Wilson Quotient

 

John Wilson

Quick Info

Born: 6 August 1741, Applethwaite, Westmorland, England.

Died: 18 October 1793 (aged 52) Kendal, Westmorland, England.

Known for: Wilson Quotient

                        Wilson primes

                      Wilson's theorem

Introduction

The Wilson Quotient

\begin{equation}  W\left ( {\color{Red} p} \right )=\frac{\left ({\color{Red} p\textbf{}}-1  \right )!+1}{{\color{Red} p}}\end{equation}

If p is a prime number, the quotient is an integer.

if p is composite, the quotient is not an integer.

A Wilson prime is a prime p that divides its Wilson quotient w(p) (see A007619). The known Wilson primes are 5, 13, 563 (see A007540).

References

• 1 R. Crandall & C. Pomerance, Prime Numbers: A Computational Perspective. New York: Springer (2001): 29.