Wilson's Theorem is a mathematical theorem that states that if a number is prime, then the factorial of that number minus one, divided by the number, will always result in a remainder of either 0 or (number-1).
Wilson's Theorem has significant applications in number theory and cryptography. It is used to determine if a number is prime and to generate large prime numbers for use in encryption algorithms.
To use Wilson's Theorem to determine if a number is prime, you must first calculate the factorial of that number minus one. Then, divide that factorial by the number and check the remainder. If the remainder is 0 or (number-1), then the number is prime. If the remainder is any other number, then the number is not prime.
No, Wilson's Theorem can only be used to determine if a specific number is prime. It cannot be used to find all prime numbers as there are infinitely many prime numbers and the theorem only applies to a specific number.
Yes, there are a few exceptions to Wilson's Theorem. The theorem only applies to positive integers, so it cannot be used for numbers less than 1. Additionally, numbers that are not prime can also sometimes satisfy the theorem. These numbers are known as pseudoprimes.