Found with PFGW Version 3.6.0

555^3964-3964^555 is 2-PRP! (5.0081s+0.0017s)
555^3964-3964^555 is 3-PRP! (5.0301s+0.0018s)
555^3964-3964^555 is 5-PRP! (5.0124s+0.0019s)
555^3964-3964^555 is 7-PRP! (5.1021s+0.0043s)
555^3964-3964^555 is 11-PRP! (5.0972s+0.0021s)

Primality testing 555^3964-3964^555 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 7+sqrt(11)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.16% proof)
555^3964-3964^555 is Fermat and Lucas PRP! (24.1922s+0.0020s)

To be completed...