# Dirichlet's Theorem on Arithmetic Progressions

## Phil Tootill, Undergraduate Maths Seminar

One of the best known proofs in mathematics is Euclid’s proof that there are infinitely any prime numbers. Arguments similar to Euclid’s can be used to show that infinitely many primes lie in certain progressions, but fail to show the result in full generality. Using the methods of analysis, Dirichlet’s theorem shows the result for any progression \((a+cn)\), with \(a\) and \(c\) coprime.