Found with PFGW Version 3.6.0

3555^5096-5096^3555 is 2-PRP! (12.5905s+0.0019s)
3555^5096-5096^3555 is 3-PRP! (15.8114s+0.0039s)
3555^5096-5096^3555 is 5-PRP! (14.9848s+0.0025s)
3555^5096-5096^3555 is 7-PRP! (15.1281s+0.0022s)
3555^5096-5096^3555 is 11-PRP! (14.6769s+0.0018s)

Primality testing 3555^5096-5096^3555 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N+1 BLS with factored part 0.05% and helper 0.04% (0.21% proof)
3555^5096-5096^3555 is Fermat and Lucas PRP! (69.1897s+0.0034s)

To be completed...