Definition:Prime Enumeration Function

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

1 & : n = 0 \\ \mbox{the } n \mbox{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).