Fred, I topped off the tank with gas because I was told that the primer was gravity fed and works better with full tank.
WRONG!
NO FUEL goes thru that tiny primer hose. What happens is that when you activate the primer, it pushes air into the fuel chamber in the carb & pressurizes it. Then, with the fuel under "pressure", it escapes thru the main well tube to PRIME the carb throat with available fuel for the engine to burn immediately.
As long as there is SOME fuel in the tank, the primer SHOULD work. If not, the hose could be loose, disconnected or broken, the atmospheric vent in the carb might be clogged, the primer bulb may have a hole in it (not to be confused with the hole in the center on some primers), or the carb's internals are clogged up.
Hope that sheds some light on the subject...
Marty