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).

Examples

Examples of the prime enumeration function are as follows:

\(\ds \map p 0\)

\(=\)

\(\ds 1\)

\(\ds \map p 1\)

\(=\)

\(\ds 2\)

\(\ds \map p 2\)

\(=\)

\(\ds 3\)

\(\ds \map p 3\)

\(=\)

\(\ds 5\)

Also see

• Results about the prime enumeration function can be found here.