From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Reply-To: The Great Internet Mersenne Prime Search list <[EMAIL PROTECTED]>
To: The Great Internet Mersenne Prime Search list <[EMAIL PROTECTED]>
Subject: Re: [Prime] 41st Mersenne Prime reported!
Date: Mon, 17 May 2004 06:36:02 +0000
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
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