  We show that the Hodge numbers of the moduli space of stable rank two sheaves
with primitive determinant on a K3 surface coincide with the Hodge numbers of
an appropriate Hilbert scheme of points on the K3 surface. The precise result
is: Theorem: Let $X$ be a K3 surface, $L$ a primitive big and nef line bundle
and $H$ a generic polarization. If the moduli space of rank two $H$ semi-stable
torsion-free sheaves with determiant $L$ and second Chern class $c_2$ has at
least dimension 10 then its Hodge numbers coincide with those of the Hilbert
scheme of $l:=2c_2-\frac{L^2}{2}-3$ points on $X$.
