Consider the following statements -

If n is a prime number such that ( n + 2 ) is also a prime number, then

S1 : { n ( n + 2 ) + 1} is a perfect square.

S2 : ( 2n + 2 ) is divisible by 6 if n is greater than 3.

Which of the statements given above is/are correct?

The Correct answer is Option 3. 

Key Points

Considering statement -1:

If n = 3, then (n + 2) = 5

∴ 3 × 5 + 1 = 16, which is a perfect square.

Same is true for n = 5, 11, 17, 29, 41.

So, S1 is true.

Considering statement -2:

If n = 5, then n + 2 = 7 and 5, 7 are both prime numbers.

Now, (2n + 2) = 10 + 2 = 12 and it is divisible by 6.

Same is true for n = 11, 17, 29, 41.

So, statement 2 is also true.

Thus, both S1 and S2 are correct.

Hence, option (c) is correct.