For 20 points, name this theorem that states that there exist arbitrarily long arithmetic progressions of primes with arbitrary common difference, named for a British and Australian-Chinese mathematician.
Chen and Shi used this theorem to prove Goldring's conjecture, and the namesakes of this theorem used to to prove a case of the "Mobius and nilsequences conjecture". The proof of this theorem relies on a generalization of the Koopman-von Neumann structure theorem and the Goldston-Yildirim truncated divisor sum. It was extended by one of its namesakes and Ziegler to polynomial progressions, and its namesakes proved a transference principle in order to obtain this result. Its namesakes relied on extending the statement that every subset of the integers 1 through N contains an arithmetic progression of length k, known as Szemerdi's theorem, and this theorem is similar to Dirichlet's theorem on arithmetic progressions. For 20 points, name this theorem that states that there exist arbitrarily long arithmetic progressions of primes with arbitrary common difference, named for a British and Australian-Chinese mathematician.
Chen and Shi used this theorem to prove Goldring's conjecture, and the namesakes of this theorem used to to prove a case of the "Mobius and nilsequences conjecture".
{Green}-{Tao} theorem