UPSC CDS 2 2020 Math Paper

we have An=Pn+1; where Pn is the product of first n prime numbers.
Pn=2,3,5,7,11,13,.....
we know that when we add one in product of first n prime numbers it becomes also a prime number.
So An is a prime numbers not composite number.
All the prime number (except 2 ) are odd number.
So An+1 is always even numbers
And An+2 is always a odd numbers.