Finite Set of Primes, n is prime

There is a finite set $$\{p_1, \ldots, p_r\}$$ of all primes and $$n = p_1 p_2 \cdots p_r + 1 $$ is prime $$\Rightarrow$$ Contradiction.

Explanation

n is prime, but is not contained in the set of primes $$\{p_1, \ldots, p_r\}$$.