Show that a number is not prime? Show that for any integer $n>1$, all the numbers $n!+2, n!+3, \ldots, n!+n$ are composite (i.e. not prime).

Hint:
Try to show, that if for two numbers $a$ and $b$, $a$ is divisible by $d$ and $b$ is divisible by $d$, then so is their sum. Then go looking for such a common divisor in your sums.
