After application of full throttle during the takeoff run, a severe vibration developed which rapidly stopped the engine from rotating. When the aircraft came to rest the pilot noted that one of the two propeller blades had cleanly separated from its hub. The hub failed as a result of fatigue cracking which extended around approximately half of its circumference. The cracking originated in the root of the blade retention thread and grew progressively over about 850 flights. The cracking was not visible during normal periodic inspections because the hub had been painted to help prevent corrosion.