Mersenne: Error 12002
I've seen sporadic episodes of error messages before during temporary server outages. However, haven't seen one that lasted this long. I now have several machines that have been unable to report for six days in a row. One of them is nearly out of work (though I can reserve assignements manually if I need to.) Looking through the Forum archives it appears Error 12002 is a version 21-specific problem that occurs when entropia.com is down even if mersenne.org is up. On Saturday entropia.com was indeed down. However, entropia's website has been up since sometime Sunday, and I have *still* been getting hourly 12002s on three different systems. No firewalls on my end, and no settings have changed on my end either. Any advice? I would also ask the "keeper of the faq" to add a few new lines to it about these "new" (since 2 years or so ago) error messages that aren't described in the online information. GRB _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Factoring hiccup?
An odd thing happened today. I have version 21.4.1 on my laptop (a PIII-1000, but only turned on a few hours a day so that LL tests would take months) doing trial factoring. I ahppened to see the following in the screen display tonight: [Feb 13 01:44] Factoring M21632497 to 2^67 is 14.43% complete. [Feb 13 01:45] Factoring M21632497 to 2^67 is 14.46% complete. [Feb 13 01:46] Factoring M21632497 to 2^67 is 14.49% complete. [Feb 13 01:47] Factoring M21632497 to 2^67 is 14.52% complete. [Feb 13 01:48] Factoring M21632497 to 2^67 is 14.55% complete. [Feb 13 01:49] Factoring M21632497 to 2^67 is 16.14% complete. Strange. Do we know if this is just a minor glitch in the GUI, or if the factoring algorithm actually misses factors? GRB _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re Factoring Progress
Previous posters wrote about how some exponents jumped around between 1
and 15 a lot, while they "should" progress steadily forward, reaching
level 9 as they start factoring the final bit.
George asked if perhaps this was a bug in an old version.
No: each version of the software I have used for factoring (17, 18, 19,
and 21) worked this way. BUT:
Only a computer that is on and connected more or less continuously to the
internet will report reliably. If a computer is past due for a report when
it is booted, it always reports 1 for factoring progress regardless of
actual progress made. ("Connecting primenet server" happens *before* work
resumes on the exponent itself, and the program doesn't bother to check
where it is, I think. Curiously, LL tests don't suffer the same glitch.)
This was a great irritation to me a couple years ago, on a Cyrix that was
used erratically (sometimes off for a week, sometimes used a few hours
each day, sometimes left on overnight): I was unable to keep a 2nd
exponent queued reliably, because the rolling average was so low that it
would estimate months to complete an exponent, see that "1", and unreserve
any work that was waiting, even if it was in fact going to finish
the current exponent the same day.
GRB
_
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Mersenne: On v18 factoring
An odd thing happened to me a little while back. The machine which I used at a previous job, up to April 1999, started doing trail-factoring again a couple months ago! It's nice to see it working, and apparently not bothering its new owner by working -- but the machine is now out of my control, indeed I don't even know where the machine IS now. It is running version 18, which was, of course, the latest version out at the time the machine was last under my control. It's beginning to experience difficult getting assignments below the the 20.x-million limit. Most of the time everything is fine .. but over the weekend it tied up some 100 exponents in the 20.7-20.9 range, then immediately abandoned them. (It is set to report every day, and reported progress on lower exponents, and, mysteriously, on two higher exponents, yesterday, but has not checked in a report on the other 100 or so exponents since checking them out.) I manually released the abandoned exponents today. This time. But I'd rather not have to do this on a daily basis -- and would rather not cause a meltdown when the server finally runs out of assignments within v18's range altogether. Does anyone have any suggestions for how to stop a runaway copy of v18? Perhaps in a few weeks the server can be updated to return an "out of exponents" error to v18 instead of offering it an assignment it can't handle? GRB _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Mersenne Digest V1 #978
