Found with PFGW Version 3.6.0

4817^6762-6762^4817 is 2-PRP! (27.5313s+0.0027s)
4817^6762-6762^4817 is 3-PRP! (31.3233s+0.0032s)
4817^6762-6762^4817 is 5-PRP! (28.1466s+0.0033s)
4817^6762-6762^4817 is 7-PRP! (27.9046s+0.0023s)
4817^6762-6762^4817 is 11-PRP! (27.4480s+0.0024s)

Primality testing 4817^6762-6762^4817 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.12% and helper 0.04% (0.40% proof)
4817^6762-6762^4817 is Fermat and Lucas PRP! (128.4437s+0.0039s)

To be completed...