Supriya Ghosh (Editor)

Wilson quotient

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The Wilson quotient W(p) is defined as:

W ( p ) = ( p 1 ) ! + 1 p

If p is a prime number, the quotient is an integer by Wilson's theorem; moreover, if p is composite, the quotient is not an integer. If p divides W(p), it is called a Wilson prime. The integer values of W(p) are (sequence A007619 in the OEIS):

W(2)=1 W(3)=1 W(5)=5 W(7)=103 W(11)=329891 W(13)=36846277 W(17)=1230752346353 W(19)=336967037143579 ...

References

Wilson quotient Wikipedia