### A Friendly Introduction to Sieves, with a Look Towards Recent Progress on the Twin Prime Conjecture

By David Lowry-Duda

October 9, 2013

#### Abstract

In this very, very friendly talk, we will investigate the progression of sieves. We start with (and spend most of our time on) the Sieve of Eratosthenes, classically used to find primes and count primes, but which we'll use to show that there are 'few' twin primes. We'll move towards Selberg's Sieve and try to understand why it works and (partly) how Yitang Zhang adapted it to show that there are infinitely many pairs of primes separated by a fixed distance. Finally, we'll review recent progress from Polymath 8 to improve Zhang's result.This talk emphasizes approachability and scope over vigor. It is not just for number theorists! All are welcome.