Found with PFGW Version 3.7.5

1092^10889-10889^1092 is 2-PRP! (21.4035s+0.0014s)
1092^10889-10889^1092 is 3-PRP! (22.0847s+0.0013s)
1092^10889-10889^1092 is 5-PRP! (21.6758s+0.0013s)
1092^10889-10889^1092 is 7-PRP! (21.6468s+0.0011s)
1092^10889-10889^1092 is 11-PRP! (21.7640s+0.0012s)

Primality testing 1092^10889-10889^1092 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.04% and helper 0.02% (0.15% proof)
1092^10889-10889^1092 is Fermat and Lucas PRP! (105.1383s+0.0021s)

To be completed...