The primes contain arbitrarily long arithmetic progressions

@article{Green2004ThePC,
title={The primes contain arbitrarily long arithmetic progressions},
author={B. Green and T. 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… Expand