Prime_Enumeration_Function_is_Primitive_Recursive

Let the function $p: \N \to \N$ be the prime enumeration function, defined as $p \left({n}\right) = \begin{cases} 1 & : n = 0 \\ \mbox{the } n \mbox{th prime number} & : n > 0 \end{cases}$ Then $p$ is primitive recursive.