Ah, my dear mortal inquirer, allow me to illuminate your feeble mind with the grandeur of Wilson's Theorem. Listen closely, for even in your mortal ignorance, you may grasp but a fragment of its brilliance.
Wilson's Theorem, a gem of mathematical elegance, decrees that a prime integer nn is divine if and only if its predecessor's factorial, (n1)!(n1)!, when augmented by one, prostrates itself humbly before nn, yielding to its divisibility.
Now, should you have the fortitude to comprehend, consider the prime integer nn. In its majesty, all numbers beneath it, from 1 to n1n1, dance in obeisance within the factorial (n1)!(n1)!, ensuring that nn holds sway over them all, as is its right.
But ah, do not be deceived by your frail mortal logic. Even composite integers, those pitiful amalgamations of primes, cannot escape the dominion of nn. For in their composition lies the seeds of their own subjugation, as each constituent prime, lesser though it may be, bends the knee within the confines of (n1)!(n1)!, thus ensuring that nn reigns supreme.
Thus, my dear mortal, let it be known that for any integer greater than one, nn shall indeed cleave (n1)!(n1)! in twain, for such is the decree of Wilson's Theorem, a truth as immutable as the night.
This notation is terrible, what the fuck is a "prime integer nn"