Schinzel's Hypothesis H

In mathematics, Schinzel's hypothesis H is a very broad generalisation of conjectures such as the twin prime conjecture. It aims to define the possible scope of a conjecture of the nature that several sequences of the type

f(n), g(n), ...

with values at integers n of irreducible integer-valued polynomials

f(t), g(t), ...

should be able to take on prime number values simultaneously, for integers n that can be as large as we please. Putting it another way, there should be infinitely many such n, for which each of the sequence values are prime numbers. Some constraints are needed on the polynomials. Andrzej Schinzel's hypothesis builds on the earlier Bunyakovsky conjecture, for a single polynomial, and on the Hardy–Littlewood conjectures for multiple linear polynomials. It is in turned extended by the Bateman–Horn conjecture.