Linear equations in primes

@article{Green2006LinearEI,
  title={Linear equations in primes},
  author={Ben Green and Terence Tao},
  journal={Annals of Mathematics},
  year={2006},
  volume={171},
  pages={1753-1850}
}
Consider a system ψ of nonconstant affine-linear forms ψ 1 , ... , ψ t : ℤ d → ℤ, no two of which are linearly dependent. Let N be a large integer, and let K ⊆ [-N, N] d be convex. A generalisation of a famous and difficult open conjecture of Hardy and Littlewood predicts an asymptotic, as N →∞, for the number of integer points n ∈ ℤ d ∩ K for which the integers ψ 1 (n), ... , ψ t (n) are simultaneously prime. This implies many other well-known conjectures, such as the twin prime conjecture and… 

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