Re: A quick discussion of Mersenne Numbers

In a message dated 96-12-01 16:17:01 EST, you write:
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
I agree, my discussion was toooooo quick and the statement:
M(p) = 2**p -1 results in a prime when p is a prime.
is misleading. I was thinking the second paragraph when I was writing the statement statement above. A case of the mind working faster than the fingers?
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Scottauge@aol.com