Links with high hull number

Let L be a link (a disjoint collection of simple closed curves) in R^3. We say that a point x lies in the n-th hull of L if every plane through x intersects L at least 2n times. If for every realization of the link L, the n-th hull is non-empty and n is maximal with this property, then n is called the hull number of L. Cantarella, Kuperberg, Kusner, and Sullivan showed that the hull number of any nontrivial knot is at least 2 and asked for knots and links with high hull number. We show that a link with p pairwise linked components has hull number at least 3p/5. At the beginning of the talk I will explain where the strange factor 3/5 comes from.