Use Mathematica. The positive integers less than or equal 1000 that are not prime but (2^n - n)/n is an integer are 1; 341 = 11*31; 561 = 3*11*17; and 645 = 3*5*43. The largest less than 10,000 is 8911 = 7*19*67. However, the significant fact is that the claim (Jeremy Cooper)

The integer N is prime if:

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

is actually fermat's little theorem as observed by Ray Cromwell. Walter A. Kehowski <wak@next1.math.pitt.edu>