The rank two bundle conjecture

Let $\mathbb{P}^N$ be a projective space of dimension at least six, and let $\mathcal{E}$ be a vector bundle of rank two on it. The rank two bundle conjecture. The bundle $\mathcal{E}$ splits. The source presents this as a well-known conjecture related to Hartshorne's codimension-two conjecture; its resolution is not established by the supplied text.