Found with PFGW Version 3.8.0

10568^10993-10993^10568 is 2-PRP! (36.3540s+0.0044s)
10568^10993-10993^10568 is 3-PRP! (36.3522s+0.0045s)
10568^10993-10993^10568 is 5-PRP! (36.4827s+0.0045s)
10568^10993-10993^10568 is 7-PRP! (36.9952s+0.0047s)
10568^10993-10993^10568 is 11-PRP! (36.2304s+0.0049s)

Primality testing 10568^10993-10993^10568 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
10568^10993-10993^10568 is Fermat and Lucas PRP! (222.8309s+0.0076s)

To be completed...