2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75963This is an article for a general mathematical audience on the author's work, joint with Terence Tao, establishing that there are arbitrarily long arithmetic progressions of primes. It is based on several one hour lectures, chiefly given at British universities.19 pages, submitted to Proceedings of the Gauss-Dirichlet Conference, Gottingen, June 20-24 2005Number TheoryClassical Analysis and ODEstext