Prime Time

Types of Prime Numbers

There are several types of primes, however there are two main ones. These are Fermat primes, and Mersenne primes. Each is described as two to the power of a number, and then plus or minus one. The format for Fermat primes is Fn= 2^{2^n} + 1. One example of this would be-
Fn =2^{(2^0)}+1
Fn =2¹+1
Fn =3

Three is a prime number. Some other Fermat primes are 5 and 17. There is only a limited number of Fermat primes, and not every number put into this equation turns out to be prime.

Mersenne primes can be expressed as Mn = 2ⁿ - 1. Here’s an example

Mn =2²-1
Mn =4 -1
Mn =3

Three is a prime number, and it is unique because it is both a Mersenne prime and a Fermat prime. There are many more Mersenne primes, such as 7 and 31.

Many very large prime numbers have been found using these formulas. In fact, the largest known prime (as of May 1st, 2007) is 2^32582657 -1. Many of the largest primes found are mersenne primes, because they are easy to check for primality with a computer.

As I mentioned, there are many other types of primes, such as twin primes, Wieferich primes, Wall-Sun-Sun primes, Wilson primes, and Wolstenholme primes.