Found with PFGW Version 3.7.5

24^36397+23 is 2-PRP! (34.4359s+0.0050s)
24^36397+23 is 3-PRP! (35.6041s+0.0042s)
24^36397+23 is 5-PRP! (34.7613s+0.0059s)
24^36397+23 is 7-PRP! (34.5020s+0.0058s)
24^36397+23 is 11-PRP! (34.3388s+0.0059s)

Primality testing 24^36397+23 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.03% and helper 0.00% (0.10% proof)
24^36397+23 is Fermat and Lucas PRP! (273.9143s+0.0056s)

To be completed...