Mathematical Conversations

Unfortunately counting prime numbers is hard. Fortunately, we can cheat by counting 'approximate prime numbers' which is much easier. Moreover, this allows us to say something about the primes themselves, and works in situations which seem well beyond the reach of the Riemann Hypothesis! I'll give a gentle intro to these 'approximate primes', and show how they play a key role in the Green-Tao theorem on arithmetic progressions of primes, as well as bounded gaps between primes.