Advanced Mathematical Formulas to Calculate Prime Numbers

Abstract

Prime numbers are the core of mathematics and specifically of number theory. The application of prime numbers in modern science, especially in computer science, is very wide. The importance of prime numbers has increased especially in the field of information technology, i.e., in data security algorithms. It is easy to generate the product of two prime numbers but extremely difficult and a laborious to decompose prime factors combined together. The RSA system in cryptography uses prime numbers widely to calculate the public and the private keys. Diffie-Hellman Key Exchange in cryptography uses prime numbers in a similar way and in computing hash codes also we use Prime numbers. Since prime numbers can only divisible by 1 and themselves, they are not factored any further like whole numbers. Their appearance within the infinite string of numbers in random fasion that devising a functional equation to correctly predict them, infinitely, has been belived by many mathematician as impossible task. The problem to calculate prime number using a formula posed for long periods. Though different formulae to calculate prime number were developed by Euler, Fermat and mersenne, the formulae work for limited natural numbers and calculate limited prime numbers. However, on this paper the author wants to show how prime number calculated for all values of integers(x).