Found with PFGW Version 3.8.0

3099^11132-11132^3099 is 2-PRP! (26.8469s+0.0009s)
3099^11132-11132^3099 is 3-PRP! (27.0579s+0.0016s)
3099^11132-11132^3099 is 5-PRP! (27.8111s+0.0010s)
3099^11132-11132^3099 is 7-PRP! (27.9030s+0.0008s)
3099^11132-11132^3099 is 11-PRP! (27.7306s+0.0009s)

Primality testing 3099^11132-11132^3099 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 8+sqrt(13)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
3099^11132-11132^3099 is Fermat and Lucas PRP! (192.9198s+0.0050s)

To be completed...