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81 is: the square of 9 and the second fourth-power of a prime; 3 4 . with an aliquot sum of 40 ; within an aliquot sequence of three composite numbers (81, 40 , 50 , 43 , 1 ,0) to the Prime in the 43 -aliquot tree.
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.
The progressions of numbers that are 0, 3, or 6 mod 9 contain at most one prime number (the number 3); the remaining progressions of numbers that are 2, 4, 5, 7, and 8 mod 9 have infinitely many prime numbers, with similar numbers of primes in each progression.
In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number. For example: 7 = 7 1 , 9 = 3 2 and 64 = 2 6 are prime powers, while 6 = 2 × 3 , 12 = 2 2 × 3 and 36 = 6 2 = 2 2 × 3 2 are not.
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 2 p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1.
The prime signature of a number having prime factorization … is the multiset {,, …,}. For example, all prime numbers have a prime signature of {1}, the squares of primes have a prime signature of {2}, the products of 2 distinct primes have a prime signature of {1, 1 } and the products of a square of a prime and a different prime (e.g. 12 ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.