Easier guessed than proven

Level pending

The sequence \(p_{1}\), \(p_{2}\) ... is defined as follows:

\(p_{1} = 2\) and for \(n \geq 2\), \(p_{n}\) is the largest prime divisor of \(p_{1}p_{2}....p_{n-1}+1\). Find the first prime number which is not a member of the sequence.

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