  We will describe an algorithm to arrange all the positive and negative
integer numbers. This array of numbers permits grouping them in six different
Classes, $\alpha$, $\beta$, $\gamma$, $\delta$, $\epsilon$, and $\zeta$.
Particularly, numbers belong to Class $\alpha$ are defined as $\alpha=1+6 n$,
and those of Class $\beta$, as $\beta=5+6n$, where
$n=0,\pm1,\pm2,\pm3,\pm4,...$ These two Classes $\alpha$ and $\beta$,contain:
i) all prime numbers, except + 2, -2 and $\pm$3, which belong to $\epsilon$,
$\delta$, and $\gamma$ Classes, respectively, and ii) all the other odd
numbers, except those that are multiple of $\pm$3, according to the sequence
$\pm$9, $\pm$15, $\pm$21, $\pm$27, ... Besides, products between numbers of the
Class $\alpha$, and also those between numbers of the Class $\beta$, generates
numbers belonging to the Class $\alpha$. On the other side, products between
numbers of Class $\alpha$ with numbers of Class $\beta$, result in numbers of
Class $\beta$. Then, both Classes $\alpha$ and $\beta$ include: i) all the
prime numbers except $\pm$2 and $\pm$3, and ii) all the products between
$\alpha$ numbers, as $\alpha\cdot\alpha^{\prime}$; all the products between
$\beta$ numbers, as $\beta\cdot\beta^{\prime}$; and also all the products
between numbers of Classes $\alpha$ and $\beta$, as $\alpha\cdot\beta$, which
necessarily are composite numbers, whose factorization is completely
determined.
