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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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The Green-Tao Theorem on arithmetic progressions in the primes: an ergodic point of view
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by Bryna Kra PDF
Bull. Amer. Math. Soc. 43 (2006), 3-23 Request permission


A long-standing and almost folkloric conjecture is that the primes contain arbitrarily long arithmetic progressions. Until recently, the only prog- ress on this conjecture was due to van der Corput, who showed in 1939 that there are infinitely many triples of primes in arithmetic progression. In an amazing fusion of methods from analytic number theory and ergodic theory, Ben Green and Terence Tao showed that for any positive integer $k$, there exist infinitely many arithmetic progressions of length $k$ consisting only of prime numbers. This is an introduction to some of the ideas in the proof, concentrating on the connections to ergodic theory.
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Additional Information
  • Bryna Kra
  • Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Rd., Evanston, Illinois 60208-2730
  • MR Author ID: 363208
  • ORCID: 0000-0002-5301-3839
  • Email:
  • Received by editor(s): July 20, 2005
  • Published electronically: October 6, 2005
  • Additional Notes: This article is an expanded version of a lecture presented January 7, 2005, at the AMS Special Session on Current Events, Joint Mathematics Meetings, Atlanta, GA. The author was partially supported by NSF grant DMS-0244994.
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 43 (2006), 3-23
  • MSC (2000): Primary 11N13, 37A45, 11B25
  • DOI:
  • MathSciNet review: 2188173