Primality Testing and Factorization by using Fourier Spectrum of the Riemann Zeta Function

Abstract

In number theory, integer factorization is the decomposition of a composite number into a product of smaller
integers, for which there is not known ecient algorithm. In this article, the author tries to make primality testing
and factorization of integers by using Fourier transform of a correlation function generated from the Riemann zeta
function. From the theoretical analysis, we can see that prime factorization for the integer composed of two dierent
primes can be conducted within a polynomial time and it can be seen that this special case belongs to the P class.