# Definition:Prime Enumeration Function

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## 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**.