On the Brun–Titchmarsh theorem

Abstract

The Brun–Titchmarsh theorem shows that the number of primes which are less than $x$ and congruent to $a$ modulo $q$ is less than $(C+o(1))x/(\phi(q)\log{x})$ for some value $C$ depending on $\log{x}/\!\log{q}$. Different authors have provided differ