The Proth-Gilbreath Conjecture -display of the process for the 256 first prime numbers- [La conjecture de Proth-Gilbreath -visualisation du processus pour les 256 premiers nombres premiers-].




This picture displays the process for the 256 first prime numbers:

{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619

-top row of the picture- with the following colors regarding the numbers:


when all other numbers -{3,4,5,6,7,8,...}- are Grey (Dark and Light Grey respectively for the negative and positive numbers).

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


See some related pictures (including this one):

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x =  
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x =  
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[Plus d'informations à propos de la conjecture de Gilbreath -en français/in french-]
[More information about the Gilbreath Conjecture -in english/en anglais-]


Please note that this picture displays only 136 lines and not the expected 256. This is due to G(Pi(10^7))=135 and to go beyond 256, G(Pi(10^10))=329 would be necessary and it means too much computations...


(CMAP28 WWW site: this page was created on 11/07/2025 and last updated on 11/07/2025 14:03:39 -CET-)



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