A number theory problem by Anandmay Patel

Let \(P_i\) denote the \(i^\text{th} \) smallest prime number.
Can \( \displaystyle \left(\prod_{j=1}^m P_j \right) + 1 = 2\times3\times5\times \cdots \times P_m + 1 \) ever be a prime number?

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