Found with PFGW Version 3.7.5

368^8299-8299^368 is 2-PRP! (9.3775s+0.0010s)
368^8299-8299^368 is 3-PRP! (9.1896s+0.0011s)
368^8299-8299^368 is 5-PRP! (9.3080s+0.0014s)
368^8299-8299^368 is 7-PRP! (9.2247s+0.0017s)
368^8299-8299^368 is 11-PRP! (9.2019s+0.0010s)

Primality testing 368^8299-8299^368 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
368^8299-8299^368 is Fermat and Lucas PRP! (54.1810s+0.0021s)

To be completed...