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}
}
  • B. Green, T. Tao
  • Published 8 April 2004
  • Mathematics
  • Annals of Mathematics
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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