Re: Mersenne: Factoring numbers...
On Tue, 12 Oct 1999, Jukka Santala wrote: Is it just me, or does factoring smaller Mersenne numbers take propotionally much longer? I would expect M727 to be much faster than the 33M range to a fixed depth, yet the opposite _seems_ to be true. It's not just you, it's a natural consequence of the property that all factors of Mp must be of the form 2kp+1, so with a fixed depth and larger p there are fewer possible factors to check. Ofcourse, I can't be sure about this, because the real complaint I have is that factoring numbers to depths beyond the "default" seems nearly impossible. The manual factoring assignment seems like the only possibility to force these, yet it doesn't work like the normal factoring (Doing one bit depth at time) and is a pain on a dual-CPU machine. Is it possible we'd get a third parameter to the Factor= work-line specifying the intended depth for the factorization? Also, usually for some reason Prime95 seems to reject most (all?) Factor= statements I've tried, could we get some more detailed instructions on this? -Donwulff _ 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/ No, power off on shutdown is not SMP safe. It kind of happens to work on a lot of boards. If making that APM call reformats your disk and plays tetris on an SMP box, the bios vendor is within spec (if a little peculiar).Alan Cox, on the Linux Kernel list _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: glitches in mprime v19?
On Mon, Oct 11, 1999 at 12:06:07PM -0500, jason wrote: Well, I also downloaded mprime.tar.gz, and I had a slightly different problem trying to connect to the PrimeNet server. To summarize: mprime.tar.gz v19.0.2: results in "ERROR: Primenet error 1" sprime.tar.gz v19.0.2: results in "Error 2250: Server unavailable" mprime.tar.gz v18.1.2: No problems. I wonder why the two versions give different error messages (and why I'm getting them at all)? Anyway, I just compiled mprime from source (debugging not enabled), and it's working just fine. Except for the fact that I will not receive credit for my work, since I compiled it myself... so much for initiative. :-) Indeed - this is the problem I reported a little while ago (again with sprime, since I don't have glibc 2.1 as yet). If v19 works faster, I might as well use it even if I can't currently report results. My temporary solution has been to grab 90 days' of work, switch the machines to run as dialup hosts even if they aren't, and wait for someone else to fix it, reporting via the web interface if necessary :-) -- Robin Stevens [EMAIL PROTECTED] http://www-astro.physics.ox.ac.uk/~rejs/ (+44) (0)1865: 273212 (work) 726796 (home) 273275 (fax) Pager: 0839 629682 Oxford University Computing Services, 13 Banbury Road, Oxford OX2 6NN, UK "Life, loathe it or ignore it, you can't like it." -- Marvin _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: splitting up 10m digit primes
At 11:00 AM 10/12/99 -0400, you wrote: I'm okay with that. But I think, if possible, it'd be good to break up primes into like, 1 month chunks, distribute them. I'm sure it'd be possible, I just don't know if/how much it'd impact speed. Not possible. Well, POSSIBLE, but it would actually slow the effort down. The problem is that the test you're performing uses the results of the last "loop" to compute the next value. To make the math simpler, I won't use the actual LL test, but something much simpler: X = 0; DO 32,722,124 times X = X + 1; Now, if you're running this prgram, forget for a moment that you and I can easily look ahead and see that after a thousand times, X is 1000. Unfortunately, there's no "shortcut" in the Lucas-Lehmer test whereby one can look ahead. You have to do this: X = 0 Prior result was 0 so 0 + 1 = 1 Prior result was 1 so 1 + 1 = 2 Prior result was 2 so 2 + 1 = 3 Prior result was 3 so 3 + 1 = 4 Prior result was 4 so 4 + 1 = 5 Prior result was 5 so 5 + 1 = 6 etc. Note that you cannot just "jump ahead" to the 120th loop, because you need to know what the RESULT of the 119th loop was before you can start. And you need the 118th loop to start the 119th, etc, all the way back to loop # 1. If you're testing an exponent of 32,361,147 (for example), you *must* do all 32,361,144 calculations, and they have to be done in order. If you tried to "break them up", with, say, 100,000 "iterations" per user, then the person with 100,001 through 200,000 cannot even start 100,001 until all 100,000 iterations of the last person had been finished. If you tried this, you'd only slow things down, because you'd have to send the "mid-test results" back to Entropia, and then out to the next tester, before they can start. That's what would slow things down -- the back-and-forth of the intermediate results. Yes, it takes a while, but its very much best for one person to just do the whole test, even though it's going to take two years. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factoring numbers...
