De Loera–La Haye–Oliveros–Roldán-Pensado conjecture on the Helly number of the prime lattice

Let $\mathcal{P}$ be the set of prime numbers, and let $h(S)$ denote the Helly number of a set $S\subseteq\mathbb{R}^2$. De Loera–La Haye–Oliveros–Roldán-Pensado conjecture.

$$h(\mathcal{P}^2)=\infty.$$

This conjecture concerns the finiteness of Helly numbers for discrete planar sets and was cited as an open problem motivating the paper's study of exponential lattices.