Wilson's theorem states that a natural number $n > 1$ is a prime number if and only if the product of all the positive integers less than $n$ is one less than a multiple of $n$.

Is there a version of the theorem in $\mathbb Z/p\mathbb Z[t]$ where $p$ is a prime?

Are there any other non-trivial versions?

My motivation is the following.

There is no space or time efficient algorithm for primes without Cramer's conjecture but perhaps working with irreducible polynomials requires **no unproven conjectures** and so is finding an irreducible in $\mathbb Z/p\mathbb Z[t]$ any easier?