George Woltman wrote: Since factors are of the form 2kp+1 there are many more factors to test when you factoring M727. Yes each factor can be tested in less time, but this is overwhelmed by extra factors to test. Thanks to everybody pointing this one out, I missed the obivious implication of the form of factors earlier. It does make sense now, though. You will find more factors using ECM. Compare the cost of running 700 curves at B1=25 (this will find most 30-digit factors) against trial factoring to 99 bits! It is true that ECM can miss a factor, but for M727 which has had thousands of curves run at bounds as high as 50,000,000 - the chance of finding a factor smaller than 30 digits is.well, zero. By now it should be obivious I'm not too well versed in this stuff, however... I've always been told that ECM is "not guaranteed to find all factors", is it however expected (or guaranteed, if you will) to find all factors under X bits given _enough_ curves? And is the probability of finding any given factor by ECM only a function of it's number of bits, or do other things affect it as well..? -Donwulff _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factoring numbers...
"Brian J. Beesley" wrote: // Regarding factoring Mersennes to v19 depth... If you do decide to do this, you're on your own - don't be surprised if someone else does the same thing independently - there's no mechanism for coordination to avoid wasted effort. Partially. There now exists software to automate most of this, with intent to update the shared status files every month. Don't remember the URL, but little browsing of the Prime95 homepage should turn this stuff up. It's not exactly what I was looking for, though, I'm playing on filling some of the holes in Cunningham-tables and this means expending some extra effort on the lower Mersenne numbers. I'd like to have trial-factoring beyond the v19 limit among the options to go at this, altough I'm understanding this isn't apparently very fruitful method. Anyway, still waiting to hear if ECM will, eventually, find all factors or if it leaves "factors" in the range... -Donwulff _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: splitting up 10m digit primes
On Tue, 12 Oct 1999, George Woltman wrote: I admire your patience! Thank you :) I think it said 1 in 250,000 chance if finding a prime. So.. on average, it would probably take that one computer, by itself, 241,250 years to find a 10m digit prime. Right ? Define "probably". 241,250 years gives you a 50% chance. Actually it will take longer since the exponents get bigger and bigger. Mathmatical probability... on average, it'll take 50% of the whole thing. At the time I didn't know it took longer toward the end. it'd be good to break up primes into like, 1 month chunks, distribute them. A good idea but the Lucas-Lehmer primality test is a "serial" algorithm. That is, I can't have 33 machines each do a million iterations and get the answer in a month. The second million iterations can't start until the first million complete. I see. Well, we need more people involved either way :) Other thing I gotta calculate... how long it would probably take us if we converted everyone from distributed.net to GIMPS. This is actually the biggest reason why I wanna calculate prize/probability ratio of the 2. I also think it would have been better to award $5k per new prime, of any length. But that's just my opinion. The prize fund was set up by the EFF and the anonymous donor. I agree with you and have tried to encourage an orderly progression by awarding $5,000 to all smaller Mersenne primes (but only if we also find the 10 million digit prime). I understand the contest was not set up by you, but it's good to hear you're trying to incourage $5k/prime. I doubt there are many people who's input could be more valued for this. And how is the probability of finding a prime calculated ? It is roughly how-far-factored-in-bits * 2 / exponent Okay.. what's "how-far-factored-in-bits" mean ? I wanna do a comparison of the prize money to probability ratio between distributed.net's rc5-64 project ($2k prize), GIMPS 10m digit prime ($55k prize). But it'll take me a chunk of time. Any estimates ? There is now a prize for factoring Fermat numbers too. Neat. Where's the info ? Also, the link pertaining to the EFF $100k award on the GIMPS page goes directly to the EFF rules page, instead of http://www.mersenne.org/prize.htm. I think it'd be nice to have a link from the main GIMPS page to something w/ info on all prizes which could be won with GIMPS. You were probably planning on doing that though... However, the best investment is probably to turn off your computer and pocket the $30 you save in electricity! Of course, that's no fun. So pick whichever project gives you the biggest thrill. Alright then, it's a gamble, not an invenstment. Wait, no, I'd leave my computer on all the time anyway. It's still an investment. Yeah yeah, so if I didn't run one of these, the CPU would be off less draw less power. It doesn't matter, I like distributed processing. I'm not in it for the money. __ 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
