Found with PFGW Version 3.7.5

4859^9390-9390^4859 is 2-PRP! (22.6616s+0.0009s)
4859^9390-9390^4859 is 3-PRP! (22.6814s+0.0009s)
4859^9390-9390^4859 is 5-PRP! (22.4893s+0.0009s)
4859^9390-9390^4859 is 7-PRP! (22.3407s+0.0010s)
4859^9390-9390^4859 is 11-PRP! (22.5111s+0.0012s)

Primality testing 4859^9390-9390^4859 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 8+sqrt(17)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
4859^9390-9390^4859 is Fermat and Lucas PRP! (111.1635s+0.0028s)

To be completed...