# Definition of Mersenne number in English:

## Mersenne number

### noun

Mathematics
• A number of the form 2p−1, where p is a prime number. Such a number which is itself prime is also called a Mersenne prime.

• ‘Usually you download a screensaver or something, and when your computer isn't busy it turns itself on and cranks away at calculating a Mersenne prime or a SETI signal or some other worthy semi-scientific endeavor.’
• ‘The divisor itself is the fifth largest known prime number, and it is the largest that is not a Mersenne prime.’
• ‘This project is seeking the largest Mersenne prime number, which is, at the moment, also the largest prime number of any form.’
• ‘And the Great Internet Mersenne Prime Search continues to unearth new Mersenne primes.’
• ‘Written in the form 2 p - 1, where the exponent p is a prime number, Mersenne numbers hold a special place in the never-ending pursuit of larger and larger primes.’
• ‘One must be the Lucas Lehmer primality test which uses the Fermat congruence, and in particular his application to testing whether a Mersenne number was prime.’
• ‘Primes of the form 2 n - 1 are known as Mersenne primes, and these numbers figure prominently in the search for the largest known prime.’
• ‘How can you calculate a perfect number from a Mersenne prime?’
• ‘In 1876 he used his methods to prove that the Mersenne number 2 127-1 is prime.’
• ‘The largest known prime is the 40th Mersenne prime: M 20996011 which has 6320430 decimal digits.’
• ‘‘Fermat had this idea that there were families of primes other than Mersenne primes, and there would be an infinite number of them,’ he adds.’
• ‘A computer search turned up the 40th Mersenne prime.’
• ‘After reading up on how known perfect numbers relate to Mersenne Prime Numbers, I wrote another program, this time to find Mersenne prime numbers and perfect numbers.’
• ‘A few months later an engineer at Cray Research discovered a new record Mersenne prime number, and I wrote a 700-word piece describing the discovery.’
• ‘Primes of the form 2 p - 1 are called Mersenne primes.’
• ‘Primes of the form are now known as Mersenne primes, and these numbers figure prominently in the search for the largest known prime.’
• ‘Expressed in the form 2 p - 1, where the exponent p is itself prime, Mersenne numbers have characteristics that make it relatively easy to determine whether a candidate is prime.’

### Origin

Late 19th century: named after Marin Mersenne (1588–1648), French mathematician.

/məːˈsɛn/