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


def emit_until(cond; stream): label $out | stream | if cond then break $out else . end;
 
# For 0 <= $n <= ., factorials[$n] is $n !
def factorials:
   reduce range(1; .+1) as $n ([1];
    .[$n] = $n * .[$n-1]);
 
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
 
def primes: 2, (range(3; infinite; 2) | select(is_prime));