Found with PFGW Version 3.7.5

4785^9544-9544^4785 is 2-PRP! (22.7632s+0.0016s)
4785^9544-9544^4785 is 3-PRP! (22.7046s+0.0015s)
4785^9544-9544^4785 is 5-PRP! (23.0266s+0.0014s)
4785^9544-9544^4785 is 7-PRP! (22.6362s+0.0014s)
4785^9544-9544^4785 is 11-PRP! (22.8284s+0.0016s)

Primality testing 4785^9544-9544^4785 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.08% proof)
4785^9544-9544^4785 is Fermat and Lucas PRP! (135.3425s+0.0022s)

To be completed...