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. --Ed Pegg Jr Michael Reid <reid@math.ucf.edu> wrote: X^2 + X + 4 will never produce prime values. mike

Let f(X) be a nonconstant polynomial in Z[X] not of the form

f(X) = g(X) h(X)

where g(X), h(X) are in Z[X] - {1,-1}.

Does there necessarily exist an integer N such that f(N) is a (positive or negative) prime number ?

If so, is there known to be a minimum number m(d) of such N, where d = deg(f) ?

(What if f(X) is further assumed to be monic?)

--Dan

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