##  [Wilson's Theorem](/wilsons-theorem) 

  ##  [Wilson's Theorem](https://algebra.quantumdictionary.io/wilsons-theorem-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A number-theoretic characterization stating that a positive integer p is prime if and only if (p − 1)! ≡ −1 (mod p); equivalently, the factorial of p − 1 is congruent to −1 modulo p precisely for prime p.