RE: Mersenne: splitting up 10m digit primes
From: [EMAIL PROTECTED] How about an option when you hit "QUIT GIMPS" to upload your P and Q files to Primenet, so someone can at least finish the job? I'm running an exponent in the 33 million area and the save-files are over seven megabytes in size! That would require no small amount of server space... 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
Re: Mersenne: splitting up 10m digit primes
There is now a prize for factoring Fermat numbers too. Neat. Where's the info ? I think Richard Crandall is offering a prize for Fermat factors (http://www.perfsci.com). John Selfridge is also anouncing a prize for factors of various numbers which "ought to be prime". I don't think that there is a website yet. I'll repost the list if you are interested. -Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: [Windows net utilities]
On Mon, Oct 11, 1999 at 10:10:04PM +0100, Brian J. Beesley wrote: Windows users might care to try a nice program called CyberKit, which is freeware does ping, traceroute NS lookup (amongst other things). I don't know if Windows does `other things', but it certainly has ping (ping) and traceroute (tracert). It lacks a decent `host', though, but ping will do most of the work for you. /* 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
Re: Mersenne: Factoring numbers...
Jukka Santala wrote: Is it just me, or does factoring smaller Mersenne numbers take propotionally much longer? I would expect M727 to be much faster than the 33M range to a fixed depth, yet the opposite _seems_ to be true. For any given factoring bit-depth, larger exponents will take a shorter period than smaller exponents. This is due to the number of potential factors that are available in at any given depth. Each bit-depth takes twice the amount of time to test as the previous one (ie: 2^57 takes 2x the length of 2^56) To determine the approximate number of potential factors that must be tested at any given depth, take the bit-size of the first pontentail factor, 2p+1, and double for each bit-depth up to the bit-depth you want. Finally, divide by 2 (eliminating potentials not meeting the 8n-1 or 8n+1 rule). So, the first potential factor of 727 would be 1455 (an 11-bit number). Take 1 for the number of potential 11-bit factors, and double over and over until you get where you want (2 12-bit potentials, 4 13-bit, 8 14-bit, etc.). However, 33,219,283's first potential factor is 66,438,567 (a 26-bit number). It has 1 26-bit potential, 2 27-bit, 4 28-bit, etc. Take these numbers and divide by 2 for the numbers of potential factors that need testing. You can see how there are *way* more potential 57-bit factors for 727 than 33,219,283. NOTE: These figures are approximate as 727 may only have say 3 potential 14-bit factors to test. (Actually, it only has 2!). It will give you a good idea of the number of potential factors you are looking at testing for any given bit-depth though... To illustrate better: To test the exponent 727 at 2^57 (only 57-bit factors), you must test approx. 7 x 10^13 potential factors. To test the exponent 33,219,283 at 2^57 (only 57-bit factors), you must only test approx. 2.15 x 10^9 potentail factors. BTW, there is a more accurate way to determine the exact number of potential factors that need to be tested at any given depth, but requires a little more effort. And when we're talking a difference of a couple million potential factors with a total of 100 trillion potential factors to test, is it really important to know the exact number?? Eric Hahn _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: splitting up 10m digit primes
On Tue, 12 Oct 1999, Rick Pali wrote: From: [EMAIL PROTECTED] How about an option when you hit "QUIT GIMPS" to upload your P and Q files to Primenet, so someone can at least finish the job? I'm running an exponent in the 33 million area and the save-files are over seven megabytes in size! That would require no small amount of server space... Wow. I'd been assuming this was basically being done. How unfortunate. I believe I would not have stopped processing the number I was working on to start a 10m digit number if I'd known this... I would have just set it to work on a 10m digit number as soon as it finished the current one. It might be good to make this very clear.. maybe in the client or something, when somebody opts to give up on a number, that their work so far on it will be lost. __ 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
Mersenne: stopping a LL test
[ Joth Tupper explained] ...why we cannot stop in the "middle"
of a Lucas-Lehmer test. The essential answer is that we
know a property of particular terms in the sequence 4, 14, 192...
