  Let $(M, g)$ be a compact Riemannian manifold of dimension $N \geq 5$ and
$Q_g$ be its $Q$ curvature. The prescribed $Q$ curvature problem is concerned
with finding metric of constant $Q$ curvature in the conformal class of $g$.
This amounts to finding a positive solution to \[ P_g (u)= c
u^{\frac{N+4}{N-4}}, u>0 {on} M\] where $P_g$ is the Paneitz operator. We show
that for dimensions $N \geq 25$, the set of all positive solutions to the
prescribed $Q$ curvature problem is {\em non-compact}.
