Mersenne Digest Wednesday, March 22 2000 Volume 01 : Number 709 ---------------------------------------------------------------------- Date: Mon, 20 Mar 2000 17:54:50 EST From: "Nathan Russell" <[EMAIL PROTECTED]> Subject: Mersenne: IRC? When I was in distributed.net, there was an official IRC channel in which people could ask questions and discuss the project much more rapidly than is possible on a mailing list. It has occured to me that this could be something positive for GIMPS. Dalnet and certain other networks allow maintaining control over a channel without someone needing to remain on it continously. As a newbie, I know that I have asked questions to which the answers were relatively basic, albeit not covered by the FAQ. If newbies were able to go to an IRC channel, they could get immediate responce to their questions, and more experienced participants could have their concerns addressed or debate issues without inconviencing those who have no immediate interest. Nathan Russell ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 20 Mar 2000 19:03:06 -0500 From: George Woltman <[EMAIL PROTECTED]> Subject: Mersenne: Re: Possible V20 issue Hi, At 05:46 PM 3/20/00 -0500, Nathan Russell wrote: >I have noticed that, when I finish the v20 P-1 of an exponent and send in >the result, there is no "sending results" line but only a "sending text >message" line. Does this mean I am not getting CPU time credit? Correct. However, if you do find a factor you will get credit. In fact you get credit for trial factoring up to the size of the factor. In the long run, you will end up with more time credited than you actually invested. In the short run, it is like a CPU credit lottery. Scott does not have the free time to accurately credit P-1 factoring. However, it affects every one and is less than a 1.5% impact on your totals. Regards, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 20 Mar 2000 20:14:49 EST From: "Nathan Russell" <[EMAIL PROTECTED]> Subject: Mersenne: Re: Possible V20 issue >From: George Woltman <[EMAIL PROTECTED]> >To: "Nathan Russell" <[EMAIL PROTECTED]>,[EMAIL PROTECTED] >CC: [EMAIL PROTECTED] >Subject: Re: Possible V20 issue >Date: Mon, 20 Mar 2000 19:03:06 -0500 > >Hi, > >At 05:46 PM 3/20/00 -0500, Nathan Russell wrote: >>I have noticed that, when I finish the v20 P-1 of an exponent and send in >>the result, there is no "sending results" line but only a "sending text >>message" line. Does this mean I am not getting CPU time credit? > >Correct. However, if you do find a factor you will get credit. In fact >you get credit for trial factoring up to the size of the factor. In the >long >run, you will end up with more time credited than you actually invested. >In the short run, it is like a CPU credit lottery. > >Scott does not have the free time to accurately credit P-1 factoring. >However, it affects every one and is less than a 1.5% impact on your >totals. > >Regards, >George > George, Thanks for straightening this out for me. The eight hours twice a month of P-1 factoring will make a very small dent in my standing - certainly much less than my prior (to this week) practice of turning my machine off at night (I was not used to leaving the fan on). Another potential issue that just occured to me: If someone has an exponent partially done under version 19.x or 18.x and upgrades and it finds a factor, will they get more credit for the factor than they lost for the partial LL run? This is something that might be a significant issue for those who are running P-100's and comperable machines, where it would be a loss of months rather than weeks. If this has already been thought through, I still feel that it would be good for the list to be aware of that fact. Best regards, Nathan ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 20 Mar 2000 20:28:39 -0600 From: Ken Kriesel <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: Possible V20 issue At 08:14 PM 3/20/2000 EST, you ("Nathan Russell" <[EMAIL PROTECTED]>)wrote: > >Another potential issue that just occured to me: > >If someone has an exponent partially done under version 19.x or 18.x and >upgrades and it finds a factor, will they get more credit for the factor >than they lost for the partial LL run? This is something that might be a >significant issue for those who are running P-100's and comperable machines, >where it would be a loss of months rather than weeks. If this has already >been thought through, I still feel that it would be good for the list to be >aware of that fact. > >Best regards, >Nathan George has previously indicated that P-1 factoring is attempted, before continuing on, if the