Ed wrote: << See http://demonstrations.wolfram.com/TheBouniakowskyConjecture/ In 1857, Bouniakowsky conjectured that if f(x) is an irreducible polynomial, f(x)/gcd(f(0),f(1)) generates an infinite number of primes. It's an unsolved question.

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Wow, that's fascinating. Thanks, Ed and everyone for your answers. (Btw, if on the other hand an integer polynomial of degree d take prime values at 2d+1 integers, then it must be irreducible, I think.) --Dan