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


# Factorial
sub postfix:<!> (Int $n) { (constant f = 1, |[\×] 1..*)[$n] }
 
# Invisible times
sub infix:<⁢> is tighter(&infix:<**>) { $^a * $^b };
 
# Prime the iterator for thread safety
sink 11000!;
 
my @primes = ^1.1e4 .grep: *.is-prime;
 
say
'  n: Wilson primes
────────────────────';
 
.say for (1..40).hyper(:1batch).map: -> \𝒏 { 
    sprintf "%3d: %s", 𝒏, @primes.grep( -> \𝒑 { (𝒑 ≥ 𝒏) && ((𝒏 - 1)!⁢(𝒑 - 𝒏)! - (-1) ** 𝒏) %% 𝒑² } ).Str
}