Mersenne Digest Sunday, July 25 1999 Volume 01 : Number 603 ---------------------------------------------------------------------- Date: Fri, 23 Jul 1999 16:44:39 +0200 From: Alex Kruppa <[EMAIL PROTECTED]> Subject: Re: Mersenne: Worth it? Lucas Wiman wrote: > P-1 factoring is based upon Fermat's little theorem which states that > > [...] > What if we use 2 as a base? Well, for mersenne numbers, this might be to The problem is that 2 is not a primitive root (mod Mp). From a computers point of view, the mod Mp operation is a rotate and add, so if you start with a single bit set (2d = 10b), that bit will rotate around the p possible positions like mad but you�ll only ever get values of 2^n, 2^E == 2^n (mod Mp). So you could only find factors of the form 2^n-1. Ciao, Alex. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 23 Jul 1999 14:36:35 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Re: p-1 algorithm Lucas Wiman wrote, about the p-1 algorithm: >What if we use 2 as a base? Unfortunately, 2 is not an eligible base for the powering. Example: let's attempt to factor 2^11 - 1 = 23*89 via p-1. The smaller factor has p-1 = 22=2*11, so raising the base to the powers 2 and 11 and gcd'ing should reveal the factor. Let's denote the product of the small primes used for the powering by #, and try bases A = 2 and 3: A=2: 2^22 mod M11 = (2^11)^2 mod M11 == 1. You can continue to power until you're blue in the face, and all you'll ever get is one, i.e. gcd(a^#-1, M11) = 0. A=3: 3^22 mod M11 = 1013, so gcd(a^#-1, M11) = gcd(1012,2047) = 23. For Mersennes you can in fact use any base you like, as long as it's not a power of 2. EXERCISE: We wish to attempt to find an odd prime factor p of a number N via the p-1 method. What is the mathematical requirement for A to be an eligible base for the powering? EXERCISE: which movie is the following quote from? "...and three shall be the number of the counting. Four shalt thou not count, nor two, excepting thou then proceed to three. Five is right out..." - -Ernst _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 23 Jul 1999 12:59:33 -0700 From: "Joth Tupper" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: p-1 algorithm A small observation, maybe even trivial: Viewed over a finite ring (field) of Mp = 2^p - 1 elements the polynomial x^p - 1 splits (completely, of course) into linear factors of the form (x - 2^r) for 0 <= r <= p-1. Alternatively, x^p - 1 = (x-1)(x-2)(x-4)(x-8)(...)[ x - 2^(p-1)] (mod Mp) As a buddy once asked, "So what?" I rarely had a good answer for him and I do not have one now. Joth - ----- Original Message ----- From: <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, July 23, 1999 11:36 AM Subject: Mersenne: Re: p-1 algorithm > Lucas Wiman wrote, about the p-1 algorithm: > > >What if we use 2 as a base? > > Unfortunately, 2 is not an eligible base for the powering. > > Example: let's attempt to factor 2^11 - 1 = 23*89 via p-1. The smaller > factor has p-1 = 22=2*11, so raising the base to the powers 2 and 11 > and gcd'ing should reveal the factor. Let's denote the product of the > small primes used for the powering by #, and try bases A = 2 and 3: > > A=2: 2^22 mod M11 = (2^11)^2 mod M11 == 1. You can continue to power until > you're blue in the face, and all you'll ever get is one, i.e. gcd(a^#-1, M11) > = 0. > > A=3: 3^22 mod M11 = 1013, so gcd(a^#-1, M11) = gcd(1012,2047) = 23. > > For Mersennes you can in fact use any base you like, as long as it's not > a power of 2. > > EXERCISE: We wish to attempt to find an odd prime factor p of a number N > via the p-1 method. What is the mathematical requirement for A to be an > eligible base for the powering? > > EXERCISE: which movie is the following quote from? > > "...and three shall be the number of the counting. Four shalt thou not count, > nor two, excepting thou then proceed to three. Five is right out..." > > -Ernst > _________________________________________________________________ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers > _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 23 Jul 1999 20:16:35 -0500 (CDT) From: Conrad Curry <[EMAIL PROTECTED]> Subject: Re: Mersenne: Mersenne Trivia (was Re: p-1 algorithm) On Fri, 23 Jul 1999 [EMAIL PROTECTED] wrote: > > EXERCISE: which movie is the following quote from? > > "...and three shall be the number of the counting. Four shalt thou not count, > nor two, excepting thou then proceed to three. Five is right out..." > > -Ernst Too easy. Here's more of a challenge, who wrote this about the perfection of the number six? "For six is the first number that is filled