Griffiths–Harris conjecture on degrees of curves on very general hypersurfaces

Let $X\subset\mathbb{P}^4$ be a very general hypersurface of degree $d\ge6$, and let $C\subset X$ be a curve. Griffiths–Harris conjecture. The degree of $C$ is divisible by $d$. This is the weakest of five conjectures proposed by Griffiths and Harris about curves on very general hypersurfaces. Stronger forms asserting algebraic or rational equivalence to a multiple of a plane section are known to imply it, while their strongest complete-intersection conjecture was disproved by Voisin. The degree-divisibility conjecture remains open in every degree, although the paper proves it for infinitely many degrees, beginning with $d=5005$.