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Published 2014 | Submitted
Journal Article Open

The Green-Tao theorem: an exposition


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.

Additional Information

© 2014 European Mathematical Society. Published online 2014-11-28. The first author was supported by a Royal Society University Research Fellowship. The second author was supported by a Packard Fellowship, NSF Career Award DMS-1352121, an Alfred P. Sloan Fellowship, and an MIT NEC Corporation Award. The third author was supported by a Microsoft Research PhD Fellowship. We thank Yuval Filmus, Mohammad Bavarian, and the anonymous referee for helpful comments on the manuscript.

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August 19, 2023
October 18, 2023