Re: A quick discussion of Mersenne Numbers

["Mark M." <markm@voicenet.com>]

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On Sun, 1 Dec 1996 Scottauge@aol.com wrote:

> I wake of the latest find announcement, some people maybe wondering what the
> heck is this?!!
> 
> A mercenne number is of the type:
> 
> M(p) = 2**p -1 results in a prime when p is a prime.
> 
> Hopefully this will lead the way to see the pattern of prime numbers and
> being able to compute prime numbers in a far more efficient manner (after all
> a function that when given a prime number results in a prime number would be
> quite a kicker now wouldn't it!)

It doesn't.  If q is a Mercenne prime, then p is prime if q = 2^p-1.  It
doesn't work the other way around.  If it did, then it would be very easy to
find out if a number is a Mercenne prime: just add 1 and find the base 2
logarithm and if the result is prime, then the original number is prime.  It's
much more difficult than that.  It would also be possible to find an infinite
number of Mercenne primes using a deterministic algorithm.


Mark
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