What is a Mersenne
Prime?
Math doesn't make worldwide news very often, but sometimes we hear about
mathematicians finding a new superlarge prime number. Those numbers are usually a type
called Mersenne primes.
Here is a brief introduction to this littleknown 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 2^{n} – 1. For example, (2^{3} – 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.