given recursively by squaring and subtracting 2
I understand this now, but I didnt when I first downloaded and
started GIMPS over a year ago, so heres a funny story
for you GIMPSers to add to your dumb-spike collection: {8^D
I downloaded GIMPS and started it thinking that it was doing
a brute force factorization and assuming it would stop as
soon as it found a factor. So my excitement built steadily
as it passed 50% finished, then 60%, etc, and by the time
it was in the 80s and still running, I was checking my computer
every hour or so, cheering wildly each time {8^D haaa ha haaa,
laughing maniacally, with my wife quite convinced I was going
crazier, and by the time I was in the mid 90s I was beside
myself, thinking I had perhaps nailed a mersenne prime on
my very first try, and (blush) actually calculating the probability
of this happening, etc. When my LL run hit 98 percent, I could
*not* stop watching the computer screen, nor did I dare actually
*use* the computer, expecting at any time a message like
"bzzzt. 2^3123929-1 has a factor of yakkity yak".
Since I am embarassing myself anyway, and recording a
stupid-spike story in a medium far more permanent than
any book or newspaper, I might as well admit that I stayed
up until 2 am, on a work night, to see if I had indeed hit the
jackpot on the very first try. When it hit 100% and reported:
"2^3123929-1 is not prime", well, imagine my dismay. {8-[ {8^D
Since then, I have learned all about the Lucas Lehmer algorithm,
reignited my 15-years-dormant love of number theory,
scanned the number theory websites and learned a ton of cool
math stuff. Im in nerdvana here. So, thanks George. How
about posting a picture of yourself so we can print it
out and frame it? {8^D spike
_
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RE: Mersenne: Factoring numbers...
Anyway, still waiting to hear if ECM will, eventually, find all factors or if it leaves "factors" in the range... The best way of thinking about this is that each curve at a given bound has a small but non-zero probability of finding a factor of a certain length, assuming that one exists. There are a very large number of curves available, and so the probability of missing the factor on *all* the curves can be made extremely low --- but non-zero. This handwaving approach is far from rigorous but it is an extremely good approximation of the truth. So yes, in principle it can leave factors undiscovered. In practice, it will find them within a reasonable time --- but depending on your luck that time could be short or it could be lengthy. A few examples from personal experience might be illustrative. The largest factor I've found with ECM was a 45-digit factor of 423*2^423+1 and was found in phase 1 with the curve bound set at 3 million. I estimate I had a roughly one in twenty thousand chance of finding that factor in the number of curves I ran. At the other extreme, I recently used MPQS to finish off a factorization of an 89-digit integer, only to find that one of the factors had 30 digits. I had already found a 33-digit factor of the number for which the C89 was the cofactor, but missed the P30. I estimate that I had a less than 1% chance of missing the smaller factor given the amount of ECM work I had done. In the first case I was lucky, and the second I was unlucky. That's the nature of ECM. Paul _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: gzipped binary expansion of the largest prime
Is there a copy (preferably unformatted plaintext) of the decimal expansion of the largest (2million-some digits) prime, gzipped or zipped or something, somewhere ? Anybody know how long it takes to calculate this using the calc program (which I'm currently compiling for this purpose) ? I intend to print it out in like, 2 or 3 point font wallpaper my room with it :) Somewhere I have a printout of some number of millions of digits of pi... I really want a hardbound copy of, say, 10 million digits of pi, with the greek letter stamped on the front. Some small font size. About.. 