Definition:Prime Enumeration Function

Definition
Let the function $p: \N \to \N$ be defined as:
 * $p \left({n}\right) = \begin{cases}

1 & : n = 0 \\ \text{the } n \text{th prime number} & : n > 0 \end{cases}$

Thus for example:
 * $p \left({0}\right) = 1$
 * $p \left({1}\right) = 2$
 * $p \left({2}\right) = 3$
 * $p \left({3}\right) = 5 \ldots$

This function is called the prime enumeration function.

Note, of course, that although $p \left({0}\right) = 1$, there is no suggestion of treating $1$ as prime (it definitely isn't).