Université de Montréal and University of Oxford



Small gaps between primes


It is believed that there should be infinitely many pairs of primes which differ by 2; this is the famous twin prime conjecture. More generally, it is believed that for every positive integer m there should be infinitely many sets of m primes with each set contained in an interval of size roughly m log m. Although proving these conjectures seems to be beyond our current techniques, recent progress has enabled us to obtain some partial results. We will introduce a refinement of the “GPY sieve method” for studying these problems. This refinement will allow us to show (amongst other things) that liminfn (pn+m – pn) < ∞ for any integer m, and so there are infinitely many bounded length intervals containing m primes. We will also discuss some extensions of this result.


The Catalan Mathematical Society invites participants to this first congress of a biannual series focusing on current research topics across several areas of Mathematics.

Plenary talks and thematic sessions have been selected by the Scientific Committee of the SCM. Special thanks are due to the organisers of the thematic sessions and to the local mathematical community as a whole for their support to this congress.



Societat Catalana de Matemàtiques
Institut d'Estudis Catalans
Carrer del Carme, 47
08001 Barcelona

Phone: +34 933 248 583

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