Creation of a Table of Primes in Successive order

Abstract

The sequence of prime numbers has been one of the problems that have occupied the minds of mathematicians for the last centuries. Perhaps there is no formula that gives this sequence, number by number, or it is very hard to find, but this sequence could arise from one or more sequences of composite numbers and the gaps they leave in the set of integers. This work aims at something quite simple: To categorize all odd composite numbers, smaller than a given number N and greater than number 1, with the press of a button, into three types of arithmetic progressions that is, to make possible the creation of an algorithm and thus, obtain the results. That is, to have directly all odd composite numbers which are smaller than the given number N. So having the set of odd numbers and having created a subset of the composite ones, it is easy then to give to the computer, the command to delete all the existing members of composites from the set of the odd numbers as they have been categorized in the subset of the found composites and make their set difference. This set difference can have as members only prime numbers, because the set of the odd numbers greater than number 1, consists only of primes and composites.