**This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.**

### Abstract

This article gives a formal version of Furstenberg's topological proof of the infinitude of primes. He defines a topology on the integers based on arithmetic progressions (or, equivalently, residue classes). Using some fairly obvious properties of this topology, the infinitude of primes is then easily obtained.

Apart from this, this topology is also fairly โniceโ in general: it is second countable, metrizable, and perfect. All of these (well-known) facts are formally proven, including an explicit metric for the topology given by Zulfeqarr.