This award supports the research of Andrew Granville and covers a broad range of areas of mathematics, primarily in number theory, with applications to computer science. The research builds on Granville's understanding of the distribution of primes. The award also supports his continued work in both graduate and undergraduate education as well as his exposition. This Presidential Faculty Fellow award to Andrew Granville is for excellent research and teaching in number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.