40320

This number is a composite.

8! = 40320 is the smallest factorial that can be expressed as a sum of distinct squared primes: 2^2+3^2+5^2+7^2+11^2+13^2+17^2+19^2+23^2+29^2+41^2+59^2+181^2. Found by Dmitry Kamenetsky. [Rivera]