5 1/2" x 8 1/2". I dunno, maybe this group is into numbers enough that we could actually pool our resources and get it done. Or maybe I'm the only one who'd be interested. ? I actually looked into printing services once. Yeah, I could get it printed bound, but not hard bound, with the letter pi stamped on it. Bummer, calc didn't compile in my shell account. In file included from seed.c:53: /usr/include/sys/resource.h:25: field `ru_utime' has incomplete type /usr/include/sys/resource.h:26: field `ru_stime' has incomplete type seed.c: In function `pseudo_seed': seed.c:216: field `tp' has incomplete type seed.c:241: field `tp2' has incomplete type *** Error code 1 make: Fatal error: Command failed for target `seed.o' Oh well, hope my repaired Linux drive gets back soon __ 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
Re: Mersenne: Re: [Windows net utilities]
On Tue, 12 Oct 1999, Steinar H. Gunderson wrote: On Mon, Oct 11, 1999 at 10:10:04PM +0100, Brian J. Beesley wrote: Windows users might care to try a nice program called CyberKit, which is freeware does ping, traceroute NS lookup (amongst other things). I don't know if Windows does `other things', but it certainly has ping (ping) and traceroute (tracert). It lacks a decent `host', though, but ping will do most of the work for you. If you're looking for UNIXish network related utilities to run under windows.. or actually anuthing UNIXish to run under windows, get cygwin (http://sourceware.cygnus.com/cygwin). Cygwin is basically a port of the unix API, and this package comes with a lot of the standard utilities. And a lot of stuff compiles under it out of the box.. or tarball. I look forward to an entire Linux distribution being ported to it :) They're working on porting the X server to it. __ 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
Re: Mersenne: splitting up 10m digit primes
As I posted some days back; Anyone who wants to quit an exponent after investing a PII-400-month or more, please contact me, and we'll try to carry it on, using it for the QA effort. It could take some major bandwidth-minutes if more than a few exponents are quit, however. Ken At 04:15 PM 1999/10/12 EDT, [EMAIL PROTECTED] wrote: Well, as completion time gets longer and longer, it becomes more likely that a user will give up in disgust. This could be after several months of work is already complete. How about an option when you hit "QUIT GIMPS" to upload your P and Q files to Primenet, so someone can at least finish the job? _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: probability of primeness (was: Re: Mersenne: splitting up 10m digit primes)
On Tue, Oct 12, 1999 at 10:53:18PM -0400, Darxus wrote: I'm hoping what I have to say in this email might be important. On Tue, 12 Oct 1999, George Woltman wrote: At 04:12 PM 10/12/99 -0400, you wrote: And how is the probability of finding a prime calculated ? It is roughly how-far-factored-in-bits * 2 / exponent Okay.. what's "how-far-factored-in-bits" mean ? I think trial factoring is done to 2^68 for an exponent around 33 million. Thus your chance is 2 * 68 / 3300. Okay, so as far as we know, each number is equally likely to be prime, and this probability is just based on how much has already been tested ? No, they're saying the probability is based on how deeply they've tried to factor the number before trying the LL test. The more numbers N you rule out as potential factors of M, the more likely M is to be prime. Also, although there are an infinite number of primes, their density thins out considerably as they get large because there are so many more potential factors below them. This applies to primes in general; I don't know if it applies to Mersenne primes. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Vaxen Intel
