BUILT-IN MATHEMATICA SYMBOL

PrimePowerQ

PrimePowerQ[expr]
yields True if expr is a power of a prime number, and yields False otherwise.

PrimePowerQ[n, GaussianIntegers->True] determines whether n is a Gaussian prime power.

Test whether a number is a power of a prime number:

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Integers:

Gaussian integers:

PrimePowerQ works with numbers of any size:

PrimePowerQ threads automatically over lists:

Gaussian rationals:

Test whether a number is a power of a Gaussian prime:

The first prime powers that are not prime:

The infinite sum of reciprocals of prime powers which are not prime converges:

The number of prime powers in intervals of size

:

A graph showing the growth of the prime powers:

Recognize Mersenne numbers:

The number

is a Mersenne number;

is not:

Use FactorInteger to get the decomposition into primes:

The only square-free prime powers are prime numbers:

The sum of divisors of a prime power n is less than 2n:

Prime powers:

Gaussian prime powers: