Quebec Mathematical Sciences Colloquium

December 8, 2017 from 16:00 to 16:00 (Montreal/Miami time) On location

Primes with missing digits

Colloquium presented by James Maynard (University of Oxford)

Many famous open questions about primes can be interpreted as questions about the digits of primes in a given base. 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^{1­c} elements less than X) which is typically very 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


UQAM, Pavillon Président-­Kennedy, 201, ave du Président­-Kennedy, room PK­5115