Prime planar integral point sets containing any prescribed distance

Let $\mathfrak{M}(2,n)$ denote planar integral point sets with $n$ points. An integral point set is prime when it cannot be obtained by scaling a smaller integral point set while preserving its power and structure. Prime-set distance conjecture. For every $n\geq 3$ and $d\geq 1$, there exists a prime set $M\in\mathfrak{M}(2,n)$ containing points $M_1$ and $M_2$ whose distance is exactly $d$. The source presents this as the final and apparently most approachable conjecture; it follows earlier constructive results in higher dimensions but is not proved in the supplied text.