In number theory, a prime power is a number which is divisible by a single prime number. For example, 7 = 7^{1}, 9 = 3^{2}, 28 = 2^{5} are prime powers, while 6 = 2 × 3, 10 = 2^{2} × 3 and 30 = 6^{2} = 2^{2} × 3^{2} are not. (The number 1 is not counted as a prime power.

The sequence of prime powers begins 2, 3, 4, 5, 7, 8, 9, E, 11, 14, 15, 17, 1E, 21, 23, 25, 27, 28, 31, 35, 37, 3E, 41, 45, 4E, 51, 54, 57, 5E, 61, 67, 69, 6E, 75, 81, 85, 87, 8E, 91, 95, X1, X5, X7, X8, XE, E5, E7.

The prime powers are those positive integers that are divisible by exactly one prime number; prime powers are also called **primary numbers**, as in the primary decomposition.