Prime degree conjecture for branched-cover branch data

Let $d$ be a positive integer, and let $\mathcal{D}$ be a collection of nontrivial partitions of $d$. A collection satisfying the Riemann–Hurwitz formula is called a candidate branch datum; it is realizable if it occurs as the branch data of a branched covering. Prime degree conjecture. If $d$ is prime, then every candidate branch datum $\mathcal{D}$ is realizable. Edmonds, Kulkarni, and Stong reduced the conjecture to candidate branch data with exactly three partitions. It remains open, despite strong supporting evidence and computational progress on low-degree cases.