Twin Prime Factorial

Number Theory Level pending

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.

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