On Monday 17 May 2004 04:58, you wrote: > On reading this message, an old principle of logic comes to mind: > > IT'S IMPOSSIBLE TO PROVE A NEGATIVE. > > :)
NO! Remember that (afaik) no-one has even managed to prove that there are an infinite number of Mersenne numbers with prime exponents which are _composite_ - an assertion which, at first sight, seems much more obvious. If it were to turn out that there are a finite number of composite prime-exponent Mersenne numbers, then it would automatically follow that there are an infinite number of Mersenne primes - in which case it would have been possible to "prove a negative". I think you mean, you can't prove by observation that an event never happens. Which is true enough - though a single positive observation disproves that theory. For Mersenne primes, the best we have is a heuristic argument which predicts an infinite number of Mersenne primes... the predicted distribution for "small" exponents matches what we "observe" reasonably well. Regards Brian Beesley _______________________________________________ Prime mailing list [EMAIL PROTECTED] http://hogranch.com/mailman/listinfo/prime
