Found with PFGW Version 3.7.5

4544^8759-8759^4544 is 2-PRP! (18.2473s+0.0014s)
4544^8759-8759^4544 is 3-PRP! (18.0695s+0.0011s)
4544^8759-8759^4544 is 5-PRP! (18.0000s+0.0012s)
4544^8759-8759^4544 is 7-PRP! (18.0064s+0.0012s)
4544^8759-8759^4544 is 11-PRP! (17.8707s+0.0010s)

Primality testing 4544^8759-8759^4544 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 8+sqrt(7)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.08% proof)
4544^8759-8759^4544 is Fermat and Lucas PRP! (110.5753s+0.0021s)

To be completed...