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A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the difference of two primes not exceeding p. 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , ... ( OEIS : A038134 )
Twenty-three is also the next to last member of the first Cunningham chain of the first kind (2, 5, 11, 23, 47), [3] and the sum of the prime factors of the second set of consecutive discrete semiprimes, (21, 22). 23 is the smallest odd prime to be a highly cototient number, as the solution to () for the integers 95, 119, 143, and 529.
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.
These numbers have been proved prime by computer with a primality test for their form, ... 23 April 2023 5,538,219 37 7×2 18233956 + 1 1 October 2020 5,488,969 38
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.
A number is only considered a Mersenne prime if it can be written in the form 2ᵖ-1. Unlike other large prime numbers used in some applications to protect internet security, Mersenne primes are ...
Jon Pace, a flight operations finance manager, is credited with discovering the largest prime number currently known. It’s 23.2 million digits long.
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.