Found with PFGW Version 3.7.5

992^5251-5251^992 is 2-PRP! (7.7348s+0.0022s)
992^5251-5251^992 is 3-PRP! (7.8962s+0.0016s)
992^5251-5251^992 is 5-PRP! (8.4320s+0.0016s)
992^5251-5251^992 is 7-PRP! (9.2961s+0.0022s)
992^5251-5251^992 is 11-PRP! (9.7061s+0.0017s)

Primality testing 992^5251-5251^992 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.07% and helper 0.03% (0.26% proof)
992^5251-5251^992 is Fermat and Lucas PRP! (51.8868s+0.0029s)

To be completed...