prime number

Number that can be divided only by 1 and itself, that is, having no other factors. There is an infinite number of primes, the first ten of which are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 (by definition, the number 1 is excluded from the set of prime numbers). The number 2 is the only even prime because all other even numbers have 2 as a factor. Numbers other than primes can be expressed as a product of their prime factors.

Over the centuries mathematicians have sought general methods (algorithms) for calculating primes, from Eratosthenes' sieve to programs on powerful computers.

Mersenne primes are in the form 2^q−1, where q is also a prime.

As of 2003 only 40 Mersenne prime numbers were known. In that year the largest prime number was discovered, as part of the Great Internet Mersenne Prime Search (GIMPS), which involves volunteers downloading software to search for primes while their computers are idle. The largest prime number – calculated by the computer of Michael Shafer, an engineering student at Michigan State University, USA – was 2^20,996,011−1.