mathematically equivalent to using an irrational-base number system, in practice one uses a mixture of base 2^s and 2*2^s, where s = floor(p/N), i.e. is an integer. Thus, one doesn't actually use irrational bases anywhere in the actual algorithm. - -Ernst _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 15:40:24 -0500 From: Pierre Abbat <[EMAIL PROTECTED]> Subject: Re: Mersenne: NTPrime and Prime9x simultaneously ? On Fri, 11 Feb 2000, Alex Phillips wrote: >Dear All, > Can anyone tell me if it is possible to have both the NT Prime service >(under NT) and Prime95 (Under Win98), both installed in the same directory, >and sharing files on a dual boot machine (NT for work and 98 for games). My guess is yes, as long as the executables have different names. I have had mprime and Prime95 running in the same directory, one picking up where the other left off. > Because I can't seem to get the NT setup program to report on it's status. >So I don't know if it's working ? Look for a file with a name beginning with a p and ending in a bunch of numbers. It should be the last file when sorted by mtime. If the program is running, it will write to that file at intervals. phma _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 15:19:07 -0600 From: Jeremy Blosser <[EMAIL PROTECTED]> Subject: RE: Mersenne: pi I think the mistake you are making is that the *precision* of PI is infinite (never ending), but PI itself is not "infinity". 3.14159.....->ininite number of numbers Since it is 3.something we know it is > 3 and < 4. Take 1/3 for example. Its decimal value us 0.333333333....-> infinte # of 3's But it is < 3 and > 0. Just because the number of 3's in it is infinite does not mean it is "infinity". _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 16:45:21 -0500 From: Pierre Abbat <[EMAIL PROTECTED]> Subject: Fwd: Re: Mersenne: Re: Base e arithmetic >This led to a discussion as to whether or not it is possible to have a number >system based on a non-integer base. Maybe the great minds of GIMPS >can contribute to this. Base phi is easy to compute in. The similar Fibonacci representation counts the integers as follows: 0,1,10,100,101,1000,1001,1010,10000,10001,10010,10100,10101... No number has two 1-bits adjacent. Complex bases can also be used. i-1 is usable as a base, but i+1 is not, because 2 cannot be finitely represented. Gosper's representation uses seven digits, the sixth roots of 1 and 0, in base 2.5+sqrt(-3/4). phma _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 16:51:37 -0500 (EST) From: Chip Lynch <[EMAIL PROTECTED]> Subject: Re: Mersenne: pi > >> Infinite to me means never ending. A precisely defined value to me is a > >> finite value. > > > > Your definition of infinite is not correct. > > Just glanced at my Websters Dictionary. infinite: 1. lacking limits; endless. > Endless and never ending seem synonymous to me. > What dictionary are you using? > > >> A never ending value is not finite. > > > > Pi is greater than 3 and less than 4, therefore it is finite. I don't mind people using their own definitions of words; it's a shortcoming of mathematics that fundamentally needs improvement. However, once definitions are agreed upon, they must be at least internally consistent. If you take finite and infinite to be exact opposites, then we can't discuss the magnitude of pi (the fact that it is greater than three and less than four) to mean its "finite"ness, and it's length in decimal digits to mean its "infinite"ness. If we did, it could be both finite and infinite at the same time which is apocryful if those are opposites. Language, NOT Mathematics, is (precisely) why these discussions are problematic. If you've ever read original works by Archimedes, Euclid, and others who try to define mathematics with a common language, you understand the frustration. While I think the topic is stimulating and important, the Mersenne list probably isn't the best medium for it, unfortunately. Anyone recommend a few good links on the subject? (Pi, The Language of Mathematics, any of that) - ---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: Fri, 11 Feb 2000 16:55:59 -0600 From: [EMAIL PROTECTED] Subject: Re: Mersenne: pi At 04:51 PM 2/11/00 -0500, Chip Lynch wrote: >Language, NOT Mathematics, is (precisely) why these discussions are >problematic. If you've ever read original works by Archimedes, Euclid, >and others who try to define mathematics with a common language, you >understand the frustration. > >While I think the topic is stimulating and important, the Mersenne list >probably isn't the best medium for it, unfortunately. Anyone recommend a >few good links on the subject? (Pi, The Language of Mathematics, any of >that) > >---Chip > Disclaimer: I am not a mathematician. It is a hobby. I am a cabinetmaker. It is my understanding that this list is for the promotion of the search for mersenne primes. I may be a laymen when it comes to mathematics, but to my knowlege, this is not a requirement of the list. I believe that pi and mersenne prime numbers may have a relationship. I could be and might be wrong. I have tried three times now to put forth my observations on the mersenne list, but for some reason, my pi-4 posts are not being posted. All my other posts are posted on the list. The