Browse Definitions :

Mersenne prime (or Marsenne prime)

A Mersenne (also spelled Marsenne) prime is a specific type of prime number. It must be reducible to the form 2 n - 1, where n is a prime number. The term comes from the surname of a French monk who first defined it. The first few known values of n that produce Mersenne primes are where n = 2, n = 3, n = 5, n = 7, n = 13, n = 17, n = 19, n = 31, n = 61, and n = 89.

With the advent of computers to perform number-crunching tasks formerly done by humans, ever-larger Mersenne primes (and primes in general) have been found. The quest to find prime numbers is akin to other numerical searches done by computers. Examples are the decimal expansions of irrational numbers such as pi (the circumference-to-diameter ratio of a circle) or e (the natural logarithm base). But the 'next' prime is more difficult to find than the 'next' digit in the expansion of an irrational number. 

It takes the most powerful computer a long time to check a large number to determine if it is prime, and an even longer time to determine if it is a Mersenne prime. For this reason, Mersenne primes are of particular interest to developers of strong encryption methods.

In August 2008, Edson Smith, a system administrator at UCLA, found the largest prime number known to that date. Smith had installed software for the Great Internet Mersenne Prime Search (Gimps), a volunteer-based distributed computing project.  The number (which is a Mersenne prime) is 12,978,189 digits long. It would take nearly two-and-a-half months to write out and, if printed, would stretch out for 30 miles.


Learn More About IT:
> Wikipedia has an entry about Mersenne primes.
> See Mersenne Primes: History, Theorems and Lists.
> The Guardian explains 'Why 2 to the power of 43112609 - 1 = $100000 for prime number hunters.'

This was last updated in March 2011

Join the conversation

1 comment

Send me notifications when other members comment.

Please create a username to comment.

I think that there shouldn't be any largest prime number, because if M44 is the largest prime by mersenne's prime, then 2^M44-1 should be the largest prime and so on.


File Extensions and File Formats

Powered by:



  • cybersecurity

    Cybersecurity is the protection of internet-connected systems, including hardware, software and data, from cyberattacks.

  • asymmetric cryptography (public key cryptography)

    Asymmetric cryptography, also called public key cryptography, uses a pair of numerical keys that are mathematically related to ...

  • digital signature

    A digital signature is a mathematical technique used to validate the authenticity and integrity of a message, software or digital...



  • business continuity plan (BCP)

    A business continuity plan (BCP) is a document that consists of the critical information an organization needs to continue ...

  • disaster recovery team

    A disaster recovery team is a group of individuals focused on planning, implementing, maintaining, auditing and testing an ...

  • cloud insurance

    Cloud insurance is any type of financial or data protection obtained by a cloud service provider. 


  • hard disk drive (HDD)

    A computer hard disk drive (HDD) is a non-volatile memory hardware device that controls the positioning, reading and writing of ...

  • byte

    In most computer systems, a byte is a unit of data that is eight binary digits long. Bytes are often used to represent a ...

  • network-attached storage (NAS)

    Network-attached storage (NAS) is dedicated file storage that enables multiple users and heterogeneous client devices to retrieve...