Ciliberto–Di Gennaro conjecture for nodal hypersurfaces

Let $X\subset\operatorname{\mathbb{P}}^4$ be a nodal hypersurface, meaning a hypersurface of degree $d$ whose singularities are all ordinary double points. Assume that $X$ has at most $2(d-2)(d-1)$ singular points. Ciliberto–Di Gennaro conjecture. One of the following holds: (1) $X$ is factorial; (2) $X$ contains a plane and has at least $(d-1)^2$ nodes; or (3) $X$ contains a quadric surface and has exactly $2(d-2)(d-1)$ nodes. The conjecture concerns the factoriality of nodal hypersurfaces, a property equivalent here to $\operatorname{\mathbb{Q}}$-factoriality and relevant to questions of rationality. Its status is not resolved in the supplied source context.