argument I propose, in this illusive post, is partly observation, facts, and a Biblical metaphysical outlook of the world. I have contributed to the GIMPS project and I am interested in furthering the search. I have and continue to learn much from the many posts. I enjoy logging on and reading them. I must admit that I have been bored by some of the long lists of prime95 primesearch programming and implementation posts about different computers etc. But I realise these play their part too. My opinion is that just because we have prime95 doesn't mean that a better way will not be found at some point. I may not be able to speak in "state of the art mathematical terms" but as I become more educated by participating in these discussions, I may be able to contribute something substantial. Perhaps not. These posts increase and hold my enthusiasm for math and mersennes. I hope this enthusiasm spreads. I would hope that your opinion is in the minority. It smacks of elitieism. I have admired the understanding people have shown me in replies to mine and other posts. I bear no grudge. I am just trying to stand on the shoulders of Giants. Dan- _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 17:08:06 -0600 From: [EMAIL PROTECTED] Subject: RE: Mersenne: pi Disclaimer: I am not a mathematician. It is a hobby. I am a cabinetmaker. At 03:19 PM 2/11/00 -0600, Jeremy Blosser wrote: >I think the mistake you are making is that the *precision* of PI is infinite >(never ending), but PI itself is not "infinity". > >3.14159.....->ininite number of numbers > >Since it is 3.something we know it is > 3 and < 4. > >Take 1/3 for example. > >Its decimal value us 0.333333333....-> infinte # of 3's > >But it is < 3 and > 0. Just because the number of 3's in it is infinite does >not mean it is "infinity". > 1/3 is a ratio. The decimal value .3333333......-> Circumference/diameter is a ratio. The decimal value 3.1415....-> !/3 of a 12 inch rope is 4 inch d/c of a 12 inch rope is ? (3.1415......->something * 12) Seems to me a ratio is needed for pi. Dan- _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 21:30:31 EST From: [EMAIL PROTECTED] Subject: Mersenne: Mersenne Digest Archives Is there an accessible archive of Mersenne Digests written in the past year+. I may be using an old web address. The latest archived issue that I can find is dated August 1998 (number 408). Irv Rosenfeld _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 11 Feb 2000 18:47:17 -0800 From: "John R Pierce" <[EMAIL PROTECTED]> Subject: Re: Mersenne: pi > Circumference/diameter is a ratio. The decimal value 3.1415....-> ... > Seems to me a ratio is needed for pi. you already gave it, the 'ratio of pi' is circumference / diameter There are NO two integers which can divide to create PI. Thats why PI is considered a 'irrational' number. It has no simple ratio. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 12 Feb 2000 02:23:07 -0500 (EST) From: Chip Lynch <[EMAIL PROTECTED]> Subject: Re: Mersenne: pi On Fri, 11 Feb 2000 [EMAIL PROTECTED] wrote: > It is my understanding that this list is for the promotion of the search > for mersenne primes. I may be a laymen when it comes to mathematics, but to > my knowlege, this is not a requirement of the list. ... > I would hope that your opinion is in the minority. It smacks of elitieism. Ouch. Sorry, there. Perhaps I misspoke; I was certainly misunderstood. I applaud anyone who is interested in math, and this mailing list is certainly full of such people. We often have good conversations here about all sorts of topics related to math, pi, infinities, whatever; last I recall we have Math PHD's and, well, cabinetmakers on the list and anyone in between. All welcome, and while it's not my place to do so, I encourage people to post; the archives are rich with posts on every topic and at every level of math. My apologies, anyway, if I sounded off the mark. I meant no ill will, and I believe I mentioned how enthusiastic I was about the thread. I just thought there may be better resources than here for certain discussions. Not so much that they don't belong here than that your questions may well be better answered somewhere else. I was, unbelievably, trying to be helpful. Anyway, sorry again. It shan't happen again. - ---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: Fri, 11 Feb 100 23:48:28 -0800 (PST) From: [EMAIL PROTECTED] (Gordon Irlam) Subject: Mersenne: Re: pi and 4 Aha! You're message was getting blocked because it was larger than 10k in size. This irestriction is intended to help prevent people from sending attachments to the list. Try splitting your message up into several separate parts and sending them to the list individually. gordoni (list admin) _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 12 Feb 2000 03:38:06 -0500 (EST) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: pi > > At 10:50 AM 2/9/00 -0500, Jeff Woods wrote: > > >You're bumping up against the Fundamental Theorem of Calculus here. Pi > > >DOES have a precisely defined value, but you cannot express it in decimal > > > >form. You can express it as an infinite expansion, however. Q: What does this have to do with fundamental theorem of calculus? The fundamental theorem equates anti-derivitives with area. This has more to do with the proof that there are numbers which cannot be expressed as the ratio of integers (i.e. irrational numbers) due originally to pythagroeus (SP), as well as the proof of the irrationality of pi (due to Newton, I think). The first is proved *long* before the fundamental theorem, and is in some ways more fundamental. - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 12 Feb 2000 10:16:10 +0100 (MET) From: [EMAIL PROTECTED] Subject: Mersenne: Summer research opportunities for undergraduates The deadlines are approaching for many summer research programs for undergraduates. See http://www.nsf.gov/mps/dms/reulist.htm for a partial list of programs in the USA. For a hardcopy, see p. 20 of the January/February 2000 SIAM News. