  We show that on conformal manifolds of even dimension $n\geq 4$ there is no
conformally invariant natural differential operator between density bundles
with leading part a power of the Laplacian $\Delta^{k}$ for $k>n/2$. This shows
that a large class of invariant operators on conformally flat manifolds do not
generalise to arbitrarily curved manifolds and that the theorem of Graham,
Jenne, Mason and Sparling, asserting the existence of curved version of
$\Delta^k$ for $1\le k\le n/2$, is sharp.