At 12:03 PM 1999/10/12 -0400, Jud McCranie [EMAIL PROTECTED] wrote: At 12:54 PM 10/12/99 +1000, Simon Burge wrote: "John R Pierce" wrote: a year on one of these [a vax] wouldn't equal one day on a pentium-II. Probably a bit generous there even, given that older vaxen wouldn't have pipelined FPU's so you might get one result every 10 (or perhaps even 100) clocks, as opposed to one result almost every clock on modern hardware. In his book "Programming Pearls", Jon Bentley gives the figure of 570 seconds for sorting 10,000 integers on a VAX-11/750. My PII-300 does it 1160 times faster and my C-400 is 1780 times faster. But that is comparing working with integers instead of FP. Hmm, a vax3900 is definitely not slower than a 780. The original Vax was the 780, followed by the slightly slower 750, both designed in the 1970's. A VS2000 was a tiny, almost shoebox size vax, and those were about 780 speed. A VS3100-38 (circa 1990) was about 4 x a 780; a VS4000-60 was about 12 times; I think a 4000-90 was about 30 times. My recollection was that for multiple precision programs in integer in C, a VS3100-38 was about half the speed of an Intel 386-33 with cache, and a VS4000-60 was about the equal of a 486-33. What sort algorithm are those figures for? In what programming language? Which compiler? There are lies, damned lies, and statistics. Then there are benchmarks... Ken _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: probability of primeness (was: Re: Mersenne: splitting up 10m digit primes)
I think trial factoring is done to 2^68 for an exponent around 33 million. Thus your chance is 2 * 68 / 3300. Okay, so as far as we know, each number is equally likely to be prime, and this probability is just based on how much has already been tested ? Umm, no. The probability that a number is prime is inversly proportional to the number of digits (or more precisely, the probability that a number on the interval [1,x] is prime is asomtotically 1/ln(x)). However, the probability that a number is prime increases with the amount that has been trial factored (without finding a factor). The precise estimation is based on Mertel's theorem. Ugh... I apparently had bad math teachers, and GIMPS is really making me feel it. I *really* wanna play with these numbers, but I feel intellectually cripled. You certainly seem to have done a good job! You found the two big conjectures about Mersenne distribution. That is Curt Noll's (poorly defined) island theory (your pairs observation), and your observation about it being roughly exponetial (a conjecture due to Wagstaff, and others, though Wagstaff's has hueristic evidence to back it up). I took the numbers from http://www.utm.edu/research/primes/mersenne.shtml#known See http://www.utm.edu/research/primes/notes/faq/NextMersenne.html, as well as http://www.tasam.com/~lrwiman/FAQ-mers, Q4.2. Does anybody see what I'm talking about ? Is there any significance to this ? Has somebody already written extensive papers on this ? Yes, see above. Good work! -Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: gzipped binary expansion of the largest prime
Is there a copy (preferably unformatted plaintext) of the decimal expansion of the largest (2million-some digits) prime, gzipped or zipped or something, somewhere ? Yes! Landon Curt Noll has all the Mersenne primes on his website. http://reality.sgi.com/chongo/prime/merdigit/index.html#largest (Ack! I'm slipping, I had to look it up!) Also (if you want it in poster form) look at www.perfsci.com (though last I checked it was ~$30 US). Bummer, calc didn't compile in my shell account. In file included from seed.c:53: /usr/include/sys/resource.h:25: field `ru_utime' has incomplete type /usr/include/sys/resource.h:26: field `ru_stime' has incomplete type seed.c: In function `pseudo_seed': seed.c:216: field `tp' has incomplete type seed.c:241: field `tp2' has incomplete type *** Error code 1 make: Fatal error: Command failed for target `seed.o' Oh well, hope my repaired Linux drive gets back soon Hmm, you might want to sent this to Noll. He is big on getting Calc to compile without errors on darn-near everything. Also look at Pari/GP. It has binaries for windows! (It seems faster than Calc too!) ftp://megrez.math.u-bordeaux.fr/pub/pari/windows (take off the /windows for linux/msdos/mac/etc versions). Hope this helps, Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne Digest V1 #641
