Found with PFGW Version 3.8.0

1017^14888-14888^1017 is 2-PRP! (40.3016s+0.0075s)
1017^14888-14888^1017 is 3-PRP! (38.0777s+0.0078s)
1017^14888-14888^1017 is 5-PRP! (38.6930s+0.0049s)
1017^14888-14888^1017 is 7-PRP! (38.9456s+0.0079s)
1017^14888-14888^1017 is 11-PRP! (39.0052s+0.0103s)

Primality testing 1017^14888-14888^1017 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 8+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
1017^14888-14888^1017 is Fermat and Lucas PRP! (229.7143s+0.0088s)

To be completed...