The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers.
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p.
In mathematics, a Fermat number, named after Pierre de Fermat, the first known to have studied them, is a positive integer of the form: where n is a non-negative integer. The first few Fermat numbers are: 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ....
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for "repeated unit" and was coined in 1966 by Albert H. Beiler in his book Recreations in the Theory of Numbers.
This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantities and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language.
In recreational number theory, a primeval number is a natural number n for which the number of prime numbers which can be obtained by permuting some or all of its digits is larger than the number of primes obtainable in the same way for any smaller natural number. Primeval numbers were first described by Mike Keith.
In number theory, a Woodall number (Wn) is any natural number of the form
Prime95, also distributed as the command-line utility mprime for FreeBSD and Linux, is a freeware application written by George Woltman. It is the official client of the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing project dedicated to searching for Mersenne primes. It is also used in overclocking to test for system stability.
The PrimePages is a website about prime numbers originally created by Chris Caldwell at the University of Tennessee at Martin who maintained it from 1994 to 2023.
The largest known prime number is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.
In number theory, Mills' constant is defined as the smallest positive real number A such that the floor function of the double exponential function
A dihedral prime or dihedral calculator prime is a prime number that still reads like itself or another prime number when read in a seven-segment display, regardless of orientation, and surface. The first few decimal dihedral primes are
In number theory, a Leyland number is a number of the form
In number theory, a prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form (p, p + 2, p + 6) or (p, p + 4, p + 6). With the exceptions of (2, 3, 5) and (3, 5, 7), this is the closest possible grouping of three prime numbers, since one of every three sequential odd numbers is a multiple of three, and hence not prime (except for 3 itself).
In recreational number theory, a minimal prime is a prime number for which there is no shorter subsequence of its digits in a given base that form a prime. In base 10 there are exactly 26 minimal primes:
In number theory, primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression. An example is the sequence of primes, which is given by for .
A Proth number is a natural number N of the form where k and n are positive integers, k is odd and . A Proth prime is a Proth number that is prime. They are named after the French mathematician François Proth. The first few Proth primes are
43,112,609 is the natural number following 43,112,608 and preceding 43,112,610.
