The type( expr, 'primepower' ) command returns true if expr is of type primepower, and false otherwise.

An expression is of type primepower if it is a positive integer of the form p^k, for some prime number p and some non-negative integer k.

Note that the number $1$ is a prime power, as is each prime number.

$\mathrm{type}\left(0\,'\mathrm{primepower}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(1\,'\mathrm{primepower}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(4\,'\mathrm{primepower}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(-8\,'\mathrm{primepower}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(6\,'\mathrm{primepower}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\frac{2}{3}\,'\mathrm{primepower}'\right)$

$\mathrm{false}$

$\mathrm{type}\left({30303030303031}^{{10}^6}\,'\mathrm{primepower}'\right)$

$\mathrm{true}$

$\mathrm{type}\left({\left(30303030303031\cdot 30303030303043\right)}^{{10}^6}\,'\mathrm{primepower}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(5^{{10}^4\mathrm{nextprime}\left({10}^4\right)}\,'\mathrm{primepower}'\right)$

$\mathrm{true}$

The type/primepower command was updated in Maple 2020.