Ballantine–Beck–Feigon–Maurischat's irreducibility conjecture for partition numerators

Let $\operatorname{num}(n,x)$ denote the ordinary partition numerator for $n\geq 1$. Ballantine–Beck–Feigon–Maurischat's irreducibility conjecture. For every $n\geq 1$, the polynomial $\operatorname{num}(n,x)$ is irreducible over $\mathbb Z$. This is one of the conjectures proposed for reciprocals of ordinary partition polynomials; its resolution is not specified in the supplied text.