Re: Prime Numbers

[rjc@gnu.ai.mit.edu (Ray)]

Jeremy Cooper writes:
> I found something interesting that I have not proven, but it has not 
> failed yet:

> The integer N is prime if:

>    2^N - 2
>   ---------
>       N              is an integer.

   This is fermat's little theorem. What you have written basically
says 2^N - 2  = 0 (mod N) or 2^(N-1) = 1 (mod N). Note, the converse
doesn't apply. If (2^N-2)/N is an integer, N isn't neccessarily
prime. For example, take N=561=(3*11*37)

    For extra credit, prove your hypothesis. ;-)

-Ray
   

-- Ray Cromwell        |    Engineering is the implementation of science;   --
-- rjc@gnu.ai.mit.edu  |       politics is the implementation of faith.     --