Graduate Number Theory Seminar
Abel Castillo
Brun's Theorem towards twin primes and improvements: a survey
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.
Wednesday January 28, 2015 at 3:00 PM in SEO 512