by conjuction of the parts, the sixth, the third, and the half: which is one, two, and three; all which conjoined are six. Parts in numbers are those that may be described by how many they are, as a half, a third, a fourth, and so forth. But four being in nine, yet is no just part of it: one is the ninth part, and three the third part. But these two parts, one and three, are far from making nine the whole. So four is a part of ten, but no just part: one is the tenth part, two the fifth, and five the second: yet these three parts one, two, and five, make not up full ten, but eight only. As for the number of twelve, the parts exceed it. For there is one the twelfth part, six the second, four the third, three the fourth, and two the sixth. But one, two, three, four, and six, make about twelve, namely sixteen. This by the way now to prove the perfection of the number of six, the first (as I said) that is made of the conjuction of the parts..." _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 23 Jul 1999 22:12:11 -0400 From: Chris Nash <[EMAIL PROTECTED]> Subject: Re: Mersenne: Worth it? Heya Lucas > P-1 factoring is based upon Fermat's little theorem which states that > with gcd(a,p)=1, p prime, a^(p-1)==1 mod p > What if we use 2 as a base? Well, for mersenne numbers, this might be to > our advantage. Note that 2^n==1 mod Mn, hence 2^q==2^(q mod n) mod Mn. Unfortunately we're in a circular argument at this point. The factors of 2^p-1 are of the form 2kp+1 - also, even for n composite, the 'new' (primitive) factors of 2^n-1 are of the form kn+1. So any prime factor q has q-1 divisible by n, and we already have 2^n=1 mod Mn and hence mod q... Alternatively, think of the values 2^0, 2^1, 2^2... 2^(n-1), which would be ALL the values 2^q mod Mn can possibly take. So if this method found a factor, it would be a common factor of 2^q-1 and 2^n-1, in other words, just one of the known algebraic factors 2^gcd(q,n)-1. P-1 is good up to a point... the prime factors P it finds will by definition either have ALL factors of P-1 very small, or your initial base is already a high power (which is very unlikely). It's good to find the 'smooth' P-1's - put it another way, the factors the P-1 algorithm finds are themselves very easy to prove prime or composite. While the vast majority of primes (and thus potential factors) certainly do not always have small factors in P-1. It will catch a few several digit factors - after that, you've pretty well exhausted the lowest cherries off the tree. Chris _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 24 Jul 1999 02:14:37 -0400 From: "Rick Pali" <[EMAIL PROTECTED]> Subject: Mersenne: Prime95 as a windows service This may be a silly question but I've only recently had the need for Prime95 having used the NT service version before. If Prime95 is running as a service, how does one get at the user interface? It doesn't have a separate interface executable like the NT service version. Do I just start the executable manually? I don't want to just go ahead and do that because it *used* to corrupt the safe file and I'm not sure that it still doesn't. :-) Even still, I don't want to start another copy crunching. If anyone can let me know, I'd appreciate it. Rick. - ----- [EMAIL PROTECTED] http://www.alienshore.com/ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 24 Jul 1999 07:23:55 -0500 From: Gary Diehl <[EMAIL PROTECTED]> Subject: Re: Mersenne: Prime95 as a windows service Rick, I just doubleclick on the system tray icon... I hope this works for you too. Gary Diehl Rick Pali wrote: > > This may be a silly question but I've only recently had the need for Prime95 > having used the NT service version before. > > If Prime95 is running as a service, how does one get at the user interface? > It doesn't have a separate interface executable like the NT service version. > Do I just start the executable manually? I don't want to just go ahead and > do that because it *used* to corrupt the safe file and I'm not sure that it > still doesn't. :-) Even still, I don't want to start another copy crunching. > > If anyone can let me know, I'd appreciate it. > > 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 _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 24 Jul 1999 12:46:06 -0500 From: "Chris and Carrie Harrison" <[EMAIL PROTECTED]> Subject: Mersenne: interations speeds of p3 500s and greater What are the interation speeds of a p3-500 or p3-550? Thanks Chris _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 24 Jul 1999 16:30:01 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Mersenne: Hardware FAQs All, On