# The primes contain arbitrarily long arithmetic progressions

@article{Green2004ThePC, title={The primes contain arbitrarily long arithmetic progressions}, author={Ben Green and Terence Tao}, journal={Annals of Mathematics}, year={2004}, volume={167}, pages={481-547} }

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemeredi�s theorem, which asserts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient of this paper, is a certain transference principle. This allows us to deduce from Szemeredi�s theorem that any subset of a suficiently pseudorandom set (or measure) of positive relative density…

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