Given a number N, the task is to check if it is prime or not using Wilson Primality Test. Print ‘1’ isf the number is prime, else print ‘0’.
Wilson’s theorem states that a natural number p > 1 is a prime number if and only if
(p - 1) ! ≡ -1 mod p OR (p - 1) ! ≡ (p-1) mod p
Input: p = 5 Output: Yes (p - 1)! = 24 24 % 5 = 4 Input: p = 7 Output: Yes (p-1)! = 6! = 720 720 % 7 = 6
Below is the implementation of Wilson Primality Test
How does it work?
- We can quickly check result for p = 2 or p = 3.
- For p > 3: If p is composite, then its positive divisors are among the integers 1, 2, 3, 4, … , p-1 and it is clear that gcd((p-1)!,p) > 1, so we can not have (p-1)! = -1 (mod p).
Now let us see how it is exactly -1 when p is a prime. If p is a prime, then all numbers in [1, p-1] are relatively prime to p. And for every number x in range [2, p-2], there must exist a pair y such that (x*y)%p = 1. So
[1 * 2 * 3 * ... (p-1)]%p = [1 * 1 * 1 ... (p-1)] // Group all x and y in [2..p-2] // such that (x*y)%p = 1 = (p-1)
- AKS Primality Test
- Lucas Primality Test
- Vantieghems Theorem for Primality Test
- Primality Test | Set 4 (Solovay-Strassen)
- Primality Test | Set 3 (Miller–Rabin)
- Primality Test | Set 2 (Fermat Method)
- Primality test for the sum of digits at odd places of a number
- Primality Test | Set 1 (Introduction and School Method)
- Primality Test | Set 5(Using Lucas-Lehmer Series)
- Wilson's Theorem
- Lychrel Number Implementation
- Implementation of K Nearest Neighbors
- Fizz Buzz Implementation
- Cubic Bezier Curve Implementation in C
- Exact Cover Problem and Algorithm X | Set 2 (Implementation with DLX)
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.