  Schinzel's Hypothesis H is a general conjecture in number theory on prime
values of polynomials that generalizes, e.g., the twin prime conjecture and
Dirichlet's theorem on primes in arithmetic progression. We prove an arithmetic
analog of this conjecture for polynomial rings over pseudo algebraically closed
fields. This implies results over large finite fields. A main tool in the proof
is an irreducibility theorems \`a la Hilbert.
