  A Riemannian manifold is called Osserman (conformally Osserman,
respectively), if the eigenvalues of the Jacobi operator of its curvature
tensor (Weyl tensor, respectively) are constant on the unit tangent sphere at
every point. Osserman Conjecture asserts that every Osserman manifold is either
flat or rank-one symmetric. We prove that both the Osserman Conjecture and its
conformal version, the Conformal Osserman Conjecture, are true, modulo a
certain assumption on algebraic curvature tensors in $\mathbb{R}^16$. As a
consequence, we show that a Riemannian manifold having the same Weyl tensor as
a rank-one symmetric space, is conformally equivalent to it.
