  Tao conjectured that every dense subset of $\mathcal{P}^d$, the $d$-tuples of
primes, contains constellations of any given shape. This was very recently
proved by Cook, Magyar, and Titichetrakun and independently by Tao and Ziegler.
Here we give a simple proof using the Green-Tao theorem on linear equations in
primes and the Furstenberg-Katznelson multidimensional Szemer\'edi theorem.