LLtest in progress is less than 50% done, and otherwise not. This is done as a total throughput optimization of GIMPS. If the LLtest is more than 50% done, the LLtest continues. But someone else may later P-1 factor the number and succeed in finding the factor. Then all the time to LLtest is uncredited, as happens for all LLtests, whether prime95 V20, V14.1 or earlier, or some other program. (Watch David Slowinski's cpu credit and number of exponents credited slowly shrink, as factoring gradually erodes his totals. Credit for dozens of my early tests has also been factored away.) If the person with the LLtest in progress finds the factor, he gets the factoring credit. Ken _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 20 Mar 2000 19:01:36 -0800 From: Stefan Struiker <[EMAIL PROTECTED]> Subject: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? $1 million math challenge issued Publishers seek solution to prime-number conundrum ASSOCIATED PRESS LONDON , March 17 � Two publishers are offering a million dollars to anyone who can prove that all even numbers are the sum of two prime numbers. No one has cracked the problem in the more than 250 years since it was first posed, and Friday�s announcement indicated the publishers aren�t too worried about having to pay up. THE THEORY, known as Goldbach�s Conjecture, was suggested by the Prussian mathematician Christian Goldbach in 1742. It�s easy enough to think of an even number that is the sum of two prime numbers � those which cannot be divided evenly by any number except themselves. For instance, 5 plus 7 equals 12, or 67 plus 3 equals 70. But so far it has been impossible to prove that it works for every imaginable even number. Faber and Faber, in conjunction with Bloomsbury Publishing in the United States, announced the challenge Friday to promote the coming release of �Uncle Petros and Goldbach�s Conjecture,� by Apostolos Doxiadis. �Proving it may well be impossible,� the publishers said, �and it is very probable that only a highly skilled mathematician would ever be able to produce a proof that meets the requirements of these rules.� The publishers set a deadline of March 15, 2002. To claim the prize, the winner would have to have the solution accepted for publication by a reputable mathematical journal and then have the proof confirmed by at least four members of a six-judge panel appointed by Faber and Faber. However, you don�t have to buy a copy of �Uncle Petros� to compete, the publishers said. �By offering this challenge, neither Faber and Faber Limited nor Bloomsbury Publishing are representing or warranting that the validity of Goldbach�s Conjecture is capable of proof in the general case,� the publishers said. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 20 Mar 2000 22:31:43 -0500 From: George Woltman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: Possible V20 issue Hi, At 08:28 PM 3/20/00 -0600, Ken Kriesel wrote: > >If someone has an exponent partially done under version 19.x or 18.x and > >upgrades and it finds a factor, will they get more credit for the factor > >than they lost for the partial LL run? I'm sure if you send an email to [EMAIL PROTECTED] with the exponent you were testing as well as what iteration you were on or your percent complete, then they will be glad to give you the CPU credit. >But someone else may later P-1 factor the number and succeed in finding >the factor. Then all the time to LLtest is uncredited, This happens in the stats at http://www.mersenne.org/top.htm but not the stats maintained by the primenet server. How's that for confusing! Regards, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 20 Mar 2000 22:41:00 -0500 From: George Woltman <[EMAIL PROTECTED]> Subject: Mersenne: V20 beta - round 2 Hi all, Thanks to all the beta testers of v20, you found a lot of bugs!! The 2nd beta is now ready. If you downloaded the first beta you should replace it with the new beta. You can download it from ftp://entropia.com/gimps/v20/p95setup.exe (the fancy installation program) or ftp://entropia.com/gimps/v20/prime95.zip (a plain old zip file) The whatsnew.txt file reads as follows: New features in Version 20.1 of prime95.exe - ------------------------------------------- 1) A bug in the new GCD code was fixed. 2) Timings in the P-1 stage are no longer cumulative. There is a new feature in undoc.txt for those that prefer cumulative timings. 3) Messages are now output prior to beginning the lengthy GCD. 4) The FactorOverride undocumented feature (not for use with PrimeNet) now supports factoring to a deeper level than prime95 would ordinarily factor. 