Q.To show that the number $N=(P_1....P_n)+1$ is not always prime (where $P_1,...,P_n$)are the first n primes) , find an n for which $(P_1...P_n)+1$ is not prime
My attempt
since $P_1,...,P_n$are the first n primes so $P_1=2$
so product is even so N is odd number
$N=2k+1$
since odd number {1,3,5,7,9,....} is not always prime so N is not always prime