Prime power

Prime power

A prime power is a positive integer of the form $p^r$, where $p$ is prime and $r$ is a positive integer. Examples include $2$, $3$, $4=2^2$, $5$, $8=2^3$ and $9=3^2$.

Prime powers occur naturally throughout number theory, including explicit formulas involving the von Mangoldt function.

See also: prime number, von Mangoldt function, Riemann zeta function. .