Small gaps between primes. (English) Zbl 1373.11069

Goldston, D. A.; Pintz, J.; Yıldırım, C. Y.

Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. II: Invited lectures. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-805-6/hbk; 978-89-6105-803-2/set). 419-441 (2014).

Summary: This paper describes the authors’ joint research on small gaps between primes in the last decade and how their methods were developed further independently by Zhang, Maynard, and Tao to prove stunning new results on primes. We now know that there are infinitely many primes differing by at most 246, and that one can find \(k\) primes a bounded distance (depending on \(k\)) apart infinitely often. These results confirm important approximations to the Hardy-Littlewood prime tuples conjecture.
For the entire collection see [Zbl 1314.00104].

MSC:

11N05	Distribution of primes
11N36	Applications of sieve methods
11N35	Sieves

Keywords:

Hardy-Littlewood prime tuples conjecture; prime numbers; sieves; gaps between primes; twin primes