Why product of primes $+1$ is not divisible by any of the product primes? Given $n$ prime numbers, $p_1, p_2, p_3,\ldots,p_n$, then $p_1p_2p_3\cdots p_n+1$ is not divisible by any of the primes $p_i, i=1,2,3,\ldots,n.$ I dont understand why. Can somebody give me a hint or an Explanation ? Thanks.

Towards a contradiction, if some prime $p_i$ ($1\leq i\leq n$) divides $p_1p_2p_3\cdots p_n+1$, then because  $p_i$ also divides $p_1p_2p_3\cdots p_n$, it follows that $p_i\mid 1$ (the difference), a contradiction. 
