Tarwyn ...... This theorem is the hardest i know of in elementary number theory. I have never seen it in any books, however, I have available a proof of this theorem, it consists of several pages. Emial this to him from me.............

Let Z be the set of integers.
Let P(n) be the n'th prime number, then if F is a polynomial with complex coefficients, then F(n) = P(n) for at most finite many n.
Here is a tip to finding the solution.
If f is a polynomial with complex coefficents such that f(n) is in Z for every n in Z, then f has rational coeficcients.