On Wed, 10 Jul 2002, Mersenne Digest wrote: > From: "Frank_A_L_I_N_Y" <[EMAIL PROTECTED]> > Subject: Mersenne: m(127) by machine > > Does anyone know which parts of the ll test are due to lucas and which = > to Lehmer? > Specifically was the MODing at the end of the function known to Lucas, = > or was it an addition of Lehmer's. I am sure someone else can answer this better than I can, but: For a start, you may want to peek at the May _Mathematics Magazine_ which has an article "A brief history of factoring and primality testing B.C. (before computers) by R A Mollin. Here's a passage from that article: To see how Lucas determined M127 is prime we state the following result that was known to Lucas... Suppose that F_k is the kth Fibonacci number and n is given. If n = +- 3 mod 10 and n divides F_n+1, but n does not divide F_m for all divisors of m with 1<=m<=n, then n is prime. Also if n = +=1 mod 10 and n divides F_n-1 but n does not divide F_m for all divisors m of n with 1<=m<=n-2 then n is prime. Based on this result, all Lucas had to establish was that M127 divides F_2^127 but M127 does not divide F_2^m for all m<127. He did this in 1876, using methods that led to a primality test... [they quote the Lucas-Lehmer test we all know and love]... Lucas knew only that teh test was sufficient for primality, and this only for certain restricted types of values of n. In 1930, Lehmer proved both that the condition is necessary and that the test holds for any value of n. [end quote] As I read that passage, Lucas came up with the testing method in its entirety, and knew that if a number passed the LL test it was prime, but didn't use it the way we do because failing the LL test wasn't known to be proof of compositeness before Lehmer. GRB _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Proth observations
After seeing a post on this list a few weeks ago I decided to branch out and try a few ranges from Michael Hartley's page looking for k*2^n-1 primes. I must say there is a bit of a thrill in actually discovering a new prime every day I run the program instead of proving two numbers a month composite. :) Anyway, a few curious observations I made, which surprised me: I have 2 computers, a P2-350 and P3-500. The program executes nearly 2 1/2 times as fast on the latter as on the former with nothing else running. Apparently the Proth code takes advantage of a lot of P3 features? With the same version of prime95 and the same version of proth on each computer, if you run them both at the same time, under Win2000 proth gets a higher priority and all the processing power, while under NT4, it's the other way round, and prime95 has to be stopped or have its priority reduced in the ini file to not smother proth. Curious. (Why run them both at once, you ask? If the computer is going to be on all night anyway, it'd be idle when proth finished a range unless prime95 was ready to take over as soon as proth was done.) I assumed that one value of k was pretty much the same as any other as far as execution time and the chance of finding primes. To my surprise this turned out not to be so: On the P3-500, for "most" 650http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: The return of poaching?
Some of you may have noticed, as I have, that the incomplete double-checks in the 2-2.5M range have been being finished up very quickly the past few weeks, much more so than the past several months. A quick look in the cleared exponents file reveals many recent results reported by a user "rick" who apparently has several fast Pentium IIs doing double-checks. A look in the the assignments file reveals not a single small exponent reserved by this user. Not a big deal in the greater scheme of things, but frustrating to people like diamonddave and myself who make an effort to seek out the smaller exponents and reserve them. I don't know exactly what our policy is on this matter, or what we can do about it the the facts are as they seem to be. But it seemed worth bringing the matter up. Gordon Bower _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: v19 and priorities
I recently decided to start switching over from v18 to v19 (yes, I know I could have months ago, but I thought I'd give the rest of you time to find all the bugs first.) I did notice a performance improvement -- about 8% on a 350 doing LL tests, about 2% on an old P-120 doing double-checks. As the opportunity arises I will probably switch over the other 5 machines I also am allowed to run the program on. Something strange happened, though. Version 19 slows down considerably more in response to my doing other low-demand things on my machine, reading email/web browsing/etc. Is this just in the nature of v19, something to do with the optimizations that were added to speed it up? (It does still average a faster rate in the long run). I did not change any of the priority settings in prime.ini when switching versions. As long as I am writing to the list -- perhaps someone could explain in a little more detail than readme.txt does as to what the valid range of values for the Priority variable are and what the effect of each is on NT and 95? I experimented a little by trial and error last summer when a friend running a 3-D screen saver offered to let me run the program on his machine, but we never had much success fine-tuning it so as to not interfere with his work. GRB _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: types of work to request - 10m digit prime vs. nextprime
