Remove the +/-1 and add +/-k and divide by k where k | x!^n

Things will get interesting Ali candidates will be proveable via N-/+1 method since they will be of form where N has prime factors equal to or less than x.

Additionally if both (x!^n+/-k)/k are prime then they are twin primes.

Here is non twin, n=1 example:

https://www.mersenneforum.org/showpo...8&postcount=19
ETA Unlike non-generalized factorial primes there are plenty of twin-primes in the generated form which are highly unreserved.