From https://en.wikipedia.org/wiki/Bunyakovsky_conjecture, the Bunyakovsky Conjecture is an open problem that states that $f(x)$ has infinitely many primes in sequence $f(1),f(2),...$ if
1) The leading coefficient is positive.
2) The polynomial is irreducible over the integers.
3) The coefficients of $f(x)$ are relatively prime.
It is conjectured as a generalization of Dirichlet's theorem on arithmetic progressions, which states that $a+xd$ contains infinitely many primes for $a$ and $d$ relatively prime.
I am curious whether it is known that $f(x)$ must contain at least one prime if the three conditions are met, or whether we know that $f(x)$ must have infinitely many composites for certain conditions, even just in the case of first degree polynomials.