Since P is a prime number greater than 3 and P is an odd number, P+ 1 must be an even number, so 2 is a factor of P+ 1.

Because p, P+ 1 and P+2 are three continuous natural numbers, the remainder of their division by 3 can only be 0, 1, 2. P+ 1 can be divisible by 3 because both P and p+2 are prime numbers greater than 3. That is, 3 is a factor of p+ 1

To sum up, 6 is a factor of p+ 1