Prove or Disprove that for p1p2....pn +1 is prime for every positive integer n, where p1,p2,....pn are the n smallest prime numbers.

What I did to answer this, I used the fact that n^2 + 1 is prime for all postive integers.

Then substituted (p(1n) x p2(n+1))^2 +1.

is this a valid proof for this question? after all the multiplying and factoring is done?