Let $N$ be a positive integer not equal to $1$. Then note that none of the numbers $2, 3, \ldots, N$ is a divisor of $N! - 1$. From this we can conclude that:
(A) $N! – 1$ is a prime number;
(B) at least one of the numbers $N + 1, N + 2, \ldots, N! – 2$ is a divisor of $N! - 1$;
(C) the smallest number between $N$ and $N!$ which is a divisor of $N! - 1$, is a prime number.
My working: $N! - 1$ is not necessarily a prime, as $5! - 1 = 119$ and $7 \mid 119$. I cannot proceed further. Hints are appreciated.