AVirtualMachineForExploringSpaceTimeAndBeyond : The Proth-Gilbreath Conjecture -display of the process for the 128 first prime numbers- (La conjecture de Proth-Gilbreath -visualisation du processus pour les 128 premiers nombres premiers-).

The Proth-Gilbreath Conjecture -display of the process for the 128 first prime numbers- [La conjecture de Proth-Gilbreath -visualisation du processus pour les 128 premiers nombres premiers-].

This picture displays the process for the 128 first prime numbers:

{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,,73,79,83,89,97,101,103,107,109,113,,127,131,137,139,149,151,157,163,167,173,,179,181,191,193,197,199,211,223,227,229,,233,239,241,251,257,263,269,271,277,281,,283,293,307,311,313,317,331,337,347,349,,353,359,367,373,379,383,389,397,401,409,,419,421,431,433,439,443,449,457,461,463,,467,479,487,491,499,503,509,521,523,541,,547,557,563,569,571,577,587,593,599,601,,607,613,617,619,631,641,643,647,653,659,,661,673,677,683,691,701,709,719}

-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 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):