The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 613247...- (La conjecture de Proth-Gilbreath -visualisation du processus pour les 1024 nombres premiers suivant 613247...-) {a chapter of 'Mathematics - A Virtual Instrument For Exploring Space Time And Beyond'}

The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 613247...- [La conjecture de Proth-Gilbreath -visualisation du processus pour les 1024 nombres premiers suivant 613247...-].

This picture displays the process for the 1024 prime numbers following 613247327866031 (that is close to the G(Pi(6.150*10¹⁴))=800 absolute 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):