Abel Castillo : Brun's Theorem towards twin primes and improvements: a survey

Posted by Dylon Chow , part of the Graduate Number Theory Seminar.

At

Jan. 28, 2015, 3 p.m.

In

SEO 512

Abstract

A theorem of Viggo Brunn from the beginnings of modern sieve theory is that there are infinitely many primes p such that p+2 has at most nine (not necessarily distinct) prime factors. In this talk we'll discuss this result, as well as later improvements; most notable among these is the theorem of Chen which shows that there are infinitely many primes p such that p+2 has at most two prime factors. We will also discuss some of the ideas used to obtain these results, including some basic ideas from sieve theory. As time permits, we'll mention analogues of Chen's theorem in number fields.