I think I found a better version of Wilson's theorem for prime numbers.

It is a division version of the theorem.

So, for Wilson you do:

n = 2
(n-1)! = 1 + 1 = 2 which is divisible by 2 so 2 is prime.

For mine you do the anti-factorial or counter-factorial which is each number divided by the previous number.

So 2/1 then you add 1 to the denominator and see if it can be divided by n.

So 1+1 = 2 which is divisible by n so 2 is prime.

3/2 > 2+1 = 3
5/4/3/2/1 = 5/24 > 24+1 = 25 which is divisible by 5 so 5 is prime.
7/6/5/4/3/2/1 = 720 > 720 + 1 = 721 which is divisible by 7 so 7 is prime.
Now is where it becomes better than Wilson, with n = 9:

Wilson says that 8! + 1 should be divisible by 9 if 9 is prime 8! is 40320 which is big.

For me:
9/8/7/6/5/4/3/2/1 = 4480 which is smaller than wilson's number then you add 1 and 4481 is not divisible by 9 so you get the same conclusion with less numbers because Wilson forces you to use big numbers but I am dividing fractionally each step of the way which allows for easier numbers to be used in simplicity.