CIRM - Videos & books Library - Polignac numbers and the consecutive gaps between primes

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twin prime conjecture small gaps conjecture distribution level of primes Bombieri-Vinogradov theorem Elliott-Halberstam conjecture bounded gaps conjecture Dickson's conjecture admissible k-tuples of primes Hardy-Littlewood's prime k-tuple conjecture twin prime conjecture bounded gaps conjecture twin prime conjecture conjecture DHL (k,2) bounded gap conjecture Goldson-Pintz-Yildirim Motohashi-Pintz theorem Zhang's theorem Tao's Polymath project Maynard-Tao's theorem Erdös-Turàn conjecture Szemerédi's theorem Green-Tao's theorem arithmetic progressions of generalized twin primes Green-Tao's theorem bounded gaps conjecture Polignac number Polignac conjecture bounded gaps conjecture bounded gaps between Polignac numbers Erdös's conjectures on gaps of consecutive primes conjectures of Erdös and Erdös-Mirsky Zhang's theorem Motohashi-Pintz theorem Zhang's theorem Fouvry-Iwaniec's method Friedlander-Iwaniec theorem Linnik's and Heath-Brown's identity Friedlander-Iwaniec theorem

Résumé : We prove a number of surprising results about gaps between consecutive primes and arithmetic progressions in the sequence of generalized twin primes which could not have been proven without the recent new results of Zhang, Maynard and Tao. The presented results are far from being immediate consequences of the results about bounded gaps between primes: they require various new ideas, other important properties of the applied sieve function and a closer analysis of the methods of Goldston-Pintz-Yildirim, Green-Tao, Zhang and Maynard-Tao, respectively.

Codes MSC :
11B05 - Density, gaps, topology
11N05 - Distribution of primes

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https://videos.cirm-math.fr/2014-02-11_Pintz.mp4

Informations sur la Rencontre

Nom de la rencontre : Prime numbers : new perspectives / Nombres premiers : nouvelles perspectives
Dates : 10/02/14 - 14/02/14
Année de la rencontre : 2014

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DOI : 10.24350/CIRM.V.18479003
Citer cette vidéo: (2014). Polignac numbers and the consecutive gaps between primes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18479003
URI : http://dx.doi.org/10.24350/CIRM.V.18479003

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