Prime numbers formula was discovered in 5th August 2003 by Seyyed Mohammad Reza Hashemi Moosavi English language                                                                                      Persian Language

You can  Freely download  prime numbers formula package in an exe file format and executable in windows by Seyyed Alireza Hashemi Moosavi.

Using prime numbers formula software by Alireza is the best and quickest way to check numbers and find its prime or composite.

Note :  In Year of 2007 (AAAS) " National Association Of Academies Of Science " (USA) Awarded A++ grade (Equals to excellent) to the prime numbers formula and its results by Prof S.M.R Hashemi Moosavi.  

Note :  The discovery of prime numbers formula and its results has been published under an article in journal of "Roshd of Borhan "  associated with the Ministry of Education in Iran.

 Infinity proof of prime numbers being was propound 300 years B.C. by Euclid and since that time great mathematicians like Euler tried to discover a formula to produce prime numbers. Many of other mathematicians after many other researches finally found that discovery of prime numbers formula is impossible and this problem will be unsolvable. This discovery shows that one of the complicated and unsolvable problems of mathematics was solved and this discovery proves that there could be no unsolvable problem. I spent twenty years of my life researching and I found this fact that I can't comeback from this path which I came through and I promised myself to keep on searching for the rest of my life to find the solution even if I couldn't achieve the proof.

 One of the results of discovering the prime numbers formula is to achieve the solution of Riemann Zeta equation which is on of the popular universal unsolvable problems in mathematics and it's solution needs to achieve the number of the prime numbers for any desirable number of  N carefully (with prime numbers formula). Another result is to determine k-th desirable prime number and other uses are definition of prime numbers set, proof of infinity of twin prime pairs considering  to the conjectures of Gold Bach and Hardy, find the generator formula for Mersenne prime numbers and also very unknown and big prime numbers and other problems related to prime numbers. In fact the main use of this formula is in coding and decoding that usually use from very big prime numbers for this reason and in the past it was necessary to gain them with complicated mathematics methods and had a hard way to pass through But with presenting of prime numbers formula, definition of coding and decoding systems became easy and convenient.

After Euclid’s theory about infinite prime numbers in 300 B.C. Most of the mathematicians and other researchers have been curious to find a formula which could generates prime numbers. After many years later some mathematicians like Euler and Fermat presented some formulas to generate prime numbers limitedly. Great mathematicians like Hardy and Courant and many other researchers finally officially announced that such a formula can’t be found and to prove their wrong idea they started to publish some Algebraic theorems in their books. Furthermore, determining the number of prime numbers was very important problem. So Gauss and other mathematicians started to set some tables for them. We knew that so far there was no exact formula to determine the number of prime numbers exactly. This problem is known as Zeta Riemann equation which was one of the seven known unsolvable problems of the world that after my discovery on 5^th August 2003, one of them is no more unsolvable with the prime numbers formula accurately you can absolutely generate all prime numbers to the nth one. Its consequent generate of prime numbers formula resulted in defining the set of prime numbers and so many other unbelievable results until now like breaking the code of RSA and AES by the use of prime numbers formula and other sets like Mersenne prime, perfect numbers and so many important sets and results just related to the field of number theory and basic sciences.

    Discovery of prime numbers formula by Prof. Seyyed Mohammadreza Hashemi Moosavi caused so many results in basic sciences that we will mention part of it in the following:

• 1.         Distinction of prime numbers.

• 2.       Defining a formula for generating prime numbers.

• 3.       Definition of prime numbers set by using the generating function of prime numbers.

• 4.       Defining a formula to generate the Mersenne prime numbers.

• 5.       Determination of Nth prime number.

• 6.       Solving Riemann Zeta equation by using the determination of the number of prime number less than or equal to arbitrary number N exactly.

• 7.       The proof of guesses of Gold Buch and Hardy.

• 8.       The proof of infinity of the prime twin couples.

• 9.       Determining a general series of answer for Diophantine equations.

• 10.   This formula has so many unknown applications in Cryptography, generating Titan Mersenne prime numbers and other sciences like solving NP.