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.
The minimum number of taps that must be opened so that the tank is filled within 106 seconds is