What is the correct formula to calculate propeller efficiency? How to calculate in the right way the efficiency of a propeller?

If we know the engine power, speed of the plane and the thrust of its propeller, what is the correct method, (1) or (2), for calculating the efficiency of the propeller?



Assuming that Method 1 is the correct one, it appears that the efficiency of a propeller must satisfy the inequality:



Update:

It looks like Method 1 is correct and 2 is wrong as long as the page Performance of Propellers, MIT calculates the efficiency on an ideal propeller and gets the same inequality.
If a propeller of diameter, d, delivers the thrust, T, while the plane travels at the speed, V, it always has a maximum possible efficiency that can be calculated, is below 1 and can not be improved. Not even an ideal propeller of diameter, d, has, in general, an efficiency that reaches 100%. The absolute minimum, reference power, is always $TV$ and not something else and the efficiency is always:
$$TV/Power_{absorbed}$$
where the minimum absorbed power is calculated with Froude's Propeller Theory.
Propellers are designed for an optimal tip speed being a certain multiple of the air speed they are flying inside. The angle of the propellers aerofoil shape to the propellers axel changes as you move from the Center to the tip. The more pronounced the blade rotation the higher the intended tip speed.

From memory having the tip speed running at 1-3 times the the air flow speed is not efficient, but at least the propeller works over a wide range of air speeds.

Highly tuned propeller tips are moving at 6x the air speed. However, their effectiveness at moving air disappears rapidly if the air flow is too slow. (The propeller blades are stalled)

The last thing you want on a propeller plane is an efficient propeller.