The factoriality conjecture for threefolds with ordinary multiple points

Let $X \subset \mathbb{P}^4$ be a hypersurface of degree $d$ whose singular locus consists of $k$ ordinary multiple points $p_1,\ldots,p_k$ of multiplicities $m_1,\ldots,m_k$. Factoriality conjecture. If

$$\sum_{i=1}^k (m_i-1)^2 < (d-1)^2,$$

then $X$ is factorial.

This conjecture generalizes results of Ciliberto, Di Gennaro and Cheltsov on factoriality and is motivated by the known criterion for threefolds with ordinary double and triple points. Its status is not resolved in the supplied source context.