this talk is an introduction to analytic number theory via two very classical results. we will start with a discussion of the riemann zeta function, including a quick proof of the functional equation and some discussion of the location of the zeros. then we will go through dirichlet's proof that there are infinitely many primes congruent to a modulo $q$ when $(a, q) = 1$. to keep the talk at a survey level, some results will be stated without proof. (translation: i'm going to avoid long, techincal calculations as much as possible.)