The primes contain arbitrarily long arithmetic progressions

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.