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.