the subject of a hardware type FAQ/section in FAQ, here are the few FAQs that I could think of off the top of my head. I'm guessing others can think of more. I'm really not qualified at all to write about win95/nt/os2 questions. I've never used os2/nt, and I haven't used win95 in over 3 months. I haven't had it on one of my computers in over 6 months. I never ran any Mersenne related software on any of these platforms. Etc... Q: Does Prime95 decrease battery life on a laptop? Q: What is a Roundoff error? Is my computer broken? Q: Why does my computer start making noises when I run Mprime/prime95/NTprime? These I can answer pretty well. For other suggested questions, I should probably be able to get the answers out of the archives. - -Lucas P.S. Are archives available past February 1998? _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 24 Jul 1999 22:23:32 -0700 From: Luke Welsh <[EMAIL PROTECTED]> Subject: Re: Mersenne: Mp and E-Cash At 08:58 PM 7/21/99 +0100, Brian J. Beesley wrote: >On 20 Jul 99, at 0:26, Luke Welsh wrote: > >> Eventually, PrimeNet should be able to move small (and large) >> amounts of money around the world with ease. >> >Unfortunately, e-cash opens several other cans of worms! [....] >what happens if the winner comes from an "unfriendly" country? >Can we transfer e-cash to a citizen of, e.g., Iraq, How does this differ from the current situation? What if Nayan was North Korean? The can of worms is already open. GIMPS/PrimeNet would not be the only organization in the e-cash boat. It is a problem to be worked out by the big boys. (Anyway, if we're in that boat, at least we have our can of worms to fish with :-) >> We really do need a formula for [e]. Set aside $25,000 and each >> x% improvement in GIMPS throughput wins x% of the $25,000? > >What's wrong with having a panel (possibly consisting of previous >Mersenne prime discoverers) to evaluate any contenders for this & >judge how much, if any, of the fund should be awarded for each >improvement? Sensible idea. The panel could come up with their own set of rules. I'm not sure I'd want to be on such a panel unless my vote was anonymous ("Sorry, Heloisa, but I think your idea was worth only...."). >> Award $10,ooo for each new Mp, regardless of size. Suppose M(7777777) >> is prime. The finder is credited $10,ooo (to be awarded when GIMPS >> finds a decamega prime). The decamega finder also gets $10,ooo. [...] >This would seem to be a bit unfair. I think the decamega finder >should definitely get a large share (25% minimum). See remarks, below. >The point here is >that, if I can freely download a program & use it to check Mersenne >numbers in the 10 million digit range, why should I bother to >contribute to a cooperative project if, by doing so, I'm going to >have to give up almost all the prize if I get lucky? We didn't have this problem when there was no prize. Can't we simply promote it as a $10,000 prize, not a $100,000 prize? My counter-argument is Distributed.net. They are going for the US$10,000 offered by RSA Labs. http://www.distributed.net/rc5 10% of that will go to the winner. And I *think* they are bigger than GIMPS. S@H is much bigger. >The fact that >even poor people are prepared to throw a few dollars at the remote >chance of a lottery jackpot would tend to indicate that a few dollars >recompense for CPU cycles contributed to a cooperative project will >not attract contributors in the way that a large cash prize will. Do we have a feel for how many contributors have been attracted solely by the large cash award ? >I'd prefer to keep a slice (smaller than the discoverer's slice) for >discoverers of non-qualifying Mersenne primes, but don't pay anything >out until the range up to 10 million digits is (more or less) >completely searched. Then divide it equally between them. Carry the >sum forward if it happens that we discover that we already know all >the Mersenne primes with less than 10 million digits. It might be years before the range has been completely checked. Double checked? What's the phrase? "a sticky wicket"? >> Is $10,ooo about right? [....] >.. if we try to link the amount of the prize to income, then how >much would we have to pay Bill Gates if he won it? Exactly my point..... "Is $10,000 about right?" I still favor something along the lines of: [a] $10,ooo for decamega Mp finder [b] $20,ooo to be split amongst all other Mp finders [c] $25,ooo for algorithm improvements [d] $45,ooo for 1st LL, 2nd LL, factors, Cunningham factors There's another reason I like [d]. If [d] were in place, I'd stand a better chance of convincing a couple large