If the integer n is greater than 1, is n equal to 2?

(1) n has exactly two positive factors

(2)The difference of any two positive factors of n is odd.

OA is B

Please explain me how second statement alone is sufficient?

Let n be 12. it has 3,4 as factors. difference of 3,4 is odd.
Let n be 2, it has two factors 2,1.
2-1 =1 is also odd.
So for the same premise we are getting 2 answers(yes and No). Hence it is insufficient.

What is the mistake i am making?