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.
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 number theory, a Woodall number (Wn) is any natural number of the form
In mathematics, a primorial prime is a prime number of the form pn# ± 1, where pn# is the primorial of pn.
In mathematics, a palindromic prime is a prime number that is also a palindromic number. Palindromicity depends on the base of the number system and its notational conventions, while primality is independent of such concerns. The first few decimal palindromic primes are:
666 is the natural number following 665 and preceding 667.
A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers x and y.
In number theory, a Wagstaff prime is a prime number of the form
The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes.
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 mathematics, a prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes. The even number 2p + 2 therefore satisfies Chen's theorem.
In number theory, a Pierpont prime is a prime number of the form
In number theory, Proth's theorem is a primality test for Proth numbers.
In number theory, a Leyland number is a number of the form
Twin Prime Search (TPS) is a volunteer computing project that looks for large twin primes. It uses the programs LLR and NewPGen. It was founded on April 13, 2006 by Michael Kwok. In number theory, it is conjectured that there are infinitely many twin primes, and this is known as the twin prime conjecture.
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 megaprime is a prime number with at least one million decimal digits.
The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737.
A tetradicnumber, also known as a four-waynumber, is a number that remains the same when flipped back to front, flipped front to back, mirrored up-down, or flipped up-down. The only numbers that remain the same which turned up-side-down or mirrored are 0, 1, and 8, so a tetradic number is a palindromic number containing only 0, 1, and 8 as digits. The first few tetradic numbers are 1, 8, 11, 88, 101, 111, 181, 808, 818, ....
