The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers) [La spirale d'Ulam montrant les premiers nombres premiers jumeaux (nombres premiers '2-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 '2-twin' prime number pair is a set of two prime numbers {P1,P2} such that on the one hand P2-P1=2 and on the other hand there are no prime number between P1 and P2. The yellow squares display the first '2-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:

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

See the generalized Ulam spiral:

[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 01/08/2019 11:31:49 -CET-)

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