companies to come onboard GIMPS and funnel their earnings to charity. Now Gordon and Glenn see things differently. At 04:50 PM 7/22/99 +0100, Gordon Spence wrote: >In fact the answer is simple, the person who discovers it is >*entitled* to it, end of story. >I would hope that they would *choose* to donate some to George >and Scott, but if they decide not to well then that is up to them. I would also hope so, but I think this is unlikely... taxes, family pressures, etc. >Direct quote from eff page >> Through the EFF Cooperative Computing Awards, EFF will confer prizes of: >> $50,000 to the first individual or group who discovers >> a prime number with at least 1,000,000 decimal digits > >Seems clear to me, the GIMPS s/w is given away free to the individual >who runs the test. "individual or group". It seems clear to me that the award should go to the group, since this is not an individual effort. I think eff.org was very deliberate in their language. >Now that would be interesting, what would the EFF do then given that >they are entirely about freedom and the rights of the infividual. I think they foresaw many of the amicable disagreements we are experiencing. I just *knew* this award business would be a "tar baby" :-( >As a Mersenne prime discoverer it would appear that I would be on the panel(s) >that have been suggested, and my vote goes to allowing the discoverer to keep >it and do what their conscience tells them is the right thing to do. Do you get one vote, or 1/2? Do I split my vote with Walt Colquitt? Can Walt delegate his half to me? Does Alex Hurwitz get two? How many votes does George Woltman get? Landon Noll is disqualified. Does Arial Glenn get his vote(s)? Vote by majority or plurality? What a mess. >I don't agree with Luke's sentiments about orderly progress, having >already tested one number in the 20m range. OK, let's talk about this. >As long as they all get tested does it matter in what order? But they all won't get tested, not for another 20+ years. After the 10Mdigit prime, there will be the 100Mdigit prime, then the giga-digit prime. GIMPS has been lauded for conducting an orderly search, even more so for double checking. Jumping ahead, the search space will once again become horribly fragmented -- a giant step backwards into the Cray era. Having said that, I am confident that there will be nothing in V19 to prevent one from jumping ahead. I just don't think it should be encouraged. And I agree, it is a fine line to draw. To quote eff.org again: "EFF hopes to spur the technology of cooperative networking..." Perhaps another collective will form, an modern version of the Amdahl group .... just look for the World's Largest Prime, one that has 10 million digits? Since we know there are an inifitude of primes, I do not find such a search very interesting. I would wish them luck, but it's just not something for me. At 02:55 PM 7/22/99 -0400, Glenn McLaren wrote: >I agree with Gordon.[...] >The moment you start splitting the prize is the moment someone else >will release software in competion to us, I think we will see another group form regardless. I will not join them as I do not think their discoveries will contribute very much. Others will disagree and that's OK. So I respectfully stand by my position. >Gordon Spence (finder of M2976221 which earned me precisely $0.00 <G> ) I, however, garnered a free pitcher of beer! Unfortunately, it was mass produced American beer, so I think you got the better deal. - --Luke, who'd sure like a Schneider Weiss right now :-( _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 25 Jul 1999 00:44:23 -0600 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Mp and E-Cash > >The point here is > >that, if I can freely download a program & use it to check Mersenne > >numbers in the 10 million digit range, why should I bother to > >contribute to a cooperative project if, by doing so, I'm going to > >have to give up almost all the prize if I get lucky? > > We didn't have this problem when there was no prize. Can't we simply > promote it as a $10,000 prize, not a $100,000 prize? There is a problem though. Neither GIMPS nor Primenet have *any* legal claim for any prize for any discovery made using Prime95/NTPrime/mprime, or any code modified and compiled that was based on George's code. Let's face it, there is nothing stipulated in the use of any of those programs, or the use of Primenet as a coordinator, that implies in any way shape or form that they would legally be entitled to any prize money at all. I don't know if that's fair or not, I won't get into that. But the discoverer of a prime found using GIMPS and/or Primenet would receive all the money him/herself and then it's up to him/her what to do with it; whether sharing some with George/Scott is something they would do is entirely up to them. Unless George/Scott set some legal mumbo jumbo that ties into use of the program/source/services, they're simply not "entitled" to any prize money. For the record, if I won some prize money, you bet I'd want to feed some back to George/Scott for their excellent efforts and to promote further advancements. After all, that is the intent of the EFF prizes. But would I be required to by law? No. > My counter-argument is Distributed.net. They are going for the > US$10,000 offered by RSA Labs. > http://www.distributed.net/rc5 > 10% of that will go to the winner. And I *think* they are bigger > than GIMPS. S@H is much bigger. I would imagine that the way they dole out the prize money is because use of their software implies agreement with certain terms, i.e. that you agree with the prize money disbursement outline. Otherwise, they'd be in the same boat since the prize money is actually offered by RSA. Any bozo could write their own program (well, not any bozo) and hope to find the key, getting all $10K, but if you use the distributed.net software and database, you're agreeing to a software license of sorts that spells out certain things. GIMPS/Primenet doesn't have any such thing. And it was mentioned before...if George and/or Scott setup such a legal contract regarding software usage, there probably would be people writing their own software, hoping to get the big cash all to themselves. And the whole effort of coordinating who works on what exponents could get messy if Scott says that using his Primenet database to check out/in numbers means you agree to share prize money with him. People will start grabbing their own numbers or setting up competing databases of their own or who knows what. I vote for freeware, free usage of Primenet, and just *hope* that any winner of big cash will do the honorable thing and recognize, monetarily, the efforts that George and Scott put into all of this. And again, the first deca-mega-digit prime may not be a Mersenne anyway...who can say? :-) > It might be years before the range has been completely checked. > Double checked? What's the phrase? "a sticky wicket"? That reminds me, I was on vacation the past couple weeks and I ate at "The Sticky Wicket" in Victoria, BC. If you're there, do go there...yummy! > "individual or group". It seems clear to me that the award should > go to the group, since this is not an individual effort. I think > eff.org was very deliberate in their language. If that's the case, it is up to that "group" to decide, in some legally binding way, how prize money is disbursed. I suppose it's too late to worry about such things now, since the $50K prize-winner has been found, but it's something to think about, if we choose to go down that perilous road, sometime before the $100K winner becomes imminent. As such, I think the EFF would have to award the money solely to the individual since no prior stipulations existed between him and George/Scott on how the money would be split. > >As a Mersenne prime discoverer it would appear that I would be on the > panel(s) > >that have been suggested, and my vote goes to allowing the > discoverer to keep > >it and do what their conscience tells them is the right thing to do. > > Do you get one vote, or 1/2? Do I split my vote with Walt Colquitt? > Can Walt delegate his half to me? Does Alex Hurwitz get two? How many > votes does George Woltman get? Landon Noll is disqualified. Does > Arial Glenn get his vote(s)? Vote by majority or plurality? What > a mess. I agree also...like I mentioned above, setting up legalities will only muddle the entire issue and give rise to competing databases and programs. Not that competition is bad, but it will only add to the headaches of coordinating the testing of all exponents, in my opinion. And that's the point...testing all exponents in an orderly fashion, not winning "lotsa money". We need to stay focused, yes? I'd hope that George and Scott continue in their efforts even if they don't get a share of any prize money. After all, they've done all of this for so long *without* the added "carrot on a stick" that the EFF dangled in front of us all. Their "carrot on a stick", prior to the EFF's involvement, has been (I hope) to systematically, and effectively, test all exponents for Mersenne primality, end of sentence. Don't let that change now. Just my $0.02 worth (of course anyone who disagrees with me will be