Found with PFGW Version 3.7.5

10484^12433-12433^10484 is 2-PRP! (88.3151s+0.0043s)
10484^12433-12433^10484 is 3-PRP! (92.5862s+0.0056s)
10484^12433-12433^10484 is 5-PRP! (93.0829s+0.0050s)
10484^12433-12433^10484 is 7-PRP! (93.1763s+0.0049s)
10484^12433-12433^10484 is 11-PRP! (92.0355s+0.0043s)

Primality testing 10484^12433-12433^10484 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
10484^12433-12433^10484 is Fermat and Lucas PRP! (634.3848s+0.0056s)

To be completed...