The aim of this paper is to show, through the regularities that emerge on composite numbers, some formal representations of primality, set of prime numbers and sequence of prime numbers. These regularities will also be seen in the context of the Riemann hypothesis. This work has been divided into three parts (paragraphs). In the first part two formulas will be identified, defined in N_(>0)^2→N_(>8), that describe the infinite sequences of infinite composite odd numbers. On the basis of these formulas, two definitions will follow, both of primality and of sets of prime numbers. In addition, graphs will be used to better represent the results and the regularities that have emerged, as well as some examples on the efficiency of the formulas found for the purposes of primality. In the second part, through an indicator function (or characteristic) and a generating function, we will try to represent a sequence of prime numbers starting both from the two primality definitions identified above, and from the simple definition of prime number. In the third part we will try to generalize the two formulas found in the first part to domains other than N_(>0). The definitions given above will be adapted to the new formulas and, lastly, the results obtained will be analysed in the context of the Riemann hypothesis, an unprovable hypothesis. These are the conclusions.