Found with PFGW Version 3.7.5

1789^9000-9000^1789 is 2-PRP! (14.9586s+0.0014s)
1789^9000-9000^1789 is 3-PRP! (15.4030s+0.0013s)
1789^9000-9000^1789 is 5-PRP! (15.3459s+0.0012s)
1789^9000-9000^1789 is 7-PRP! (15.5285s+0.0014s)
1789^9000-9000^1789 is 11-PRP! (15.3614s+0.0012s)

Primality testing 1789^9000-9000^1789 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N-1 BLS with factored part 0.04% and helper 0.04% (0.16% proof)
1789^9000-9000^1789 is Fermat and Lucas PRP! (78.6753s+0.0024s)

To be completed...