# Schinzel's hypothesis H

It is known for linear polynomials (Dirichlet's theorem), but is open for higher degree (most notably for $n^2+1$).
A stronger version of this hypothesis (the Bateman-Horn conjecture) would assert that there is a k-digit prime of the form f(n) for all sufficiently large n. If this is the case, one can solve the weak version of the finding primes project by searching the k-digit values of a degree d irreducible polynomial, such as $n^d-2$, to find a prime in $O( (10^k)^{1/d} )$ steps for any given d.