Prime Conditions for Integers

Abstract

   In this paper we suggest to break down natural numbers, P, in two coefficients, i and j, reported to their subscript N which is defined by the equation P = 6N ± 1; i and j are defined by an other equation, N = 6 * |i| * |j| ± (i ± j). N is a natural whole number but i and j are not necessarily natural whole numbers. They could be irrational. By using such unusual approach of number theory, we would propose a simple relation between two square numbers as a necessary condition for any prime number. We would like to suggest that such relationship could be looked as a corollary of the last Fermat’s theorem.