5) A bug where the worktodo.ini entry was not removed if P-1 found a factor was fixed. 6) If P-1 finds a factor it now deletes any Lucas-Lehmer intermediate files. 7) A crash bug when continuing from a P-1 stage 2 save files with different available memory parameters was fixed. 8) Resuming an LL test now outputs a line to the screen, 9) The Test/Status display now correctly calculates the estimated completion time for an LL test when P-1 factoring is in progress. 10) Advanced/Factor menu choice was deleted. 11) A bug in computing P-1 stage 2 percentage complete was fixed. Have fun, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 20 Mar 2000 22:18:51 -0800 From: Stefan Struiker <[EMAIL PROTECTED]> Subject: Mersenne: Releasing Exponents Reserved During A Malfunction TWIMC: It's possible to download V20.1.1 ( or anything else) to the wrong directory, missing the whole point of an update process. Re-running the setup program with the correct target directory solves the problem, except that you've re-registered as an apparently new account even though accountname, password and so on are the ones you've always used. Contacting PrimeNet picks up new exponents and merges them with your existing account, although with incorrect completion dates. One further problem remains: releasing the incorrectly mustered exponents. How do I go about doing this? Thanks In Advance, Stefanovic _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 21 Mar 2000 10:03:57 +0000 From: Alexander Kruppa <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: Possible V20 issue George Woltman wrote: > Correct. However, if you do find a factor you will get credit. In fact > you get credit for trial factoring up to the size of the factor. Umm.. I found some 30-digit factors with moderate bounds. Does that mean I'd get credit for trial-factoring up to 100 bits? Trial factoring that far would take many centuries, so the top producers list might soon be populated with lucky P-1 factorers, no? Ciao, Alex. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 21 Mar 2000 20:03:20 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? On 20 Mar 00, at 19:01, Stefan Struiker wrote: > LONDON , March 17 � Two publishers are offering a > million dollars to anyone who can prove that all > even numbers are the sum of two prime > numbers. No one has cracked the problem in the > more than 250 years since it was first posed, and > Friday�s announcement indicated the publishers > aren�t too worried about having to pay up. The piece on BBC Radio 4's "Today" program suggested that the publishers would only lose whatever money they paid in as a premium to their insurance company against the possibility that a proof would be found. Since it appears that noone has any real idea about how to set about the job, an eminent mathematician suggested that $100 would be a reasonable premium. I think it's probably a lot more likely that someone will claim $250,000 for finding a 1,000,000,000 digit prime number this year than that Goldbach's Conjecture will be proved in my lifetime. Of course, a counterexample to Goldbach could crop up at any time. Have fun ... Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 21 Mar 2000 20:03:20 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: IRC? On 20 Mar 00, at 17:54, Nathan Russell wrote: > When I was in distributed.net, there was an official IRC channel in which > people could ask questions and discuss the project much more rapidly than > is possible on a mailing list. The problem here is that using IRC you only get immediate response from those who happen to be online at the time. Personally I dislike IRC for two reasons:- (1) IRC (like voice telephone) is on-line and you therefore tend to mouth off before thinking out a logical, coherent reply; (2) Previous experience with joining an IRC group, leaving soon afterwards but taking ages to lose the vast pile of commercial spam which seems to be attracted to anyone who uses IRC at all. > It has occured to me that this could be something positive for GIMPS. Provided that someone competent could moderate it. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 21 Mar 2000 15:59:34 -0500 From: "Vincent J. Mooney Jr." <[EMAIL PROTECTED]> Subject: Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? At the new gigahertz speed, it would not take that long to check out all even numbers, would it? :-) :-) Or find an exception less than 10^100 or so. At 07:01 PM 3/20/00 -0800, you wrote: > > $1 million math challenge issued > Publishers seek solution to prime-number conundrum > ASSOCIATED PRESS > > LONDON , March 17 � Two publishers are offering a > million dollars to anyone who can prove that all > even numbers are the sum of two prime > numbers. No one has cracked the problem in the > more than 250 years since it was first posed, and > Friday�s announcement indicated the publishers > aren�t too worried about having to pay up. > > > THE THEORY, known as Goldbach�s Conjecture, > was suggested by the Prussian mathematician Christian > Goldbach in 1742. > It�s easy enough to think of an even number that is the > sum of two prime numbers � those which cannot be > divided evenly by any number except themselves. For > instance, 5 plus 7 equals 12, or 67 plus 3 equals 70. But so > far it has been impossible to prove that it works for every > imaginable even number. > Faber and Faber, in conjunction with Bloomsbury > Publishing in the United States, announced the challenge > Friday to promote the coming release of �Uncle Petros and > Goldbach�s Conjecture,� by Apostolos Doxiadis. > > > �Proving it may well be impossible,� the publishers > said, �and it is very probable that only a highly skilled > mathematician would ever be able to produce a proof that > meets the requirements of these rules.� > The publishers set a deadline of March 15, 2002. > To claim the prize, the winner would have to have the > solution accepted for publication by a reputable > mathematical journal and then have the proof confirmed by > at least four members of a six-judge panel appointed by > Faber and Faber. > However, you don�t have to buy a copy of �Uncle > Petros� to compete, the publishers said. > �By offering this challenge, neither Faber and Faber > Limited nor Bloomsbury Publishing are representing or > warranting that the validity of Goldbach�s Conjecture is > capable of proof in the general case,� the publishers said. > > >_________________________________________________________________ >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: Tue, 21 Mar 2000 16:39:39 EST From: "Nathan Russell" <[EMAIL PROTECTED]> Subject: Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? >From: "Vincent J. Mooney Jr." <[EMAIL PROTECTED]> >To: [EMAIL PROTECTED] >Subject: Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? >Date: Tue, 21 Mar 2000 15:59:34 -0500 > >At the new gigahertz speed, it would not take that long to check out all >even numbers, would it? :-) :-) > >Or find an exception less than 10^100 or so. Okay, your first statement is obviously intended flippantly. The second, OTOH, looks good on the surface. However, even assuming that we can check a trillion (I am using the American meaning of trillion, 1,000,000,000,000= 1000 billion = 1 million million, or 10^12) even numbers per second on one computer for each person on Earth, it will take (5*10^87)/(6*10^9) seconds to check them to one googol (the pseudoformal way of stating 10^100). This is equal to 8.33*10^77 seconds. I will abbreviate this number and future numbers as 8.33E87, since it is easier to type. 8.33E77 seconds 2.31E74 hours 9.65E72 days 1.38E72 weeks 2.94E70 years This is about eight thousand times as many years than there are atoms in the sun: 2E30 metric tons = 2E42 grams = 1.2E66 atoms of pure hydrogen-1, which the sun is not. We can certainly attempt to find a counterexample, and I would not be surprised if an idle-time project to do just this were started. However, I would be highly surprised if the search (if unsuccessful) made it into the googol range, especially since finding even one probable prime, yet alone two, takes more than one clock cycle, and a terahertz processor (which is what I figured on) would certainly overheat in seconds if it were made of current materials. Giving a computer to every person on the planet, OTOH, is an admirable goal, and one that would benefit mankind in far more ways than disproving the Goldbach Conjecture would. Quantom computing might be adapted for this, but there is so much hype on that topic that it is hard to know what the truth is. Regards, Nathan Russell ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 21 Mar 2000 23:21:42 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: (OTT) Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? On 21 Mar 00, at 15:59, Vincent J. Mooney Jr. wrote: > At the new gigahertz speed, it would not take that long to check out all > even numbers, would it? :-) :-) _All_ even numbers? However big an even number is, I can always make a bigger one by adding 2. Or doubling it. A negative search for a counterexample is as bad a "proof" as my casual observation that every not-pink object I can see at the moment happens not to be an elephant, therefore all elephants are pink ;*) A proof