Mersenne Digest Tuesday, October 12 1999 Volume 01 : Number 641 -- Date: Tue, 12 Oct 1999 12:54:34 +1000 From: Simon Burge [EMAIL PROTECTED] Subject: Re: Mersenne: Re: GIMPS "John R Pierce" wrote: a year on one of these [a vax] wouldn't equal one day on a pentium-II. Probably a bit generous there even, given that older vaxen wouldn't have pipelined FPU's so you might get one result every 10 (or perhaps even 100) clocks, as opposed to one result almost every clock on modern hardware. Simon. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Tue, 12 Oct 1999 01:38:01 EDT From: [EMAIL PROTECTED] Subject: Mersenne: DOSville 'ello. This is quoting multiple people. They know who they are. Most of this is s'posed to be funny, by the way. :-D It suddenly links up to the server and downloads new exponensI am sure testing LL 9xx is enough on a cyrixits my baby! You shouldn't run LL tests on a Cyrix -- factoring will utilize your CPU much better (since Cyrixes are so bad at LL testing.). But you probably know that already. /JOKE Intel is the one true path, the middle way to Nerdvana. All other chipmakers shall pale in comparison to the glorious might of Integrated Electronics! /JOKE Seriously, I can't wait for the Merced. Better yet, McKinley. *drool* Watch Prime95 on those chips, whoo! Very dissappointed at the supplementation and interface Hrm. GIMPS gives you several FAQs, websites, easy-to-contact designers, a mailing list, etc. Doc files aren't that good anyways. Disappointmentville. The GIMPS software was never designed to be user-friendly -- it was designed to be fast. If that doesn't suit you (and it doesn't suit many people), you are entirely free to choose a different project. Preach it, brother! Testify! Gooeys would make Prime95 bloated and (in all likelihood) slower. Not to mention create places for bugs to creep in. Now what is wrong with .txt files? .TXT files are the one true document file. Pure ASCII bring it on! Mathematical notation in .TXT isn't easy, though. It's a conspiracy. FOR GOD SAKE GIVE ME A USER FRIENDLY INTERFACE, PROPER HELP MENU Give me a DOS-based command line (yet Win98 background-running capability) with a really nasty, God-awful set of fifteen switches that must be ordered in a precise way depending on the phase of the moon. :-P Now for the serious part: Lighten up. Ask questions 'bout whatever you're confused 'bout on the mailing list and the nice people here will help you. GIMPS is a great project. S. "Property of Billy and Andy" L. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Mon, 11 Oct 1999 23:43:08 -0600 From: "Aaron Blosser" [EMAIL PROTECTED] Subject: RE: Mersenne: resuming a prime 8410531 63 116988423.3 30.0 46.0 27-Sep-99 00:53 18-Sep-99 18:08 3rd -- just reinstalled the gimps client on my home PC. How do I tell my home PC to resume prime exponent 8410531, which it was working on before the crash ? Just add a line to the worktodo.ini file (or make it if you haven't started the GIMPS client yet) that reads: Test=8410531,63 A doublecheck would look like: DoubleCheck=exponent,factoredbits That's all. The 8410531 is the exponent to test, and the 63 is how many bits it's already been factored to. That particular exponent would now be factored to 64 bits under the v19 client, so if you update the client to that version, expect it to factor up to 64 bits before starting on the LL test. I guess we'll really see how well v19 is doing. I just switched my machines over (most of 'em anyway) to v19, all running the NT service version. Tomorrow I'll try updating the Win98 machines I have with the new prime95. Harder to do that since I can't do it remotely as easily as with NT boxes. Someday, Windows 95/98 will be gone and my life will be easier. So far, all are working well. And I've got about 7 boxes running Windows 2000 of various builds. Some Beta 3, some RC1 and some RC2. A couple Advanced Server and others are Win2K Professional. All are running v19 just fine (and were running v18 just fine also). Aaron _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Tue, 12 Oct 1999 13:49:55 +0200 (CEST) From: Attila Megyeri [EMAIL PROTECTED] Subject: Re: Mersenne: Mprime Error 2250 On Mon, 11 Oct 1999, Brian J. Beesley wrote: Tip for diagnosis of problems:
