RE: Mersenne: Merced and Teraprimes
> > I hope they're at least running P166s by now. > > Well, I'm still running a trio of P100s, as well as a quintet of > PIIs. They're a damn sight better than nothing; running a LL test on > an exponent in the 8 million range would be painful, but not half as > painful as testing a 10 million digit number on a PIII-500! > (Exclamation, not 500 factorial ;-) I have quite a few P-166's and they're all doing double-checks (I let Primenet assign the type of work). I even have a few PPro 200's that are getting double-checks at the moment since those machines are just busy enough to make the "rollingaverage" around the 800 or so mark, making it *seem* like a 160 MHz machine I guess. Oh well, no bother to me. > > Any word on if Mr. Woltman > > will be coding a Merced version of Prime95? > > Intel will have to release the Merced architecture documentation to > developers, and George will have to beg, borrow, steal or maybe even > buy a set of the documentation, and some Merced hardware to practise > on. I thought Intel had already released developer info on the Merced, but maybe they only have the marketing stuff out. Either way, I know that most major manufacturers have already been given to paper info on the Merced specs, including electrical info, instruction set, etc. Whether this is public or not is something else. Like I said, anything I can grab from Intel during the Compaq conference, I will. If it's not covered by NDA, I'll share what I can. > If no-one improves the algorithm, then I'd _expect_ finding a > teraprime to take about 10^9 times as long as finding a gigaprime. > There are (obviously) 1000 times as many iterations to do, each > iteration will take (a bit more than) 1000 times as long to execute, > and the chance that a single exponent will prove to generate a > Mersenne prime is only 1/1000 as much. We're really going to need some factoring code that can do trial factoring well beyond 2^64, to eliminate as many full LL tests as we can. What would be a good bit size to trial factor a teradigit prime up to? I know there's some point in the bell curve to optimize how deep to trial factor for any given exponent... > 10^9 is about 2^30, so I'd suggest a timeframe estimate of 30 Moore's > Law periods between finding the first gigaprime and finding the first > teraprime. So, something of the order of half a century, assuming > (and it's a _big_ assumption - the laws of physics are hard to work > around) that we really can continue to double speed every 18 to 24 > months. I guess we'll just have to see how relevant the breakthrough's in making atom width traces and even quantum computers will be to the "real" world. (to quote: "Reality" is the only word in the language that should always be used in quotes.) > I'm 46 now; I expect to live long enough to see a gigaprime (and > maybe even a 13th human being's footstep on the Moon!), but I very > much doubt I will see a teraprime in my lifetime, unless there is a > major, major advance in the theory. Taking quantum computers to a "real" application might just provide the paradigm switch you're thinking of, several orders of magnitudes of improvement *could* be possible in the next, oh...say 25-30 years. Big "maybe". Aaron _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Merced and Teraprimes
On 29 Jul 99, at 3:03, [EMAIL PROTECTED] wrote: > I hope they're at least running P166s by now. Well, I'm still running a trio of P100s, as well as a quintet of PIIs. They're a damn sight better than nothing; running a LL test on an exponent in the 8 million range would be painful, but not half as painful as testing a 10 million digit number on a PIII-500! (Exclamation, not 500 factorial ;-) > Any word on if Mr. Woltman > will be coding a Merced version of Prime95? Intel will have to release the Merced architecture documentation to developers, and George will have to beg, borrow, steal or maybe even buy a set of the documentation, and some Merced hardware to practise on. > Billiard? Hee hee hee. Yup, I'm British, the only "billiards" I know is a game played with two white & one red ball on a "billiards" table (like a large pool table - interesting enough, it's still called a billiards table, even when snooker is played on it). American cultural "pollution" has wiped out the old meaning of "billion" i.e. 10^12, everyone here uses "billion" meaning 10^9. > <<(The EFF's big money appears to be safe!)>> > > Any projections on when we'll find a teraprime? *grin* > > S. "I want me a Merced!" L. You'll _need_ a Merced, or at least an Alpha - even if someone manages to speed up the algorithm enough to make starting the computation worthwhile. Suppose we could get away with storing just one copy of the work vector - that's > 3.3E12 bits, or 400 GBytes of memory. Even if you could afford that much RAM, IA32 has only a 4GB virtual address space. If no-one improves the algorithm, then I'd _expect_ finding a teraprime to take about 10^9 times as long as finding a gigaprime. There are (obviously) 1000 times as many iterations to do, each iteration will take (a bit more than) 1000 times as long to execute, and the chance that a single exponent will prove to generate a Mersenne prime is only 1/1000 as much. 10^9 is about 2^30, so I'd suggest a timeframe estimate of 30 Moore's Law periods between finding the first gigaprime and finding the first teraprime. So, something of the order of half a century, assuming (and it's a _big_ assumption - the laws of physics are hard to work around) that we really can continue to double speed every 18 to 24 months. I'm 46 now; I expect to live long enough to see a gigaprime (and maybe even a 13th human being's footstep on the Moon!), but I very much doubt I will see a teraprime in my lifetime, unless there is a major, major advance in the theory. Regards Brian Beesley _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Merced and Teraprimes
> < Not everyone > can afford a PIII/550.>> > > I hope they're at least running P166s by now. What's the average > machine a > GIMPSter runs, assuming that the average machine runs 24 hours a day? I > remember it being P181 a while ago, I think. Of course the last time we got into this (poaching thread) we learned that there are people out there who insist on running first time LL tests on P-60's and what not. :-( > <> > > I hope it will be alive, just not x86. The Merced, released in 2000, will > have IA-64 architecture and will _not_ be x86 hardware compatible, only > software compatible (thru emulation). *drool* Any word on if > Mr. Woltman > will be coding a Merced version of Prime95? If he doesn't, someone will. > < billiard 10^15, trillion 10^18 ...>> > > Billiard? Hee hee hee. Think about it. Billiards = 15 balls (not counting cue)...ahh..it all makes sense now! :-) > < press for a > while.>> > > Hee hee hee. Of course, this all depends on "why" the media is trying to get a hold of you. > S. "I want me a Merced!" L. Hehe...I'm going to the Compaq ASE conference in August and I'm sure Intel will have their own "you gotta sign this NDA" suite again. With any luck, they'll have one of their Merced prototypes and I can bug them to death on the details. Aaron _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Merced and Teraprimes
<> I hope they're at least running P166s by now. What's the average machine a GIMPSter runs, assuming that the average machine runs 24 hours a day? I remember it being P181 a while ago, I think. <> I hope it will be alive, just not x86. The Merced, released in 2000, will have IA-64 architecture and will _not_ be x86 hardware compatible, only software compatible (thru emulation). *drool* Any word on if Mr. Woltman will be coding a Merced version of Prime95? <> Billiard? Hee hee hee. <> That's my opinion as well. <> Well, that's _one_ way of looking at it. <> That'd be useful. Register it with search engines. :-D <> Hee hee hee. <> Please tell me you looked up that date and didn't memorize it! <> Evil! Evil! That that word! Aiiieee! <<(The EFF's big money appears to be safe!)>> Any projections on when we'll find a teraprime? *grin* S. "I want me a Merced!" L. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
