  A celebrated and deep result of Green and Tao states that the primes contain
arbitrarily long arithmetic progressions. In this note I provide a
straightforward argument demonstrating that the primes get arbitrarily close to
arbitrarily long arithmetic progressions. The argument also applies to `large
sets' in the sense of Erd\H{o}s-Tur\'an. The proof is short, completely
self-contained, and aims to give a heuristic explanation of why the primes, and
other large sets, possess arithmetic structure.
