Definition:Prime Enumeration Function

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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 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.