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H 1 Primes with missing digits

Auteurs : Maynard, James (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We will talk about recent work showing there are infinitely many primes with no $7$ in their decimal expansion. (And similarly with $7$ replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most $X^{1-c}$ elements less than $X$) which is typically vey difficult.
    The proof relies on a fun mixture of tools including Fourier analysis, Markov chains, Diophantine approximation, combinatorial geometry as well as tools from analytic number theory.

    Codes MSC :
    11A63 - Radix representation; digital problems
    11N05 - Distribution of primes

    Informations sur la rencontre

    Nom du congrès : Jean-Morlet Chair: Ergodic theory and its connections with arithmetic and combinatorics / Chaire Jean Morlet : Théorie ergodique et ses connexions avec l'arithmétique et la combinatoire
    Organisteurs Congrès : Cassaigne, Julien ; Ferenczi, Sébastien ; Hubert, Pascal ; Kulaga-Przymus, Joanna ; Lemanczyk, Mariusz
    Dates : 12/12/16 - 16/12/16
    Année de la rencontre : 2016
    URL Congrès : http://lemanczyk-ferenczi.weebly.com/con...

    Citation Data

    DOI : 10.24350/CIRM.V.19101403
    Cite this video as: Maynard, James (2016). Primes with missing digits. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19101403
    URI : http://dx.doi.org/10.24350/CIRM.V.19101403

    Voir aussi


    1. Maynard, J. (2016). Primes with restricted digits. - https://arxiv.org/abs/1604.01041