> -- > > Date: Thu, 14 Oct 1999 20:44:16 -0400 (EDT) > From: Darxus <[EMAIL PROTECTED]> > Subject: Mersenne: types of work to request - 10m digit prime vs. next prime > > As soon as I heard that there was a $100,000 prize available for finding a > prime, I decided to switch to the 10m digit test, even though my chances > of finding it were extreemly small. I mean, the tiny chance of winning > that cash is better than leaving your idle CPU time idle, right ? > > Unfortunately, this cash prize had clouded my thoughts, as I fortunately > realized when my girlfriend told me she opted not to switch to the 10m > digit tests, because she was more interested in getting her name in the > history books than getting $100,000, and there was is a significantly > greater chance of finding the next prime than there is of finding the 1st > 10m digit prime. I too am more interested in fame than fortune (and incidentally don't put much stock in the Islands) and to this end I've been latching on to smallish exponents. Speaking of fortune - for a few short weeks in April and May, joining GIMPS really was a positive-expectation bet. I could test one exponent in the 4-5M range a week for a 1-in-35000-more-or-less shot at the prize, for roughly $1 electricity per exponent (less than 2 KWH/day at 8c each, with the monitor off when I wasn't at the keyboard). Of course that meant it was more a lottery than research, and it was bound to end within a couple months. [snip] > It was what, half a million dollars total ? I think it would havebeen > much better to award $25k per new prime discovered for the next 20 primes. The purpose of the EFF awards was not to help GIMPS; it was to inspire people to find better ways to find big primes, and, more generally, encourage fresh mathematical thought. Conjecture time: The prime number earning the $150K prize will not be a Mersenne. Why do I say that? Even with processor speeds increasing, we have a good idea how long it'll take to find big primes by Lucas-Lehmer. Even for the 10M-digit prime it'll be a damn long time the way we are doing it now. Finding the monsters requires an intellectual leap by someone - possibly in processor design, more likely in number theory. Admittedly this leap may well be a better version of L-L in which case Mersennes will still be the record primes for a long while to come. But my hunch is that there is a better chance of finding some new way to either construct primes, or to test some other special-form number, than there is of dramatically improving on Lucas-Lehmer. Just a hunch. I might be wrong. I hope I live long enough to see all of the EFF prizes awarded, whether to Mersennes or not. Gordon Bower PS - On an unrelated note --- what is the smallest natural number that is not known whether it is prime or composite? Surely *someone* out there is trying to work from the bottom up and factor every number. (I don't know the answer. I am guessing the it is a smallish number of maybe 15 or so decimal digits?) _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: free sphere is half deflated
> > From: The thrill of minimalism <[EMAIL PROTECTED]> > Date: Fri, 12 Mar 1999 22:35:53 + > Subject: Mersenne: free sphere is half deflated > > "Ernst W. Mayer" wrote: > > > > Joth Tupper writes: > > > > >the Bolzano-Tarski theorem proved (what, back in the 1920's?) > > >that you could cut a solid 3D sphere into finitely many chunks, > > >then rearrange the chunks to make another solid (no holes or gaps) > > >3D sphere with _twice_ the volume. Pretty spooky, I always felt. > > > > I don't know about spooky, but 'twould seem to violate conservation > > of mass (or mass/energy, if you're a postmodern relativist :), > > 'twouldn't it? Well... no one said how easy it was to actually take hold of the pieces and rearrange them. We mathematicians tend to think of our objects as continuous, infinitely divisible, lumps, but that doesn't work so well with matter. Quarks, for instance, come in pairs and triplets, never alone. And if you try to tear a quark pair apart --- you put so much energy into the system pulling on them that you create two new quarks in the process. I wonder if anyone has tried to reconcile Banach-Tarski with physical reality by saying "yes, you can do that, but the amount of energy it takes to pull the pieces apart and reassemble them turns out to be enough energy to create the additional mater needed"... > > You can map a line segment of "length" 1 onto two line segments of > length 1 with a simple mapping function f(x)=2x+1 for instance. Banach-Tarski doesn't do any stretching, just rotating, translating, cutting. --- Gordon Bower PS: Those were SPHERICAL fishes and loaves of bread that Jesus broke to feed the thousands of people on the shores of the Sea of Galilee. :) Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
