A quick discussion of Mersenne Numbers

[Scottauge at aol.com]

In a message dated 96-12-01 16:17:01 EST, you write:

>  On Sun, 1 Dec 1996 Scottauge at 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?