Bateman–Horn conjecture

In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A. Horn who proposed it in 1962. It provides a vast generalization of such conjectures as the Hardy–Littlewood conjecture on the density of twin primes or their conjecture on primes of the form ${\displaystyle n^{2}+1}$. It is also a strengthening of Schinzel's hypothesis H.