S.Chmutov, S.Duzhin. A lower bound for the number of Vassiliev knot invariants. We prove that the number of primitive Vassiliev knot invariants of degree $d$ grows at least as $d^{\log(d)}$ when $d$ tends to infinity. In particular it grows faster than any polynomial in $d$. The proof is based on the explicit construction of an ample family of linearly independent primitive elements in the corresponding graded Hopf algebra.