shot!) :-) Aaron _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 25 Jul 1999 03:57:15 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: RE: Mersenne: Mp and E-Cash >Unless George/Scott set some legal mumbo jumbo that ties into use of the >program/source/services, they're simply not "entitled" to any prize money. I'm forced to agree with Aaron, aparently at gunpoint :-) (and I said this a while ago, BTW). Even if they (George and Scott) did this, then there would still be MacLucasUNIX, or everything else in the mers package, as well as Ernst's program, and good ol' lucas.c. Any of these could be used. We've really got to put our feet back on the ground here. If we did put a license change on all of George's program derivitives, we would still have to get Will and Ernst to change their copyrights, and Richard Crandall. In fact, is the DWT patented? If so, Richard Crandall could claim the $100,000 for himself since I think that the programs that have a prayer of finding the Deca-mega prime would use his algorithm. If someone read on George's page "running this software means that you lose most of the prize money." They could do one of 3 things: (1) Say "Oky-doky" and download/run George's program (2) Say "Well, (sensored) you" and continue surfing (3) Say "Where can I get another program?" and find the others > I would imagine that the way they dole out the prize money is because use of > their software implies agreement with certain terms, i.e. that you agree > with the prize money disbursement outline. I didn't find anything specific, but then I didn't try and join them. I either missed it, they just "fudged" over it and hope that no one notices, or the RSA announcment covers this somehow. > And again, the first deca-mega-digit prime may not be a Mersenne > anyway...who can say? :-) Yah, it could be proth, or something. - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 25 Jul 1999 03:26:06 -0700 From: Luke Welsh <[EMAIL PROTECTED]> Subject: RE: Mersenne: Mp and E-Cash At 12:44 AM 7/25/99 -0600, Aaron Blosser wrote: >Neither GIMPS nor Primenet have *any* legal claim for any prize for >any discovery made using Prime95/NTPrime/mprime, or any code modified >and compiled that was based on George's code. Let's face it, there is >nothing stipulated in the use of any of those programs, or the >use of Primenet as a coordinator, that implies in any way shape or >form that they would legally be entitled to any prize money at all. Yeah, but..... At 05:32 PM 7/17/99 -0400, George Woltman wrote: >I'm soliciting everyone's opinion before making a decision. >[....] >a policy needs to be in place before version 19 is released. Until then, none of us will be looking in the decamega range. George is considering the creation of a non-profit corporation for the purpose of dividing the prize money, so the legal issues would be addressed. George asked for opinions on how to *distribute* the money. There's a few more worms in this can. I'm thinking specifically of Ernst, but it could be somebody else. Suppose the lucky program uses PrimeNet (and George's database), but it was not George's program? What a quagmire! One interesting point of Aaron's: >or any code modified and compiled that was based on George's code. George's Merced code should render that code obsolete. - --Luke _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 25 Jul 1999 11:46:21 +0100 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Mp and E-Cash [Not in reply to any specific message - no names, no pack drill] Hey, guys, surely we don't want a war over this? Here are a few relevant points: 1. GIMPS/PrimeNet as a whole constitutes a "team" in so far as we (usually) co-operate loosely with each other in order not to waste time and effort needlessly replicating each other's work. 2. However, it is certainly the case that (a) at present, the first LL test is run by a single individual or team operating their computer system(s) independently of GIMPS/PrimeNet, and (b) at present, the only thing which participants to GIMPS/PrimeNet have agreed is that they will be listed along with George & Scott as co- discoverers in the event that a Mersenne prime is discovered. Run this through the courts if you must (assuming you have endless time & money to waste) but I think most juries would conclude that the prize money should be awarded to the individual discoverer, in the remote chance that any was left after the lawyers had taken their slice. My guess is that making participation to GIMPS/PrimeNet conditional on agreeing to share the prize would be A Big Turn-Off. Though I'm equally sure that