Found with PFGW Version 3.7.5

512^8363-8363^512 is 2-PRP! (10.0719s+0.0008s)
512^8363-8363^512 is 3-PRP! (9.8308s+0.0007s)
512^8363-8363^512 is 5-PRP! (9.7838s+0.0008s)
512^8363-8363^512 is 7-PRP! (9.8080s+0.0010s)
512^8363-8363^512 is 11-PRP! (9.8915s+0.0008s)

Primality testing 512^8363-8363^512 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 6+sqrt(7)
Calling N-1 BLS with factored part 0.06% and helper 0.05% (0.22% proof)
512^8363-8363^512 is Fermat and Lucas PRP! (49.2621s+0.0016s)

To be completed...