The Ulam spiral with display of the first '6-twin' prime numbers [La spirale d'Ulam montrant les premiers nombres premiers '6-jumeaux' ]

The Ulam spiral with display of the first '6-twin' prime numbers [La spirale d'Ulam montrant les premiers nombres premiers '6-jumeaux'].




Starting from the center of the picture -red square-, all the little squares (even the black ones) are numbered (N=1, 2, 3,...) when following a square spiral. A '6-twin' prime number pair is a set of two prime numbers {P1,P2} such that on the one hand P2-P1=6 and on the other hand there are no prime number between P1 and P2. The yellow squares display the first '6-twin' prime number pairs (light yellow for P2 and dark yellow for P1).

A famous conjecture states that there are infinitely many '2-twin' prime number pairs {2,3,5,7,11,13,17,19,23,29,31,37,41,... (INFINITY?)}.


See the Ulam spiral:

The Ulam spiral


See the 'N-twin' prime numbers (with N=2,4,6,8 respectively):

The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers) The Ulam spiral with display of the first '4-twin' prime numbers The Ulam spiral with display of the first '6-twin' prime numbers The Ulam spiral with display of the first '8-twin' prime numbers


See the generalized Ulam spiral:

The generalized Ulam spiral displaying 2025 numbers


[Plus d'informations à propos de la spirale d'Ulam et de ses généralisations -en français/in french-]
[More information about the Ulam spiral and ist generalizations -in english/en anglais-]


(CMAP28 WWW site: this page was created on 04/01/2015 and last updated on 06/04/2026 23:25:43 -CEST-)



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