Found with PFGW Version 3.6.0

992^4361-4361^992 is 2-PRP! (6.7124s+0.0015s)
992^4361-4361^992 is 3-PRP! (7.0906s+0.0016s)
992^4361-4361^992 is 5-PRP! (7.0911s+0.0017s)
992^4361-4361^992 is 7-PRP! (6.6938s+0.0014s)
992^4361-4361^992 is 11-PRP! (6.6984s+0.0018s)

Primality testing 992^4361-4361^992 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 13
Running N-1 test using base 17
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 0.15% and helper 0.08% (0.54% proof)
992^4361-4361^992 is Fermat and Lucas PRP! (51.6288s+0.0015s)

To be completed...