What is a Mersenne Prime?

Math doesn't make worldwide news very often, but sometimes we hear about mathematicians finding a new super-large prime number. Those numbers are usually a type called Mersenne primes.

News Flash! Spring, 2009: Norwegian mathematician finds 47th Mersenne prime, nearly 13 million digits long! He was aided by GIMPS (read about that group here). See National Public Radio coverage of the story.

Here is a brief introduction to this little-known branch of number theory.

Prime numbers

First, be sure you know what a prime number is. It is a number that has exactly two factors (numbers that "go into" it with no remainder): 1 and itself.

For example, 2 is a prime number, since its factors are 1 and 2.

These numbers are not prime:

• 1, since it has only one factor (1) 
• 4, since it has more than two factors (1,2,4). (Any number with more than two factors is called a composite number.) 

Mersenne numbers

A Mersenne number (named for a mathematician born in the late 1500's) is a positive number that is one less than a power of two. That means it can be written in the form 2ⁿ – 1. For example, (2³ – 1) = (8 – 1) = 7; thus, 7 is a Mersenne number.

Mersenne primes

Naturally, a Mersenne prime is a Mersenne number that is prime. How many of the first ten Mersenne numbers do you think are prime? See our Small Mersenne Primes page for a list.