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Euclid proved in the 3rd century BC that there are an infinite number of prime numbers. A prime number can be divided only by itself and the number 1. Primes serve as the building blocks for all positive integers, and have applications in cryptography and other fields.

Mersenne numbers are numbers that are one less than a power of two
(2^{n} – 1). A Mersenne number that is also a prime number is
called a Mersenne prime. These can be found and verified relatively
quickly. Before 1952, 12 Mersenne primes were known; with the aid of
computers, 30 more have been found. The eight largest have all been found
by the Great Internet
Mersenne Prime Search (GIMPS), a distributed network of volunteers
using their spare computer power to find the largest Mersenne primes.

The largest currently known prime, 2^{43,112,609}– 1, was found
by electrical engineer Hans-Michael Elvenich on 6 Sept. 2008. It has
12,978,189 digits.

*See also* Prime Numbers and Numbers.

Prime Numbers between 1 and 1,000 | Numbers and Formulas | Roman Numerals |