Well folks, I've really done it now!

In an earlier thread, I put forward a conjecture that generalized Fermat's Little Theorem. Using a related concept, I can now make a statement that generalizes *all* prime numbers!

Here it is:

For all N > 2, IFF ((s(N, N - 1) mod s(N, 1)) + 1) mod N = 0 then N is definitely prime, where s(N, E) is the sum of powers (eg: 1^E + 2^E ... + N^E).

AFAIK, the only other theorem that achieves a similar level of concision is Wilson's Theorem, so the implications of this equation may be quite significant (eg: may lead to much better primality tests).