JournalsemssVol. 1 , No. 2pp. 249–282

The Green-Tao theorem: an exposition

  • David Conlon

    University of Oxford, UK
  • Jacob Fox

    Stanford University, USA
  • Yufei Zhao

    Massachusetts Institute of Technology, Cambridge, USA
The Green-Tao theorem: an exposition cover
Download PDF


The celebrated Green-Tao theorem states that the prime numbers contain arbitrarily long arithmetic progressions. We give an exposition of the proof, incorporating several simplifications that have been discovered since the original paper.

Cite this article

David Conlon, Jacob Fox, Yufei Zhao, The Green-Tao theorem: an exposition. EMS Surv. Math. Sci. 1 (2014), no. 2 pp. 249–282

DOI 10.4171/EMSS/6