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)
-
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.
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