Definition:Prime Enumeration Function

Definition
Let the function $p: \N \to \N$ be defined as:


 * $\map p 0 = 1$


 * $\map p n =$ the $n$th prime number

This function is called the prime enumeration function.

Note, of course, that although $\map p 0 = 1$, there is no suggestion of treating $1$ as prime (it definitely is not).