Re: Testing for Primes

Cryptoad wrote:
>                                   Another Test for Primes
>
>                                      William J. Wilson
>
>
> A simple test for primes can be accomplished as follows: if an odd number i is
> the candidate prime, compute the ith Fibonacci number F.  If either F+1 or F-1
> is evenly divisible by i, then i is prime.
>
> [Note from Moderator: I queried this result and
> was told that it doesn't work for 5, or even
> numbers. -- GR.]

   I can't seem to find a numbering of the Fibonacci numbers for which
the hypothesis holds.

F  1  1  2  3  5  8 13 21 34 55 89
i  1  2  3  4  5  6  7  8  9 10 11
j     1  2  3  4  5  6  7  8  9 10
k        1  2  3  4  5  6  7  8  9

   Using F and i, the hypothesis fails for i=323,
F=14240420007076730617258541919943310440740965418798778412503676622857,
when F-1 is divisible by i (Note: 323=17*19).

   Using F and j, the hypothesis fails for j=9, F=55, when F-1 is
divisible by j.

   Using f and k, the hypothesis fails for k=9, F=89, when F+1 is
divisible by k.

--Mike Amling