In mathematics, a prime power is a positive integer power of a prime number. For example: 5=51, 9=32 and 16=24 are prime powers, while 6=2×3, 15=3×5 and 36=62=22×32 are not. The twenty smallest prime powers are:
- 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, ... (sequence A000961 in OEIS)
The prime powers are those positive integers that are divisible by just one prime number; prime powers and related concepts are also called primary numbers, as in the primary decomposition.
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Famous quotes containing the words prime and/or power:
“Ay, look: high heaven and earth ail from the prime foundation;
All thoughts to rive the heart are here, and all are vain:
Horror and scorn and hate and fear and indignation—
Oh, why did I awake? When shall I sleep again?”
—A.E. (Alfred Edward)
“The love of liberty is the love of others; the love of power is the love of ourselves.”
—William Hazlitt (1778–1830)