Question 67
We enumerate all prime numbers in ascending order: $p_1 = 2, p_2 = 3, p_3 = 5, \dots$. Find all positive integer $n$, for which $p_1!+p_2!+\dots+p_n!=a^b$, for some positive integer $a, b\gt 1$, where $k!$ denotes the product of all integers from 1 to $k$.