Donut planet

Could a planet-sized object be donut shaped? From the definition of the planet, it's:

-is in orbit around the Sun,
-has sufficient mass so that it assumes a hydrostatic equilibrium (nearly round) shape, and
-has "cleared the neighbourhood" around its orbit

If there however was a way for donut-shaped planet to exist, would it be able to hold atmosphere?

>>10
Then the gravity as seen from a small part of the torus would look similar to that of a infinite rod-like planet, except for a bias to one side due to curvature, right? There'd be a tendency to contract. You could spin it to counter that, but that'd bring other destructive forces.

I'm going to eschew calculations, simulations and the scientific method, and just pull an answer out of my ass; You can't have a stable torus-shape that is massive enough that the tube is held together primarily by gravitational forces.