Twin Prime Factorial

Let $p_{n}$ denote the $n^\text{th}$ prime number and let $Q_{n} = p_{1} \times p_{2} \times p_{3} \times \cdots \times p_{n}$ . For example, $Q_{1} = 2, Q_{2} = 2 \times 3, Q_{3} = 2 \times 3 \times 5$ . Is the following true or false?

For any positive integer $n$ , at least one of $Q_{n} + 1$ or $Q_{n} - 1$ is prime.