Read the passage below and solve the questions based on it.
There are infinite number of taps that are filling a certain tank. The taps are numbered 1, 2, 3 and so on. Any tap numbered p (p > 2) can fill the tank in (p2 − 1) minutes while the first tap does not work at all.
If all the taps from the second tap onwards are opened simultaneously, then what is the shortest time in which the tank can be filled?