Found with PFGW Version 3.7.5

4534^9039-9039^4534 is 2-PRP! (21.2841s+0.0015s)
4534^9039-9039^4534 is 3-PRP! (21.3526s+0.0015s)
4534^9039-9039^4534 is 5-PRP! (21.3962s+0.0014s)
4534^9039-9039^4534 is 7-PRP! (21.6667s+0.0014s)
4534^9039-9039^4534 is 11-PRP! (21.2452s+0.0015s)

Primality testing 4534^9039-9039^4534 [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 base 7
Running N-1 test using base 23
Running N+1 test using discriminant 31, base 1+sqrt(31)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
4534^9039-9039^4534 is Fermat and Lucas PRP! (173.5569s+0.0021s)

To be completed...