  The Schinzel hypothesis essentially claims that finitely many irreducible
polynomials in one variable over Z simultaneously assume infinitely many prime
values unless there is an obvious reason why this is impossible.
  We prove that under a restriction on the characteristic of the finite field
Fq and a smoothness assumption, finitely many irreducible polynomials in one
variable over the ring Fq[t] assume simultaneous prime values after a
sufficiently large extension of the field of constants.
