 The proof of the Green–Tao theorem does not show how to find the progressions of primes; it merely proves they exist.There has been separate computational work to find large arithmetic progressions in the primes.The Green-Tao paper states 'At the time of writing the longest known arithmetic progression of primes is of length 23, and was found in 2004 by Markus Frind, Paul Underwood, and Paul Jobling