of Goldbach's Conjecture would surely have to use induction in some way. > > Or find an exception less than 10^100 or so. Suppose we want to check whether 10^100 conforms to Goldbach's Conjecture. We would really need a list of all primes up to (very very nearly) 10^100 to do that. That's a _big_ list. What I mean is that 10^100 = 3 + (10^100 - 3) is one possible breakdown. But I don't know offhand whether (10^100 - 3) is prime, and proving that it is might take some considerable time. If that fails, I can skip 5 + (10^100 - 5) and 7 + (10^100 - 7) since in each case the larger number is clearly composite. But, in general, I'd have to check whether (10^100 - p) is prime for every odd prime p until I find a prime (proving that Goldbach's Conjecture holds for the specific odd number 10^100) or until p > 0.5 * 10^100 (a counterexample!) Even with terahertz processors, a brute force search up to a "small" limit like 10^100 would take a very considerable amount of time. There are no counterexamples up to a fairly large number and, heuristically, one would expect that it would be decreasingly likely that increasingly large even numbers could not be decomposed as the sum of two primes, since the number of decompositions increases faster than the density of suitable primes decreases. So it looks as though Goldbach is very probably right. But whether this is provable, or whether Goldbach's Conjecture is a(nother) victim of Godel's Theorem, is not (to the best of my knowledge) known. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 21 Mar 2000 23:35:28 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: (OTT) Re: Mersenne: $1 Million For Proof Of Goldbach's C Earlier I wrote [... snip ...] > (proving that Goldbach's Conjecture holds for the specific > odd number 10^100) [... snip ...] Aarggh! I must have consumed too much "pink elephant juice". 10^100 is, of course, _even_. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 21 Mar 2000 22:31:40 -0600 From: Ken Kriesel <[EMAIL PROTECTED]> Subject: Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? >On 20 Mar 00, at 19:01, Stefan Struiker wrote: > >> LONDON , March 17 � Two publishers are offering a >> million dollars to anyone who can prove that all >> even numbers are the sum of two prime >> numbers. No one has cracked the problem in the >> more than 250 years since it was first posed, and >> Friday�s announcement indicated the publishers >> aren�t too worried about having to pay up. I'm guessing the actual conjecture is worded something like, Each even number can be expressed as the sum of exactly two unequal primes. Otherwise the question would already be answered, as all evens can be expressed either as a summation of the value two, or as n= n/2 + n/2, in which n/2 may be prime or not, but if not, could themselves be expressed as the sums of primes. I wonder if this could fall to the approach used in the 4-color map problem. (If I recall correctly, a combination of subdivision into many subcases, followed by a lot of computing time.) Could someone post the actual wording of the conjecture? Ken _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 22 Mar 2000 07:08:22 +0100 From: "Martijn Kruithof" <[EMAIL PROTECTED]> Subject: Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? - ----- Original Message ----- From: "Ken Kriesel" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, March 22, 2000 5:31 AM Subject: Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? > >On 20 Mar 00, at 19:01, Stefan Struiker wrote: > > > >> LONDON , March 17 - Two publishers are offering a > >> million dollars to anyone who can prove that all > >> even numbers are the sum of two prime > >> numbers. No one has cracked the problem in the > >> more than 250 years since it was first posed, and > >> Friday's announcement indicated the publishers > >> aren't too worried about having to pay up. > > I'm guessing the actual conjecture is worded something like, > > Each even number can be expressed as the sum of exactly two unequal primes. > I guess not, 2 is 1+1 so I think (as stated in the message above) just _two_ primes (Btw this implies that every odd number except 1 can be expressed as the sum of three primes) > Otherwise the question would already be answered, as all evens > can be expressed either as a summation of the value two, or as > n= n/2 + n/2, in which n/2 may be prime or not, but if not, could themselves > be expressed as the sums of primes. > > I wonder if this could fall to the approach used in the 4-color map problem. > (If I recall correctly, a combination of subdivision into many subcases, > followed by a lot of