Mersenne prime - Wikipedia
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 M n = 2 n − 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 2 n − 1.
Mersenne Prime -- from Wolfram MathWorld
A Mersenne prime is a Mersenne number, i.e., a number of the form M_n=2^n-1, that is prime. In order for M_n to be prime, n must itself be prime. This is true since for composite n with factors r and s, n=rs. Therefore, 2^n-1 can be written as 2^(rs)-1, which is a binomial number that always has a factor (2^r-1).
Mersenne prime | Prime Number Theory, Mathematics, & History …
2024年12月27日 · Mersenne prime, in number theory, a prime number of the form 2n − 1 where n is a natural number. These primes are a subset of the Mersenne numbers, Mn. The numbers are named for the French theologian and mathematician Marin Mersenne, who asserted in the preface of Cogitata Physica-Mathematica
Mersenne Prime - GeeksforGeeks
2024年10月14日 · A Mersenne prime is a prime number that can be expressed in the form M n = 2 n-1. To be considered a Mersenne prime , n itself must be a prime number. If n is composite, then M n is sure to be composite, but if n is prime , then M n may be prime or composite.
List of Mersenne primes and perfect numbers - Wikipedia
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 .
Mersenne prime - Simple English Wikipedia, the free encyclopedia
In mathematics, a Mersenne number is a number that is one less than a power of two. Mn = 2 n − 1. A Mersenne prime is a Mersenne number that is a prime number. This however, is not sufficient. Many mathematicians prefer the definition of a Mersenne number where exponent n to be a prime number.
Mersenne Prime Discovery - 2^136279841-1 is Prime!
2 天之前 · BLOWING ROCK, NC, October 21, 2024 -- The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2 136,279,841 -1, having 41,024,320 decimal digits. Luke Durant, from San Jose, California, found the prime on October 12th. Luke is currently GIMPS' most prolific contributor.
What is Mersenne Prime? - Computer Hope
2024年8月16日 · What is Mersenne Prime? A Mersenne prime is any prime number that is a power of 2, minus 1. It is defined as Mn = 2n - 1, where n is any integer. For instance, the prime number 3 is a Mersenne prime, because it equals 2 2 - 1.
Mersenne Prime | Brilliant Math & Science Wiki
A Mersenne prime is a prime number that can be written in the form \(2^{n}-1\). For example \(31\) is a Mersenne prime that can be written as \(2^{5}-1\). The first few Mersenne primes are \(3, 7, 31, 127, 8191\). There are 50 known Mersenne primes as of June 2018, though we hope that it will change in the future.
The UCLA Mersenne Prime - UCLA Mathematics
The UCLA Mersenne Prime is the first prime discovered which has over 10 million digits. It was discovered at the UCLA Mathematics department on August 23, 2008. All Mersenne Primes are special because they're so rare, but this one has gotten extra attention because it qualifies for a prize (see below).