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= 22^n
+ 1. One example of this would be-
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 =4 -1
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 232582657 -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.