Given n polynomials with positive degrees and integer coefficients ( can be any natural number) that each satisfy all three conditions in the
Bunyakovsky conjecture, and for any prime p there is an integer x such that the values of all n polynomials at x are not divisible by , then there are infinitely many positive integers x such that all values of these n polynomials at x are prime. For example, if the conjecture is true then there are infinitely many positive integers x such that , , and x^2+x+41 are all prime. When all the polynomials have degree 1, this is the original Dickson's conjecture. This generalization is equivalent to the
generalized Bunyakovsky conjecture and
Schinzel's hypothesis H. == See also ==