What's the minimum time to cook raw prawns?
There is an optimal temperature to which they must be cooked, independent of method (boiling, frying, whatever). This temperature is 50 deg. C. (This is lower than safety guidelines; if you want to eliminate the foodborn illness risk, you must eat rubbery seafood). Once the inner temperature of seafood has risen above that, its proteins undergo an irreversible change called denaturation, which changes the texture. 

The time needed for reaching this temperature varies a lot. It depends on the size of the prawns, their initial temperature, the temperature of your water, on the total mass of water in the pot and on the total mass of prawns in the pot. 

If you find it impractical to impale a prawn on a digital thermometer every time you cook, you need to experiment. Keep the variables I mentioned constant, and boil prawns for different times. Find out how much they need before they go rubbery, and then stick to it, keeping all the other variables constant. In your case, this will probably correspond to the three minutes you mention. For somebody else, who boils a different amount of prawns per batch, it will be different.

There is no minimal time, just as there is no maximal time. The minimal temperature for them to taste cooked is 45 degrees C., but you can eat them at lower if you don't mind them tasting raw. You can find the minimum time for your case as described above. The legal minimum temperature for US food safety is 63 degrees. You can't legally approximate it by time, you must use a thermometer, or, at home, you can go much above it just to make sure - when seafood turns stiff and dry, you can be sure that it has reached 70 degrees.