Found with PFGW Version 3.7.5

1131^6524-6524^1131 is 2-PRP! (15.9771s+0.0020s)
1131^6524-6524^1131 is 3-PRP! (16.1780s+0.0019s)
1131^6524-6524^1131 is 5-PRP! (18.0127s+0.0024s)
1131^6524-6524^1131 is 7-PRP! (19.3764s+0.0035s)
1131^6524-6524^1131 is 11-PRP! (16.0691s+0.0025s)

Primality testing 1131^6524-6524^1131 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 8+sqrt(13)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.17% proof)
1131^6524-6524^1131 is Fermat and Lucas PRP! (78.5926s+0.0032s)

To be completed...