Found with PFGW Version 3.8.0

6^114433-114433^6 is 2-PRP! (157.1588s+0.0080s)
6^114433-114433^6 is 3-PRP! (164.5941s+0.0079s)
6^114433-114433^6 is 5-PRP! (158.4536s+0.0135s)
6^114433-114433^6 is 7-PRP! (156.9505s+0.0128s)
6^114433-114433^6 is 11-PRP! (161.8089s+0.0080s)

Primality testing 6^114433-114433^6 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.04% proof)
6^114433-114433^6 is Fermat and Lucas PRP! (887.4011s+0.0046s)

To be completed...