Found with PFGW Version 3.7.5

1998^6137-6137^1998 is 2-PRP! (22.7717s+0.0021s)
1998^6137-6137^1998 is 3-PRP! (18.0024s+0.0025s)
1998^6137-6137^1998 is 5-PRP! (17.3633s+0.0022s)
1998^6137-6137^1998 is 7-PRP! (17.9290s+0.0017s)
1998^6137-6137^1998 is 11-PRP! (17.3804s+0.0019s)

Primality testing 1998^6137-6137^1998 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.05% and helper 0.05% (0.21% proof)
1998^6137-6137^1998 is Fermat and Lucas PRP! (80.8936s+0.0036s)

To be completed...