Mersenne Digest Friday, May 12 2000 Volume 01 : Number 734 ---------------------------------------------------------------------- Date: Wed, 10 May 2000 14:32:36 +0200 From: Yann Forget <[EMAIL PROTECTED]> Subject: Mersenne: Prime95 pour Win9x Hi, The new version of Prime95 pop up every time Windows is restarted. So the users of my network don't like it any more. :-( Is that could be changed ? Thanks. Yann - -- Ionix Services, les services r�seaux d'aujourd'hui http://www.ionix-services.com/ Tel 04 38 12 38 90 Fax 04 38 12 38 94 _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 10 May 2000 10:06:11 -0400 From: George Woltman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Prime95 pour Win9x Hi Yann, At 02:32 PM 5/10/00 +0200, Yann Forget wrote: >The new version of Prime95 pop up >every time Windows is restarted. >So the users of my network don't >like it any more. :-( >Is that could be changed ? My guess is that you have prime95 set to run as a Windows 95/98 Service. If you used p95setup.exe to install version 20 and it created a shortcut to prime95 in the startup folder then you would get the symptoms you are describing. The fix is simple, remove the shortcut from the startup folder. The p95setup program is supposed to detect this situation and not create the shortcut. Let me know if this is the cause and I will track the bug down and fix it. Best regards, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 10 May 2000 14:37:12 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Prime95 pour Win9x On 10 May 00, at 14:32, Yann Forget wrote: > The new version of Prime95 pop up > every time Windows is restarted. > So the users of my network don't > like it any more. :-( > Is that could be changed ? Either install using Prime95.zip (as it used to be done - the file is updated) or remove the shortcut to Prime95 from Startup folder after running P95Setup.exe. I think it's irritating to add shortcuts to the startup folder without asking the user. 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, 10 May 2000 11:08:59 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Digest #732? Was there an issue of the digest numbered 732? (My inbox jumps from 731 to 733, but I don't think I deleted it or ever got it.) If there wasn't, was it because of the wacky chaos which occurred in the mailing list? Phil Brady _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 10 May 2000 09:48:44 -0600 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Prime95 pour Win9x >> The new version of Prime95 pop up >> every time Windows is restarted. >> So the users of my network don't >> like it any more. :-( >> Is that could be changed ? >Either install using Prime95.zip (as it used to be done - the file is >updated) or remove the shortcut to Prime95 from Startup folder after >running P95Setup.exe. > >I think it's irritating to add shortcuts to the startup folder >without asking the user. So the setup program does that for you irregardless of whether it was setup previously to start as a Win95 "service"? Bummer... I forgot who wrote that setup program, but basically you should have it look in the "run" key in the registry to see if it's already in there before you go and add it to the startup group. I've been tempted to write a better looking installer for Prime95 and also do one for NTPrime as well, but I just haven't gotten around to it yet. Just using either SMS Installer or WISE 8 (basically the same darn thing). Would anyone out there appreciate an automated install of the NTPrime thing? Aaron _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 10 May 2000 22:11:33 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Re: Roundoff errors I wrote: > Especially for large runlengths (and after the first few hundred iterations > or so), rounding errors tend to be randomly distributed in an approximately > Gaussian fashion, Brian Beesley wrote: > I know perfectly well what you mean, but these two statements tend to > contradict each other. Gaussian distributions are continuous & > smooth, we have instead a discrete distribution whose gaps tend to > increase with size. I added some code to the Mlucas 2.7a source (my personal copy, not the version on my website) to better-quantify this. Since fractional errors are defined in the interval [0, 0.5], I subdivided this interval into 64 equal-sized bins and counted how many fractional parts fell into each bin on each iteration. Then I ran around a hundred iterations of M1325011 using an FFT length of 64K, i.e. an exponent close to the practical roundoff limit for that FFT length on an IEEE64-compliant machine. Up to iteration 13, all fractional errors fell into bin 0, i.e. were in [0, 1/128). After that, things looked as follows - In the table below, the vertical placement corresponds to bins 0 through 64 (bin 64 corresponds to the special case of an error = 0.5), and the table entries denote the number of fractional errors in the corresponding bin: iteration bin 14 15 16 17 18 19 20 21 ... 44 - --- ----- ----- ----- ----- ----- ----- ----- ----- ... ----- 0 65530 65457 64930 61600 44951 23245 9680 7781 7555 1 6 76 555 3332 15541 19547 10589 7371 7158 2 0 3 44 475 3573 11771 12090 10433 10356 3 0 0 7 96 972 5620 7639 5971 5961 4 0 0 0 30 348 3089 8518 9169 9353 5 0 0 0 3 84 1065 4321 4033 4042 6 0 0 0 0 55 740 4751 5804 5841 7 0 0 0 0 5 164 1923 2462 2489 8 0 0 0 0 6 199 2708 4603 4730 9 0 0 0 0 0 32 743 1262 1290 10 0 0 0 0 1 48 1149 2203 2185 11 0 0 0 0 0 2 266 594 616 12 0 0 0 0 0 10 672 1803 1890 13 0 0 0 0 0 0 62 277 259 14 0 0 0 0 0 3 206 591 606 15 0 0 0 0 0 0 21 110 118 16 0 0 0 0 0 1 137 614 636 17 0 0 0 0 0 0 3 43 49 18 0 0 0 0 0 0 23 146 121 19 0 0 0 0 0 0 0 19 22 20 0 0 0 0 0 0 29 164 162 21 0 0 0 0 0 0 0 5 6 22 0 0 0 0 0 0 2 14 20 23 0 0 0 0 0 0 0 1 2 24 0 0 0 0 0 0 4 49 51 25 0 0 0 0 0 0 0 2 0 26 0 0 0 0 0 0 0 4 3 27 0 0 0 0 0 0 0 1 0 28 0 0 0 0 0 0 0 6 11 29 0 0 0 0 0 0 0 0 0 30 0 0 0 0 0 0 0 0 0 31 0 0 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 1 4 33 0 0 0 0 0 0 0 0 0 34 0 0 0 0 0 0 0 0 0 35 0 0 0 0 0 0 0 0 0 36 0 0 0 0 0 0 0 0 0 37 0 0 0 0 0 0 0 0 0 38 0 0 0 0 0 0 0 0 0 39 0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 41 0 0 0 0 0 0 0 0 0 42 0 0 0 0 0 0 0 0 0 43 0 0 0 0 0 0 0 0 0 44 0 0 0 0 0 0 0 0 0 45 0 0 0 0 0 0 0 0 0 46 0 0 0 0 0 0 0 0 0 47 0 0 0 0 0 0 0 0 0 48 0 0 0 0 0 0 0 0 0 49 0 0 0 0 0 0 0 0 0 50 0 0 0 0 0 0 0 0 0 51 0 0 0 0 0 0 0 0 0 52 0 0 0 0 0 0 0 0 0 53 0 0 0 0 0 0 0 0 0 54 0 0 0 0 0 0 0 0 0 55 0 0 0 0 0 0 0 0 0 56 0 0 0 0 0 0 0 0 0 57 0 0 0 0 0 0 0 0 0 58 0 0 0 0 0 0 0 0 0 59 0 0 0 0 0 0 0 0 0 60 0 0 0 0 0 0 0 0 0 61 0 0 0 0 0 0 0 0 0 62 0 0 0 0 0 0 0 0 0 63 0 0 0 0 0 0 0 0 0 64 0 0 0 0 0 0 0 0 0 I snipped iterations 22-43 because they are very similar to 21 and 44. There are several interesting trends visible here. Although the overall trend is approximately Gaussian, there is clearly a strong preference for even- numbered bins, and an even stronger preference for power-of-2-numbered bins. Definitely worthy of further study, but I've got to get some dinner now. Cheers, - -Ernst _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 11 May 2000 15:24:08 -0300 (EST) From: ENIO SCHUTT JUNIOR <[EMAIL PROTECTED]> Subject: Mersenne: New Options Hi. I have seen people talking about overclocking and so on. I guess that prime95 really stresses a lot any kind of system. What about if in a new version there would be an option to set the maximum percentual of the processor's usage? or maybe some time limit per day? or even a time limit in which prime95 reaches 100%, then getting to a lower percentual... lets say 75%. If there is any way to do it, I think it should be interes- ting. And somehow, more reliable. What do you from the list think about? Regards, Enio _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 11 May 2000 22:20:39 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: New Options On 11 May 00, at 15:24, ENIO SCHUTT JUNIOR wrote: > I have seen people talking about overclocking and so on. > I guess that prime95 really stresses a lot any kind of system. Yes! Though a correctly assembled system with all parts running at their rated voltage, speed & temperature should not be _over_stressed by Prime95, or for that matter by any other application. > What about if in a new version there would be an option to > set the maximum percentual of the processor's usage? or maybe > some time limit per day? The first idea cannot be implemented in any application running under a sane operating system - or even many insane OSes! - though you could probably get an approximate 50% duty cycle by running a "do nothing" compute loop avoiding the FPU as a seperate process at the same priority as Prime95 - or setting the priority of Prime95 to 0, so that the system idle process steals cycles from it. The point is that an operating system must always allocate all the CPU cycles available (except those used to do make the process scheduling decisions) to some process or other. The second idea is already possible - but the problem is that a system with a cache or FPU overheating due to overclocking (or a cooling problem like a broken fan) is probably going to take only seconds to get dangerously warm. > or even a time limit in which prime95 > reaches 100%, then getting to a lower percentual... lets say > 75%. You _may_ be able to set this in your system BIOS. Enable CPU overheat warning, set the overheat duty cycle appropriately (the default setting is usually 50% or 62.5%) and then set the CPU overheat detection temperature so that your system normally runs believing it's overheating. Not all BIOSes support this; not all motherboards have the neccessary temperature sensors fitted, and some that do will insist on sounding a warning (via the system speaker) if an overheat condition is detected. But the real problem with all these methods is that you are throwing processor cycles away trying to keep the damn thing cool. Why not simply reduce or remove the overclocking instead? The point is that if the stress imposed by Prime95 is too much for the system (in an overclocked state), then almost certainly some combination of other programs you run will also be too much. If you really _must_ keep your overclocking, try fitting an extra case fan, and/or arrange ducting so that the processor fan receives cool air from outside the system case instead of recycling warm air already "trapped" inside. These tactics could be enough to make Prime95 run reliably whilst retaining the high clock speed. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 12 May 2000 03:25:54 +0200 From: "Shot" <[EMAIL PROTECTED]> Subject: Mersenne: P-1 memory vs vacation time I just downloaded Prime95 v20.4.1 and I have two questions: 1) Where can I find some mathematical info on P-1 factoring (preferably everything, "for dummies")? 2) When I use Prime95's Vacation or Holiday feature, does the program assume that the vacation time should be treated as nighttime for the purpose of P-1 factoring? I'd suggest additional option in the Vacation feature - a checkbox allowing Prime95 treat that free time as nighttime. My reasoning: I can see two possible ways - the abandoned computer is used by some other person (not connected to GIMPS) or the computer is unused. There have to be an option to let that other person use the computer as normal (thus treating the vacation time normally), but it would be a loss if the computer was totally unused and couldn't work with all of the nighttime memory. BTW: George, I think many people (myself included) surf the web using 800x600 resolution - new Mersenne page's menu is a little to wide for that setting. Not a big issue, but a little annoying. Cheers, - -- Shot __ c"? [EMAIL PROTECTED] -- http://www.shot.prv.pl/ -- [EMAIL PROTECTED] `-' 12.05. na stronie nowe cytaty ---------------------------------------------------------------- On a faucet in a Finnish restroom: To stop the drip, turn cock to right. ---------------------------------------------------------------- _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 11 May 2000 18:27:55 -0700 From: "John R Pierce" <[EMAIL PROTECTED]> Subject: Re: Mersenne: New Options > The first idea cannot be implemented in any application running under > a sane operating system - or even many insane