An extension of Wilson's Theorem

The aim of this work is to optimize the existing formula based on Wilson's theorem to reduce the magnitude of the computation results.

Wilson's theorem states: if p is a prime number, then (p-1)! + 1 is divisible by p (p-1)! ≡ -1 (mod p).

The function (p-1)! increases very rapidly and reaches huge values.

When the values of p are large, the calculations become resource-intensive, so it is necessary to reduce the upper limit of the calculation results.