A polynomial with prime values at $2n+1$ integers is irreducible

A polynomial with prime values at $2n+1$ integers is irreducible

Suppose $f(x)$ is a polynomial with integer coefficients and degree
$n\geq2$, and suppose $|f(x_i)|$ is prime for at least $2n+1$ integers
$x_i$. Show that $f(x)$ is irreducible.
I have no idea.
Thanks.