OSes! - though you > could probably get an approximate 50% duty cycle by running a "do > nothing" compute loop avoiding the FPU as a seperate process at the > same priority as Prime95 - or setting the priority of Prime95 to 0, > so that the system idle process steals cycles from it. The point is > that an operating system must always allocate all the CPU cycles > available (except those used to do make the process scheduling > decisions) to some process or other. sure it could. (I'm *not* suggesting this is a good idea or anything, but for arguments sake...). Just put frequent calls to the OS dependent 'yield' function. To use even less CPU time, intersperse event timer waits in the code. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Thu, 11 May 2000 21:40:21 EDT From: [EMAIL PROTECTED] Subject: Mersenne: To crazy to be true, but it is.... This is totally weird, and I think I messed up in getting this, but it is true. Could someone with a lot of time and a lot of patience and a big calculator check this? Thanks. 1 = 1/(2�- 1) + 1/(2� - 1) + 1/(2^4 - 1) + 1/(2^5 - 1) + ... + 1/(3� - 1) + 1/(3� - 1) + 1/(3^4 - 1) + ... + 1/(5� - 1) + 1/(5� - 1) + 1/(5^4 - 1) + ... In other words, if set x contains integral powers, (2�, 3�, 2�, etc....) and x' is the set of integers minus set x. Then this says: 1 = sum(n=2 to n=infinity (sum( i=1 to i = infinity, 1/((x'i)^n - 1)))) please confirm!! this is a side formula I found, while working with primes. Hope it is not to off topic. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 12 May 2000 00:52:32 -0400 From: "Fred W. Helenius" <[EMAIL PROTECTED]> Subject: Mersenne: Re: To crazy to be true, but it is.... At 09:40 PM 5/11/00 EDT, [EMAIL PROTECTED] wrote: >This is totally weird, and I think I messed up in getting this, but it is >true. Could someone with a lot of time and a lot of patience and a big >calculator check this? You can't prove it with a calculator; you need to do some algebra. >1 = 1/(2^2- 1) + 1/(2^3 - 1) + 1/(2^4 - 1) + 1/(2^5 - 1) + ... + 1/(3^2 - 1) + >1/(3^3 - 1) + 1/(3^4 - 1) + ... + 1/(5^2 - 1) + 1/(5^3 - 1) + 1/(5^4 - 1) + ... >In other words, if set x contains integral powers, (2^3, 3^3, 2^2, etc....) and >x' is the set of integers minus set x. Then this says: >1 = sum(n=2 to n=infinity (sum( i=1 to i = infinity, 1/((x'i)^n - 1)))) [I've replaced the non-ASCII characters used for exponents] I think you simply mean 1 = sum 1/n, where n is in x'. This result is a theorem due to a man better known for a conjecture: Christian Goldbach. The proof that follows is based on one given in _Concrete Mathematics_, by Graham, Knuth & Patashnik, where Goldbach's theorem is exercise 2.53. Let P be the set of perfect powers greater than 1, i.e., P = {m^n | m,n > 1}. Let Q be the integers greater than 1 not in P; Q = {n>1 | n not in P}. The crucial fact we need is that every element n of P can be expressed uniquely in the form q^k, where q is in Q and k > 1, and, conversely, every such q^k is in P. (If you write n as a product of prime powers p_i^a_i, then k is the GCD of the a_i.) The sum in question is Sum 1/(m - 1). m in P Expanding each term as a geometric series yields Sum m^(-n). m in P n >= 1 Separating out the terms with n = 1, we get Sum m^(-n) + Sum 1/m. m in P m in P n >= 2 But, from the fact above, this is the same as Sum m^(-n) + Sum m^(-n). m in P m in Q n >= 2 n >= 2 Combining the sums again, we have Sum m^(-n). m >= 2 n >= 2 The terms involving a fixed m are a geometric series, so this is Sum 1/(m*(m-1)). m >= 2 Splitting into partial fractions yields a telescoping series: Sum (1/(m-1) - 1/m) = (1 - 1/2) + (1/2 - 1/3) + ... = 1. m >= 2 - -- Fred W. Helenius <[EMAIL PROTECTED]> _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 12 May 2000 01:18:26 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Re: To crazy to be true, but it is.... I've been getting a lot of mail from people who didn't get the first message, so, to clarify: 1 = 1/(2�- 1) + 1/(2� - 1) + 1/(2^4 - 1) + ... + 1/(3� - 1) + 1/(3� - 1) + 1/(3^4 - 1) + (skip 4 = 2�) ... + 1/(5� - 1) + 1/(5� - 1) + 1/(5^4 - 1) + ... + 1/(6� - 1) + 1/(6� - 1) + 1/(6^4 - 1) + ... + 1/(7� - 1) + 1/(7� - 1) + 1/(7^4 - 1) + ... (skip 8 = 2�), (skip 9 = 3�) + 1/(10� - 1) + 1/(10� - 1) + 1/(10^4 - 1) + ... + ditto 11, 12, 13, 14, 15, (skip 16 = 2^4, 4�), 17, 18, 19, 20, 21, 22, 23, 24, (skip 25 = 5�), 26, (skip 27 = 3�), 28, 29, etc... Side Note: (This avoids dupes, but this is not the reason I started this.) I hope this gets the point across. I'll explain how I got it later. PS How did you get 1.3+, McCraine? What did you do? _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 12 May 2000 00:57:00 -0700 (PDT) From: [EMAIL PROTECTED] (Gordon Irlam) Subject: Re: Mersenne: Digest #732? > Was there an issue of the digest numbered 732? (My inbox jumps from 731 to > 733, but I don't think I deleted it or ever got it.) If there wasn't, was it > because of the wacky chaos which occurred in the mailing list? Digest #732 mainly consists of repeat postings. When the list blew up I nuked all the outgoing mersenne related mail, including the digest. If you really want #732, you can temporarily find it, and all other issues of the Mersenne digest at: http://www.base.com/mersenne Note, this is a temporary not a permanent back issue archive. It will be deleted May 19th. gordon _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 12 May 2000 04:15:12 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Primorials perfect, personally, for perfect prime powers I gave this one to George, he gave a pretty good explanation, but I wanted to see what everyone else thought. I bet He's right, though >primes of the form (s# + 1), (s! +1 ), (k*(s!) +1) or (k*(s#)+1) should make >good exponents, at least in theory. 2^p -1 can be turned into 2^p -2 +1, and >that turns into 2(2^(p-1)-1) + 1 if p is one of the forms above, then this >turns into 2(2^s# -1)+1, 2(2^s!-1)+1 , 2(2^k*(s#)-1)+1 or 2(2^k*(s!)-1) +1. >the 2^s#-1, and related forms must have a lot of factors, like (2^2)-1 , >(2^3)-1 , etc. These are multiplied together, and one is added. This >virtually forms the p# + 1, Euclid formula for showing an infinite number of >primes. I hope you haven't heard this before. If you did tell me. I wonder >who would have discovered this. Probably a great prime hunter of the past. His Response: I'm not really sure how this helps. Factors of Mersenne numbers must be of the form 2kp+1. Apparently, you are looking for special forms of p where more of the 2kp+1 values are composite. An interesting idea, I'll think about it some. Remember, I'm more programmer than mathematician. My Response: >Every Mersenne prime is of the form (2^n -1). If n is composite, with >factors, t and s, the (2^n - 1) is 0 mod (2^t - 1), and (2^s - 1). >So, if n has a lot of factors, like the primorals or the factorials, it >should be divisible by a lot of numbers. If we multiply this by 2 we still >have a number full of factors. If we add 1 to this then the resulting number >is 1 mod all those factors. So, that new number is relatively prime to all >those factors, and so has a good chance of being prime. His response: Your analysis is good as far as it goes. However, we already know that Mersenne numbers have factors of the form 2kp+1. Thus, the factors you eliminated may already have been eliminated by the 2kp + 1 criteria. If that is the case, and I suspect it is, then there is no gain. Anyone want to comment, or give any idea's? Just a little something to cheer up your day. I personally think his suspicions could be confirmed, so it should be (k*2^n) - 1 to help with this, for those of you who are searching for primes other than Merensee's. