Conjecture: If p1 * p2 * p3 * ... pn + 1 is prime for every positive integer n, where p1,p2,...,pn are the n smallest prime number

So far, I have tried this

Proof (direct) :

Let pj be a prime number which is greater than 1

(p1*p2*p3*p4*...pn) % pj = 0

1 is divisible by pj

Therefore this conjecture is true?