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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.
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.
Recorde proposed three mathematical terms by which any power (that is, index or exponent) greater than 1 could be expressed: zenzic, i.e. squared; cubic; and sursolid, i.e. raised to a prime number greater than three, the smallest of which is five. Sursolids were as follows: 5 was the first; 7, the second; 11, the third; 13, the fourth; etc.
By 1772, Leonhard Euler had proven that 2,147,483,647 is a prime. The number 2147483647 is the eighth Mersenne prime, equal to 2 31 − 1. It is one of only four known double Mersenne primes. [1] The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772. [2]
Example grid for a cross-figure puzzle with some answers filled in. A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual digits are entered in the blank cells.
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.
All primes greater than or equal to 73 are non-supersingular, while 37, on the other hand, is the smallest prime number that is not supersingular. [22] F 1 {\displaystyle \mathrm {F_{1}} } contains a total of 194 conjugacy classes that involve 73 distinct orders (without including multiplicities over which letters run).
a prime number has only 1 and itself as divisors; that is, d(n) = 2; a composite number has more than just 1 and itself as divisors; that is, d(n) > 2; a highly composite number has a number of positive divisors that is greater than any lesser number; that is, d(n) > d(m) for every positive integer m < n.