AVirtualMachineForExploringSpaceTimeAndBeyond : The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 120662...- (La conjecture de Proth-Gilbreath -visualisation du processus pour les 1024 nombres premiers suivant 120662...-).

The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 120662...- [La conjecture de Proth-Gilbreath -visualisation du processus pour les 1024 nombres premiers suivant 120662...-].

An important remark: the biggest red structure S₁ is the result of the proth-Gilbreath process starting with a couple of consecutive prime numbers (on the top line) with the possible collision with other red structures S_i coming from other couples of consecutive prime numbers (on the right-hand side). By the way, the "high" of S₁ is equal of G(Pi(x)).

This picture displays the process for the 1024 prime numbers following 1206626758101918 (that is close to the G(Pi(1.2075*10¹⁵))=809 record) -top row of the picture- with the following colors regarding the numbers:

when all other numbers -{3,4,5,6,7,8,...}- are Red (the red luminance is an increasing function of these numbers)...

According to the Proth-Gilbreath Conjecture, when the first prime number used (the smallest one) is 2, the left-hand side column must be Cyan ('1') except the upper square that is Light Yellow ('2', the first prime number).

On the second top line, please note the Light Yellow ('2') squares -if any- that display the second member of the twin prime number couples.

See some related pictures (including this one):