the vast majority of participants would indeed share out any award in some more or less sensible way, even in the absence of "guidelines". I certainly agree that some of the "shares" suggested should exist, but perhaps we need to fund them in a different way. (I've already pledged $500 towards a prize fund for discovery of any Mersenne prime which _doesn't_ qualify for the EFF award). As for some of the other points mentioned: Searching for Proth primes is less efficient than searching for Mersenne primes, this is likely to remain the case unless/until someone comes up with a "free" way of executing the remaindering operation modulo k*2^n+1. Also, since there are two parameters to play with, it's going to be harder to coordinate. The positive sides are that there is almost certain to be a 10 million digit Proth prime smaller than the smallest 10 million digit Mersenne prime, and that there are some values of k which seem to yield higher densities of primes than Mersennes (though, equally, there are other values of k for which it is proved that no primes exist). The other LL testing programs available are a lot less efficient than Prime95 and its derivatives. This may change, in time, but it really is dependent on someone with the time and expertise putting in a lot of effort. If anyone really wants to start testing 10 million digit Mersenne numbers now, I would at least urge them to obtain exponents from George, in order to prevent unneccessary duplication of effort. [If George can't be bothered, I'll volunteer to do this task!] Some commercial or adacemic research organization may well claim the EFF prize. In fact, I think this is quite likely for the $100K prize, and almost certain for the bigger prizes. The likes of Sandia already have quite sufficient "clout" to make our effort pale into insignificance, if they put their mind to it. Also, it may have escaped your notice, but IBM (who _still_ have good labs & lots of working capital) recently took over Sequent (a specialist in multi- processor systems). What would be a better demonstration of the power of this particular merger than a system powerful enough to test enough 10 million digit Mersenne numbers rapidly enough to win the prize, even though such a system would certainly cost more than $100,000 to build? There is one other relevant point, which comes back to the value of encouraging co-operation. At present we find approx. 1% of the LL test results submitted are incorrect. Assuming that these are due to random errors, the proportion of incorrect results will increase with run length. By the time we get to exponents in the 10 million digit range (with run times of the order of a year) the error rate may well exceed 10%. To avoid wastage of too much time, it will be valuable to do something like issuing each exponent to two users and having automatic cross-check points during the run (instead of just at the end). Essentially this is just a refinement of double-checking in tandem with first tests, but, if we adopt this, we will surely have co-discoverers (in addition to George and Scott)? If we choose to do this, we will _have_ to get users to accept a condition forcing them to share the prize between them. In which case I don't see that it matters much whether the two users whose computer systems did the calculations split 50:50, or whether it's split 40:40:10:10 with the smaller shares going to George & Scott. But I think that trying to make the smaller shares any bigger than that would tend to cause problems. Sorry if the above seems rambling & inconclusive. It _is_ a difficult problem, and I personally have difficulty in coming to any definite opinion, except that the EFF prize certainly isn't worth destroying the cooperative nature of the project over. Regards Brian Beesley _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 25 Jul 1999 12:03:16 -0400 From: George Woltman <[EMAIL PROTECTED]> Subject: Mersenne: Changes at mersenne.org Hi all, You may have noticed that the web pages at mersenne.org haven't been updated recently. The reason is I've "lost" FTP access to update the pages. So, after several years at lushen.com, I'll be moving the web pages to entropia.com in the coming weeks. Be prepared for a few glitches as domain name servers are updated around the world. Many thanks to Marc Honey and lushen.com for hosting the site the past years and of course to Scott Kurowski for hosting it in the future. Regards, George _________________________________________________________________ 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 #603 ******************************
