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.