computing time.) > > Could someone post the actual wording of the conjecture? > > Ken > > _________________________________________________________________ > 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: Wed, 22 Mar 2000 00:02:02 -0800 From: Stefan Struiker <[EMAIL PROTECTED]> Subject: Re: Mersenne: $1 Million For Proof Of Goldbach's Conjecture? Ken Kriesel wrote: > > Could someone post the actual wording of the conjecture? > > Ken > Ken: For Goldbach's Conjecture, including a facsimile (in German) of his famous letter to Euler, go to: http://www.informatik.uni-giessen.de/staff/richstein/ca/Goldbach.html Best Wishes, Stefanovic _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 22 Mar 2000 05:14:39 EST From: "Nathan Russell" <[EMAIL PROTECTED]> Subject: Mersenne: Another Conjecture? This is something I've been toying with the last few days. I can prove that all even positive integers except 2, 4 and 8 can be written as the sum of Mersenne primes. All above 21 are either 0, 1 or 2 mod 3, and are therefore the sum of either 1, 2 or 3 sevens with a sufficient number of 3's thrown on top. I am sure this can (and should) be stated far more formerly, but my real question is this: Is it possible to strengthen this conjecture, say by putting a ceiling on the number of times that any one prime need be repeated? Such a statement can also be made for the odd positive integers. 1, 5 and 11 are the only exceptions that need be made, since all odds above 13 can be written as the sum of an even number above 8 and a Mersenne prime. To my knowledge, this line of inquiry is original with me. However, if anyone can think of any work in this direction, please by all means let me know. Regards, Nathan Russell ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 22 Mar 2000 11:56:18 +0100 (MET) From: [EMAIL PROTECTED] Subject: Re: Mersenne: Another Conjecture? "Nathan Russell" <[EMAIL PROTECTED]> Nathan Russell observes: > This is something I've been toying with the last few days. > > I can prove that all even positive integers except 2, 4 and 8 can be written > as the sum of Mersenne primes. > > All above 21 are either 0, 1 or 2 mod 3, and are therefore the sum of either > 1, 2 or 3 sevens with a sufficient number of 3's thrown on top. > I am sure this can (and should) be stated far more formerly, but my real > question is this: Is it possible to strengthen this conjecture, say by > putting a ceiling on the number of times that any one prime need be > repeated? > No. Let e1 < e2 < ... be the exponents of the Mersenne primes. If this sequence is finite, say ending at ek, then only finitely many numbers are representable if we bound the number of summands. Next suppose there are infinitely many Mersenne primes. We can bound the partial sum M(e1) + M(e2) + ... + M(ek) < 2^e1 + 2^e2 + ... + 2^ek < 1 + 2 + 4 + ... + 2^(ek) = 2^(ek+1) - 1. To represent M(e(k+1)) as a sum of these, some summand must be repeated at least 2^(e(k+1) - ek - 1) times. Both e(k+1) and ek are primes. It is an easy exercise to show that there can be arbitrarily large gaps between adjacent primes and hence between adjacent Mersenne exponents. Another proof starts with a bound m on the number of times each summand is used. Using M(e1) through M(ek) we can form at most (m + 1)^k different sums. Show that M(e(k+1)) > (m+1)^k for large k, whatever the choice of m. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 22 Mar 2000 05:26:46 -0800 From: Paul Leyland <[EMAIL PROTECTED]> Subject: RE: (OTT) Re: Mersenne: $1 Million For Proof Of Goldbach's Conjec ture? > From: Brian J. Beesley [mailto:[EMAIL PROTECTED]] > What I mean is that 10^100 = 3 + (10^100 - 3) is one possible > breakdown. But I don't know offhand whether (10^100 - 3) is prime, > and proving that it is might take some considerable time. If that However, proving it is composite is very easy. It is divisible by 13. > fails, I can skip 5 + (10^100 - 5) and 7 + (10^100 - 7) since in each > case the larger number is clearly composite. But, in general, I'd > have to check whether (10^100 - p) is prime for every odd prime p > until I find a prime (proving that Goldbach's Conjecture holds for > the specific odd number 10^100) or until p > 0.5 * 10^100 (a > counterexample!) 