Ten short algebraical notes-3. The evolution of prime numbers

3. The evolution of prime numbers

It is verified that the Pr index, applied to groups of three numbers consecutive performs a kind of modular operation it has as a consequence, the creation of classes characterized by a name coinciding with the corresponding Pr value. The index name, Pr, and surname index, defined as follows:

create a graphical map of the relationships between numbers of the whole considered. Here, in the following graph, is the result of applying this criterion to the first five hundred prime numbers of the note list. The surname is shown vertically, and horizontally the name:

The chart can be interpreted as a family tree, prime numbers, starting from their appearance at the moment of the "mathematical Big Bang"? This is the first thought I have had when I saw the previous chart. This could be a good starting point for exercising the creative abilities of potential writers? This representation, similar to the space of the phases dear to physicists, raises some questions. What is there in the empty spaces of the graph? Dark matter? And if an even number infiltrated a family of numbers first how would change the name and surname of the family of departure? The simple rule of the pair of indicators (G,Pr) yes allows you to map the evolution of a group of numbers subjected to various transformations. Obviously, research of group mathematical structures represents the natural development of algebraic speech just started. To date, I have identified some interesting transformations but the work is not done. Anyone can check the results for the numbers first using a simple excel sheet. The Fibonacci sequence is famous and that's why I have it used as a sample to evaluate the effectiveness of the Pr. Fibonacci numbers, associated in groups of three, consecutive, do not manifest, as a consequence of the application of Pr and G, the tendency to form groups characteristic as occurs with prime numbers!