Brun–Titchmarsh theorem
In analytic number theory, the Brun–Titchmarsh theorem, named after Viggo Brun and Edward Charles Titchmarsh, is an upper bound on the distribution of prime numbers in arithmetic progression. == Statement == Let π ( x ; q , a ) {\displaystyle \pi (x;q,a)} count the number of primes p congruent to a modulo q with p ≤ x.