%0 Generic %1 green2004primes %A Green, Ben %A Tao, Terence %D 2004 %K arithmetic mathematics progression %T The primes contain arbitrarily long arithmetic progressions %U http://arxiv.org/abs/math/0404188 %X 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 sufficiently pseudorandom set of positive relative density contains progressions of arbitrary length. The third ingredient is a recent result of Goldston and Yildirim. Using this, one may place the primes inside a pseudorandom set of ``almost primes'' with positive relative density.

@misc{green2004primes, abstract = {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 sufficiently pseudorandom set of positive relative density contains progressions of arbitrary length. The third ingredient is a recent result of Goldston and Yildirim. Using this, one may place the primes inside a pseudorandom set of ``almost primes'' with positive relative density.}, added-at = {2013-12-23T06:09:04.000+0100}, author = {Green, Ben and Tao, Terence}, biburl = {https://www.bibsonomy.org/bibtex/225b6c6d18862a865e5dab4be609aeb9a/aeu_research}, description = {The primes contain arbitrarily long arithmetic progressions}, interhash = {f7f47951cc397944f040ab99e5485c10}, intrahash = {25b6c6d18862a865e5dab4be609aeb9a}, keywords = {arithmetic mathematics progression}, note = {cite arxiv:math/0404188Comment: 56 pages. Further minor corrections}, timestamp = {2013-12-24T01:12:20.000+0100}, title = {The primes contain arbitrarily long arithmetic progressions}, url = {http://arxiv.org/abs/math/0404188}, year = 2004 }