Next Prime

The next prime function ${\it NP}(n)$ gives the smallest Prime larger than $n$. The function can be given explicitly as

$${\it NP}(n)=p_{1+\pi(n)},$$

where $p_i$ is the $i$th Prime and $\pi(n)$ is the Prime Counting Function. For $n = 1$, 2, ... the values are 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, ... (Sloane's A007918).

See also Fortunate Prime, Prime Counting Function, Prime Number

References

Sloane, N. J. A. Sequence A007918 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.