  Today, prime numbers attained exceptional situation in the area of numbers
theory and cryptography. As we know, the trend for accessing to the largest
prime numbers due to using Mersenne theorem, although resulted in vast
development of related numbers, however it has reduced the speed of accessing
to prime numbers from one to five years. This paper could attain to theorems
that are more extended than Mersenne theorem with accelerating the speed of
accessing to prime numbers. Since that time, the reason for frequently using
Mersenne theorem was that no one could find an efficient formula for accessing
to the largest prime numbers. This paper provided some relations for prime
numbers that one could define several formulas for attaining prime numbers in
any interval; therefore, according to flexibility of these relations, it could
be found a new branch in the field of accessing to great prime numbers followed
by providing an algorithm at the end of this paper for finding the largest
prime numbers.