1.96 seconds on a PII-300 and Francois Morain's ECPP program shows that 10^100-797 is prime. Running a composite test on all the other larger candidates took 1.80 seconds in total. Paul _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 22 Mar 2000 20:01:04 +0200 From: Jukka Santala <[EMAIL PROTECTED]> Subject: Re: Mersenne: IRC? "Brian J. Beesley" wrote: > The problem here is that using IRC you only get immediate response > from those who happen to be online at the time. That's not a problem, it's the purpose of IRC... ;) Regardless, I've (intermittently) keeping up the channel #Mersenne on DALnet IRC network at irc.dal.net (You need to grab a client from http://www.mirc.com if you use Windows or http://www.irchelp.org otherwise to connect) and people are welcome there, but we need some people or it'll be rather boring. I intended to use/mean this channel in the same way www.mersenne.org as a sort of "All distributed projects" channel. > (1) IRC (like voice telephone) is on-line and you therefore tend to > mouth off before thinking out a logical, coherent reply; s/on-line/real-time. Actually, the same holds true for instant messengers and the way most people use e-mail. It's also very much like the evil "Real World" you hear legends being told about ;) In other words, it isn't just a disadvantage, there are some advantages to that too. As for myself, the main problem is that 99% of the time nothing is happening, I pay per minute online, not to mention keeping me from doing something useful, and when something interesting happens I'm never there anyway because of timezones. On the positive side, you can have automated interactice services (bots) that for example announce changes in web-sites etc. as things happen, and presence on one of the IRC networks will always attract curious people who may decide to join the effort. > (2) Previous experience with joining an IRC group, leaving soon > afterwards but taking ages to lose the vast pile of commercial spam > which seems to be attracted to anyone who uses IRC at all. They're called channels, and mostly that depends specifically on the channel you join. If you get a message from a stranger to go to some channel for example, don't join, because those kinds of channels have usually been set up by somebody for the bizarre reason of getting high usercount alone and have nothing happening but other such people advertising their channels! Also, setting yourself "Invisible" from the mIRC login settings will remove you from the public user listings so people can't message you with advertisements out of the blue. However these days most IRC networks do pretty good work weeding out those ads. -Donwulff _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 22 Mar 2000 17:23:48 EST From: [EMAIL PROTECTED] Subject: Mersenne: Mlucas 2.7a: Solaris 2.5 binary available Dear all: Bill Rea just sent me a binary of Mlucas 2.7a which will run under Solaris 2.5 - apparently a lot of the older Sparcs still run this version of Solaris, and the binary compiled for Solaris 2.6 and 2.7 won't run under 2.5. This binary (like all the others) is available via ftp://209.133.33.182/pub/mayer/README.html Bill also sent me a detailed set of per-iteration timings for the above binary on a 167MHz Sparc 1 with 512KB L2 cache. These timings are quite interesting. For FFT lengths below 256K, the Sparc 1 behaves very similarly to an Alpha ev4. But above 256K the ev4 performance suffers somewhat of a deterioration, whereas the Sparc 1 keeps chugging onward: at 320K the Sparc timings match those of my 200MHz Alpha ev4, and above 320K they are significantly better, despite the Sparc's slightly lower clock speed. Perhaps this is the Sparc 1's non-blocking cache at work. The Sparc 1 also has a near-linear iteration time trend up to very long runlengths, and beyond 1024K has virtually identical relative performance (normalized by clock rate) as a state-of-the-art Sparc E450 with a much bigger 4MB L2 cache. Interesting... The upshot is that older Sparcs can still contribute quite valuable work for GIMPS: on a 167MHz Sparc 1 as above, double-checking an exponent ~5M should take about 3 weeks. First-time testing an LL exponent ~10M should take around 3 months, which is long, but still quite a bit faster than my P166 laptop needs, and well within the 120-day limit for manual test assignments. (And such assignments can also be extended by up to another 120 days, if need be.) Complete timings are at ftp://209.133.33.182/pub/mayer/gimps_timings.html Cheers, - -Ernst p.s.: I would also appreciate some timings for SGI workstations with pre-R10000 MIPS processors. If you have an SGI with a MIPS 3000 to 8000 version CPU and want to do some timings, please do all the 128K-4608K FFT length timing tests listed on the README page, and send them to me, along with the output of the Irix 'hinv' command. _________________________________________________________________ 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 #709 ******************************
