Recent Progress in Additive Prime Number Theory

Terence Tao, 2006 Fields Medal Recipient - on Recent Progress in Additive Prime Number Theory
2009 Moursund Lectures, Day 1

Abstract: Additive prime number theory is the study of additive patterns in the primes. We survey some recent advances in this subject, including the results of Goldston, Pintz, and Yildirim on small gaps between primes, the results of Green and myself on arithmetic progressions in the primes, and the results of Bourgain, Gamburd, and Sarnak for detecting almost primes in orbits.

Prime number theorem