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Polignac numbers and the consecutive gaps between primes

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Post-edited
Authors : Pintz, János (Author of the conference)
CIRM (Publisher )

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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
Abstract : 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.

MSC Codes :
11B05 - Density, gaps, topology
 11N05 - Distribution of primes
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 05/05/14
    Conference Date : 11/02/14
    Subseries : Research talks
    arXiv category : Number Theory
    Mathematical Area(s) : Number Theory
    Format : QuickTime (.mov) Video Time : 00:51:53
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2014-02-11_Pintz.mp4
Information on the Event

Event Title : Prime numbers : new perspectives / Nombres premiers : nouvelles perspectives
Event Organizers : Dartyge, Cécile ; Mauduit, Christian ; Rivat, Joël ; Stoll, Thomas
Dates : 10/02/14 - 14/02/14
Event Year : 2014

Citation Data

DOI : 10.24350/CIRM.V.18479003
Cite this video as: Pintz, János (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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