# 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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