By Martin Griffiths. The prime numbers 2, 3, 5, 7,  ... are the building blocks of our number system. Under certain conditions, any arithmetic progression of positive integers contains infinitely many primes, as proved by Gustave Dirichlet. For ages 16+. This book seeks to provide a complete proof which is accessible to school students possessing post-16 mathematical knowledge. All the techniques needed are carefully developed and explained.