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


func is_wilson_prime(p, n = 1) {
    var m = p*p
    (factorialmod(n-1, m) * factorialmod(p-n, m) - (-1)**n) % m == 0
}
 
var primes = 1.1e4.primes
 
say "  n: Wilson primes\n────────────────────"
 
for n in (1..11) {
    printf("%3d: %s\n", n, primes.grep {|p| is_wilson_prime(p, n) })
}