The prime-square subgroup conjecture for Helly numbers

Let $h(S)$ denote the Helly number of a subset $S\subseteq\mathbb{R}^d$, and let $\mathbb{P}$ be the set of prime numbers. Prime-square Helly conjecture.

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

This conjecture predicts that the Helly number can be infinite for a highly structured discrete subset of $\mathbb{R}^2$, highlighting connections between Helly-type finiteness and number theory. The source gives no resolution.