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.

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) 
  • Any number with more than two factors; for example, 4 has three factors (1,2,4). Any number with more than two factors is called a composite number.

 

Mersenne numbers

A Mersenne number (named for Marin Mersenne, a French friar and 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.