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 12 May 2000 10:34:03 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: P-1 memory vs vacation time On 12 May 00, at 3:25, Shot wrote: > 1) Where can I find some mathematical info on P-1 factoring > (preferably everything, "for dummies")? The mathematical background to the modern factoring methods is distinctly non-trivial. However there are accessible explanations of the ideas behind the algorithms in several standard works. For a general introduction to factoring methods, try "Primes and Programming" by Peter Giblin (Cambridge University Press (1993), ISBN 0-521-40988-8). This book is fairly accessible and very reasonably priced, but the only reference to P-1 is to stage 1 only and is presented as an exercise. For a detailed explanation of the P-1 algorithm, refer to "Prime Numbers and Computer Methods for Factorization" by Hans Riesel (Birkhauser (1994), ISBN 0-8176-3743-5), which is expensive and by no means easy going. > > 2) When I use Prime95's Vacation or Holiday feature, does the program > assume that the vacation time should be treated as nighttime for the > purpose of P-1 factoring? > Good point. My guess is that day/night setting takes no account of vacation time. However, is this really a problem? If running P-1 stage 2 and daytime begins, the program will suspend P-1 & get on with something else, resuming the suspended P-1 job when daytime ends again. So the work gets finished up anyway, whether vacation time is in effect or not. > BTW: George, I think many people (myself included) surf the web using > 800x600 resolution - new Mersenne page's menu is a little to wide for > that setting. Not a big issue, but a little annoying. > Nowadays I tend to run in 1024x768 but with the browser window size set a bit smaller than that (though not as small as 800x600). I think 1024x768 is becoming pretty well the default resolution. However, I still believe that it's helpful to users to design web pages so they can be usefully viewed when displayed at 640x480 - even if this means preparing a differently formatted version of the page to suit users with low resolution displays. What about WAP mobiles with very small displays & very limited graphics capability? What about an implementation of the LL Test for WAP mobiles? Would be a good way of making sure that the battery on the damn thing was always flat ;-) Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 12 May 2000 16:22:54 +0200 From: "Pa'l La'ng" <[EMAIL PROTECTED]> Subject: Re: Mersenne: To crazy to be true, but it is.... [EMAIL PROTECTED] wrote: > This is totally weird, and I think I messed up in getting this, but it is > true. Could someone with a lot of time and a lot of patience and a big > calculator check this? Thanks. > > 1 = 1/(2�- 1) + 1/(2� - 1) + 1/(2^4 - 1) + 1/(2^5 - 1) + ... + 1/(3� - 1) + > 1/(3� - 1) + 1/(3^4 - 1) + ... + 1/(5� - 1) + 1/(5� - 1) + 1/(5^4 - 1) + ... > > In other words, if set x contains integral powers, (2�, 3�, 2�, etc....) and > x' is the set of integers minus set x. Then this says: > > 1 = sum(n=2 to n=infinity (sum( i=1 to i = infinity, 1/((x'i)^n - 1)))) > > please confirm!! > > this is a side formula I found, while working with primes. Hope it is not to > off topic. > _________________________________________________________________ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers The above mentioned question is neither weird nor off topic on account of the following: 1) The general task (including yours) is to have the unity, i.e. the number "1" as the sum of reciprocals of natural numbers. 2) In case the number of the summands is finite, the denominators are divisors of a perfect number, - the LCM of them.- ( See: Daniel Shanks: Solved and unsolved problems in Number Theory, Vol.I.Spartan books, Washington DC.1962; page 25.) Easy to prove: the existance of such a finite summation is equivalent to the existance of perfect numbers. 3) So the existance (or non-existance) of producing the unity as the sum of a finite number of reciprocals of odd numbers is equivalent with the existance (or non-existance) of odd perfect numbers. 4) Only a comment: The Egyptians also used the reciprocals in their arithmetics, but none of the remained sources contained summands having only reciprocals of odd numbers. Every one of them has at least one reciprocal of even numbers. Best regards Pa'l La'ng Budapest, Hungary _________________________________________________________________ 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 #734 ******************************
