Euler Lucky Number Function for n equals p

Definition
Let $p$ be a prime number.

Let $f_p: \Z \to \Z$ be the mapping defined as:
 * $\forall n \in \Z: f_p \left({n}\right) = n^2 - n + p$

Then $f_p \left({p}\right)$ is not prime.

Proof
Let $n = p$.

Then:

which is not prime.