You need both the HP and the RPM's to get the prop to the desired speed to achieve the needed thrust. The actual HP and RPM's required will vary based on the prop diameter, the particular blade profile, blade pitch angle and the tip design. Ideally, the RPM's are set to keep the blade tip speed below supersonic for efficiency and noise control.
A T-6 on takeoff will have the prop tips well into the supersonic region, but the pilot reduces the blade pitch and the needed RPM's very quickly after takeoff, as not as much power is need to drive the prop at that point. It's a huge balancing game with some black art to it.