Found with PFGW Version 3.7.5

4089^10912-10912^4089 is 2-PRP! (33.0827s+0.0023s)
4089^10912-10912^4089 is 3-PRP! (33.8599s+0.0026s)
4089^10912-10912^4089 is 5-PRP! (33.9084s+0.0024s)
4089^10912-10912^4089 is 7-PRP! (34.1116s+0.0024s)
4089^10912-10912^4089 is 11-PRP! (35.0144s+0.0024s)

Primality testing 4089^10912-10912^4089 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
4089^10912-10912^4089 is Fermat and Lucas PRP! (165.1833s+0.0025s)

To be completed...