Wilson's theorem

Wilson's Theorem states that a natural number \( p \) is a prime number if and only if the factorial of \( p-1 \) plus one is divisible by \( p \). In simpler terms, if you take all the whole numbers from 1 to \( p-1 \), multiply them together (this is called a factorial), and then add 1, the result will be a number that can be divided evenly by \( p \) if \( p \) is prime. This theorem connects prime numbers with factorials, showcasing a deep relationship in number theory.