Found with PFGW Version 3.8.0

24^41317-41317^24 is 2-PRP! (61.5639s+0.0058s)
24^41317-41317^24 is 3-PRP! (64.4581s+0.0065s)
24^41317-41317^24 is 5-PRP! (62.2985s+0.0055s)
24^41317-41317^24 is 7-PRP! (63.0168s+0.0057s)
24^41317-41317^24 is 11-PRP! (61.4268s+0.0070s)

Primality testing 24^41317-41317^24 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
24^41317-41317^24 is Fermat and Lucas PRP! (354.7934s+0.0049s)

To be completed...