问题

$4!+1==25==5^2$

$5!+1==121==11^2$

$7!+1==5041==71^2$

对于 $n!+1=m^2$, 除了上面的 $n=4,5,7$ 之外, 还有解吗?

$11!+1==39916801$ is a prime

$27!+1==10888869450418352160768000001$ 很有可能是素数.

$29\mid 28!+1$

$31\mid 30!+1$

令 

\[
B=\{n\in\mathbb{N}\mid n | (n-1)!+1\}
\]

则 $B$ 中的元素是哪些?

References:

Richard K. Guy, Unsolved Problems in Number Theory, D25 Equations involving factorial $n$.