Mathematical Machine for Primality Testing of Numbers: An Advanced Research

Abstract

Like the optical prism to break white light up into its constituent spectral colors, the machine to show a prime as a single spectrum is proposed. From the theoretical analysis, it can be shown that the machine to recognize the prime number as a single spectrum can be realized by using the Fourier transform of the correlation function of Riemann zeta function. Moreover, this method can be used for a factorization of the integer composed of two primes. Integer factorization is the decomposition of a composite number into a product of smaller integers, for which there is not known efficient algorithm. From the theoretical analysis, we can see that prime factorization for the integer composed of two different primes can be conducted within a polynomial time.