The prime grid contains arbitrarily large empty polygons

This paper proves a 2017 conjecture of De Loera, La Haye, Oliveros, and Rold\'an-Pensado that the "prime grid" \big\{(p,q) \in \mathbb{Z}^2 : \text{p$and$q are prime}\big\} \subseteq \mathbb{R}^2 contains empty polygons with arbitrarily many vertices. This implies that no Helly-type theorem is true for the prime grid.