PhD in Number Theory
Various projects are available in analytic number theory. These include questions on: distribution of primes, analytic properties of the Riemann zeta-function, explicit questions from elementary number theory (for example, every N>2 is the sum of a prime and a square-free number), and the distribution of primitive roots. See the Number Theory Group.
An undergraduate degree in pure mathematics, with a focus on one or more of algebra, analysis, or number theory.