Graphic representation of the mechanism of prime numbers.

The distribution of prime numbers and related composite numbers derives from the intertwining of the respective modules of the infinite prime numbers; this intertwining is not casual but regulated by a very specific mechanism "the mechanism of prime numbers".

The purpose of this article is to graphically represent this mechanism.

It is a cyclic mechanism whose starting point are the numbers 0 and 1; each cycle is made of two phases, the result of each cycle is an ever increasing set which I call a “combined sequence”; the first two numbers of each new set will always remain 0 and 1 to which new integers are added from time to time in natural order.

In each new “combined sequence” it is possible the presence of more than one prime number, but the mechanism foresees that only one prime number for each cycle is "identified" (hereinafter I will use the term "consolidated"); the other numbers present in the “combined sequence” (at the end of each cycle) are the prime numbers and the composite numbers "consolidated" in the previous and current cycles, to these are added other numbers not yet "consolidated" but indispensable.

The numbers 0 and 1 are therefore present and fundamental in every cycle and never change their state (they are not prime numbers or even composite numbers); the "always indefinite state" of 1 combined with the "state" in which all the other numbers of the “combined sequence” are found will determine the "state" of the numbers that will form the new “combined sequence”. Each prime after it is "consolidated" behaves like a composite number.