Definition
A Wilson prime of order n is a prime number   p   such that   p2   exactly divides:

     (n − 1)! × (p − n)! − (− 1)n 



If   n   is   1,   the latter formula reduces to the more familiar:   (p - n)! + 1   where the only known examples for   p   are   5,   13,   and   563.



Task
Calculate and show on this page the Wilson primes, if any, for orders n = 1 to 11 inclusive and for primes p < 18   or,

if your language supports big integers, for p < 11,000.



Related task
 Primality by Wilson's theorem


ClearAll[WilsonPrime]
WilsonPrime[n_Integer] := Module[{primes, out},
  primes = Prime[Range[PrimePi[11000]]];
  out = Reap@Do[
     If[Divisible[((n - 1)!) ((p - n)!) - (-1)^n, p^2], Sow[p]]
     ,
     {p, primes}
     ];
  First[out[[2]], {}]
 ]
Do[
 Print[WilsonPrime[n]]
 ,
 {n, 1, 11}
]