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Fourth power. In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So: Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n4 as n “ tesseracted ”, “ hypercubed ”, “ zenzizenzic ...
Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 22 − 1.
A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth ( Play ⓘ) is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there ...
Mersenne primes M p are closely connected to perfect numbers. In the 4th century BC, Euclid proved that if 2 p − 1 is prime, then 2 p − 1 (2 p − 1) is a perfect number. In the 18th century, Leonhard Euler proved that, conversely, all even perfect numbers have this form. This is known as the Euclid–Euler theorem.
The original, called Mersenne's conjecture, was a statement by Marin Mersenne in his Cogitata Physico-Mathematica (1644; see e.g. Dickson 1919) that the numbers were prime for n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, and were composite for all other positive integers n ≤ 257. The first seven entries of his list ( for n = 2, 3, 5, 7 ...
Perfect number. In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
Prime power. In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number . For example: 7 = 71, 9 = 32 and 64 = 26 are prime powers, while 6 = 2 × 3, 12 = 22 × 3 and 36 = 62 = 22 × 32 are not. The sequence of prime powers begins:
Exponentiation (^) n th root (√) Logarithm (log) log. v. t. e. In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power. Exponentiation is written as bn, where b is the base and n is the power; this is pronounced as " b (raised) to the (power of) n ". [1]