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 12 Feb 2000 10:20:03 -0500 From: "Frank_A_L_I_N_Y" <[EMAIL PROTECTED]> Subject: 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 == 1110000 + >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 ------------------------------ Date: Sat, 12 Feb 2000 13:18:12 -0500 From: Sandy Harris <[EMAIL PROTECTED]> Subject: Re: Fwd: Re: Mersenne: Re: Base e arithmetic Pierre Abbat wrote: > Gosper's representation uses seven digits, the sixth roots of 1 and 0, > in base 2.5+sqrt(-3/4). Where do I find out more about that? _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 12 Feb 2000 18:34:17 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: pi On 11 Feb 00, at 16:51, Chip Lynch wrote: > While I think the topic is stimulating and important, the Mersenne list > probably isn't the best medium for it, unfortunately. Anyone recommend a > few good links on the subject? (Pi, The Language of Mathematics, any of > that) "The Joy of Pi" by David Blattner (1997) (published by Allen Lane, ISBN 0-713-99217-4) covers this in the sort of detail which has been discussed on this list - and some more - and includes the first million digits of the decimal expansion. I have no links with the author or the publisher except that a kind relative bought be a copy as a Christmas gift a couple of years ago. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 12 Feb 2000 11:13:24 -0800 From: Stefan Struiker <[EMAIL PROTECTED]> Subject: Re: Mersenne: Where's the flaw in my thinking? Jeremy Blosser wrote: > Okay, I was sitting there the other day thinking about a non-FFT squaring I can't find any flaw. I have lost track of any comments on this by the Prime95 coders, and am curious what they have to say. Could be a time-saved criterion, because the MOD is taken automatically as a by-product of the IFFT, and I have read there is a cache and SIMD tuning in the assembly code which is hailed as "the most efficient FFT ever coded for the Pentium series," or the like. Comments? Best Regards, Stefanovic _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 13 Feb 2000 00:54:30 -0500 From: [EMAIL PROTECTED] (Michael F. Yoder) Subject: Mersenne: multiprocessor FFT With respect to the argument that an N-processor machine can't do better than a factor of N speed improvement: the argument sounds airtight, but it's not always correct. Instances of superlinear speedup occur, and not merely as a theoretical possibility. While I was consulting at Compaq (previously Digital) a customer reported such a case (I believe they feared the numbers indicated the presence of a bug in their program or in the operating system). This was on a multiprocessor Alpha system. Hennessy & Patterson also noted an instance of it in their book (I'm referring to the 2nd edition). There was no bug: superlinear speedup can happen when each processor has its own cache, so the effective size of the cache grows as N is increased. It is most likely to occur in programs with good locality of reference where the problem size is considerably larger than the innermost local cache size. Knowing whether this really occurs for any particular processor will require actually making the experiment (though a really careful model could produce results which were likely to be accurate predictions). Achieving the effect also requires that the binding of processors to threads is sufficiently stable, either by explicit arrangement or by fortuitous properties of the OS and/or threads software. I have no time to recode the program myself, but the following is addressed to the author of MacGIMPS if he is reading this: I will soon have a 4-processor Daystar system bootable to BEOS, and I'm willing to have it serve as a guinea pig. Michael Yoder _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 13 Feb 2000 14:36:11 -0500 From: "St. Dee" <[EMAIL PROTECTED]> Subject: Mersenne: Curious Prime95 behavior? Hi, I'm running Prime95 on a machine with a PII-400 doing LL tests. The machine finished up an exponent in the 9,000,000 range (512K) and started doing an LL test on an exponent around 8280000. I expected the iteration times to speed up (384K or 448K, not sure which for the lower exponent), but they seem to have stayed the same. Even restarting Prime95 doesn't bring the iteration times down. Is this normal behavior? Thanks, Kel _________________________________________________________________ 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 #693 ******************************
