Schonzel's Hypothesis H is a generalization of Dickson's conjecture (see /JosephNoonan/is-dicksons-conjecture-true) to polynomials of all degrees, rather than just linear polynomials. It states that for any finite set P of non-constant, irreducible polynomials over the integers with a positive leading coefficient, one of the following holds:

• There are infinitely many natural numbers n such that, for all f in P, f(n) is prime.

• There is some prime p that, for any value of n, always divides at least one of the f(n). Equivalently, the product of all f in P is divisible by some integer constant, other than ±1.

The special case where P has only one element is /IsaacKing/is-the-bunyakovsky-conjecture-true