<<How about sweetening the pot for anyone who is doing double checking that discovers a mistake in the first LL analysis? >> Hrm. A small reward would be an incentive. Of course, any mistakes found would have to be TRIPLE-checked, so that no one fakes an error (easy) to get the incentive. Of course, anyone who did such a thing would have to be branded a liar and not allowed to participate in GIMPS any more. Double-checking finds errors 1/400 of the time, if I remember correctly. << But the execution of the instructions themselves are probably about the same. I have heard that FP speeds would go up some though... Prime95 may run slower on a Merced at the same clock speed as a Xeon, at least until it's recompiled. Sigh...>> The Merced, if I remember correctly, does NOT have native x86 processing capability, only through emulation. Pentium III Xeons will remain the fastest processors for x86 instructions. But Prime95 written in Merced assembler.... *begins to drool* <<Earlier I posted the notion that Mersenne primes might be used to impress extraterrestrial civilizations. After thinking it thru, I think we can make a stronger arguement than that: Mersenne primes might be the *best* yardstick to *prove* a certain level of technological achievement, perhaps the most logical yardstick.>> Interesting. I like it. But there is one way that it could be a nonreliable indicator of technological achievement. If an exoculture receives our Mersenne prime message, they will know that other life exists in the universe. Assuming we know more Mersenne primes than they do, they will have stumbled onto new "free" primes, at no computational cost. (Verification is easy, if they have a Lucas-Lehmer test and can wait long enough, even with slow computers.) If they're anything like us, one of them will raise the question if WE have heard other civilizations with 37 Mersenne primes and simply repeated the primes out ourselves. That would be a method of faking it. They can, however, definitively put an UPPER limit on our technological achievement. If the other society knows more Mersenne primes than we do, then they may or may not realize the way of "faking" it, while if they know less Mersenne primes, they'll probably realize my point. <<Nope, they will just wonder what they have overlooked that makes Mersenne Primes so basic to a culture.>> Imagine if some exoculture sees our Mersenne prime message, and they feel that THEIR culture is inferior because they only know the first four. And, there is always Myxlptlk's Theorem to consider. <<Except that it might have an unintended effect. Suppose we send out a list of Mersenne primes, and the receiving civilization realizes from the list that we do not know the Theorem of Myxlptlk, which, as every young Golurdian knows, gives an explicit formula for all Mersenne primes.>> What about the following scenario: We send the Mersenne prime message. The friendly Aeraibvca civilization receives it, and notices that we know far fewer Mersenne primes than they do. Of course, they have existed for much longer, and have known about Mersenne primes for hundreds of millennia. Thus, they're surprised that we have found 37 in just a couple of millenia, and most in the last century. We advance at a much faster rate than them. They don't know Myxlptlk's Theorem (from the Golurdians), but they do know a few more interesting facts about Mersenne primes. They even learn a couple of things from us (General Relativity is unknown to them - they only have Ntromdukian gravity), so they send us everything they know about Mersenne primes, and even send us all the primes that they know. Our comparatively primitive Terran mathematicians looks at the new facts, conjectures, and all the new primes, and see some sort of a pattern. Hrm. Separately, the Aeraibvcas and the Terrans couldn't have thought of Myxlptlk's Theorem, but together, they derive an even-easier-to-compute- with version of it (ha ha, Golurdians). Interesting. On further thought, if we're willing to wait long enough, it could be a sort of interstellar game we could play, even if we can't physically get there in a reasonable amount of time. Send the first 10 Mersenne primes to an alien civilization, including enough (hahaha) information for them to deduce our language, or a special LinguaCode specifically designed to be easy for alien civilizations to understand (why make them deal with declensions and conjugations if they don't have to? Here's what a few sentences might look like: Ted picked up a book yesterday, and he quickly read it. Ted thought that the book was very informative. Ted before-pick book before-day. Ted fast before-read book. Ted before-think book before-is very informative. Or something like that.) Then ask them how many Mersenne primes they know. Then send them a couple, and they can send us a couple, so forth. It could be a race. Can we find the 137th Mersenne prime before the Aeraibvcas do? Our superiority as a race is at stake! ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
