Primes with missing digits | Vidéo | Carmin.tv

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Primes with missing digits

By James Maynard

Appears in collections : 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, Exposés de recherche, Fields medallists - 2022

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.

Information about the video

Date of recording 13/12/2016
Date of publication 06/01/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19101403
Cite this video Maynard, James (13/12/2016). Primes with missing digits. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19101403
URL https://dx.doi.org/10.24350/CIRM.V.19101403

Domain(s)

Number Theory

Bibliography

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

MSC codes

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