how that if $P(x_1,...,x_n) \in C[x_1,...,x_n]$ takes only prime values at all non-negative integer values $x_i$, then $P$ is constant.

Question

Show that if $P(x_1,...,x_n) \in C[x_1,...,x_n]$ takes only prime values at all non-negative integer values $x_i$, then $P$ is constant.

To start, how would you express $P(x_1,...,x_n)$?

I really have no idea where to start with this proof. Any help would be appreciated.