Found with PFGW Version 3.7.5

4582^8967-8967^4582 is 2-PRP! (21.2097s+0.0014s)
4582^8967-8967^4582 is 3-PRP! (21.3469s+0.0014s)
4582^8967-8967^4582 is 5-PRP! (21.5670s+0.0014s)
4582^8967-8967^4582 is 7-PRP! (21.2395s+0.0014s)
4582^8967-8967^4582 is 11-PRP! (21.6495s+0.0014s)

Primality testing 4582^8967-8967^4582 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 9+sqrt(7)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
4582^8967-8967^4582 is Fermat and Lucas PRP! (105.2938s+0.0029s)

To be completed...