I'm scratching my head over this one. The rpm of the prop, whether constant speed prop or fixed pitch, versus the reciprocal speed of the camera shutter would seem to be the only factor. If the reciprocal shutter speed exactly matches or is an even divisor of the prop rpm, whether two, three, four or five blade; wouldn't that stop the prop in the photo? Most taken pictures should therefore be expected to show some prop blur. Most of mine do.
With a variable strobe light experiment, if you can match the strobe rate to the rpm of a constant rotation object, the strobe will always 'freeze' the rotating action, making it appear stopped. The only variable is to match the rotatory speed. I have done this in lab situations many times.
I set my digital camera for auto exposure in aircraft photography. The shutter speed range is 16 seconds to 1/2000th of a second. For aircraft takeoff or landing power, I normally get some prop blur but occasionally the prop appears virtually stopped. Idling props after engine start always seem to show as stopped. Whether the prop will be stopped by my camera is probably farthest from my mind. I pan the camera for most takeoffs and landings-this seems to stop the aircraft sufficiently with an automatic shutter, blurring sometimes the background.
As for geared prop aircraft engines, the Cessna 175 Skylark and the Beech Twin Bonanzas with GO engines come to mind. These engines did cost more, are more expensive to maintain and repair, and haven't proved very popular. Turboshaft prop engines are all geared way down to keep prop tip speeds in check , as well as are the Legendary Aircraft P-51 and TF-51s and other Experimental-classed aircraft that use, say, a Corvette automobile engine. Different gear ratios may be offered, dependent on the prop chosen in what are called PSRUs (propeller speed reduction units).
All this suggests to me we should just aim and shoot, hoping to catch a fast aircraft centered in the photo.