They are "infinite" and "few" at the same time? ;)
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-----Original Message-----
From: p k <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED]
Sent: Mon, 17 May 2004 100:13:03 -0700
Subject: Re: [Prime] 41st Mersenne Prime reported!
In layman's terms there are infinite number of numbers therefore there are and infinite number of primes. I think it safe to say that since there are infinite number of primes that are infinite number that will take the form of 2^n - 1 granted they are few and far between. I sure there is a way to represent this mathematically.
>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
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