The prime grid contains arbitrarily large empty polygons

Abstract This paper proves a 2017 conjecture of De Loera, La Haye, Oliveros, and Roldán-Pensado that the “prime grid” {(p, q) ∈ ℤ2 : p and q are prime} ⊆ ℝ2 contains empty polygons with arbitrarily many vertices. This implies that no Helly-type theorem is true for the prime grid.