Esser's coprimality conjecture for the large-index Calabi–Yau construction

For each integer $n\geq 2$, let $m'_n$ and $E_n$ be the explicitly defined integers associated with the weighted hypersurface construction. Two integers are relatively prime if their greatest common divisor is $1$. Esser's coprimality conjecture. The numbers $m'_n$ and $E_n$ are relatively prime. By the paper's criterion, this is equivalent to the associated quotient having index $m'_n$. The conjecture has been verified by computer in dimensions at most $30$; it remains open in general.