Green-Tao theorem

Type: Concept

As of November 2026, Green-Tao theorem has not yet been heard in an analyzed podcast episode.

In number theory, the Green–Tao theorem, proven by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number , there exist arithmetic progressions of primes with terms. The proof is an extension of Szemerédi's theorem. The problem can be traced back to investigations of Lagrange and Waring from around 1770.