TH-TMO 2016 Problem 5

given $p_1,p_2,...$ be a sequence of integer and $p_1=2$ , for positive integer $n$ , $p_{n+1}$ is the least prime factor of $np_1^{1!}p_2^{2!}...p_n^{n!}+1$ prove that all primes appear in the sequence

(Proposed by Beatmania)