Is $1992! - 1$ prime?

Consider the factorials, defined inductively by $1! = 0! = 1$ and $n! = n\cdot(n-1)!$ for $n \geq 2$.

Question: Is $1992!-1$ a prime number?

The question is from a book, maybe is contest math problem. Now I think 1992 is especial?

Solution 1:

No. The smallest prime factors are $3449$ and $8627$ (found with Mathematica).

For what it's worth:

$$ \{n\in\mathbb{N}:2\le n\le2000\text{ and }n!-1\text{ is prime }\}=\\\{3,4,6,7,12,14,30,32,33,38,94,166,324,379,469,546,974,1963\} $$

Should have thought of checking OEIS. This is sequence A002982