Found with PFGW Version 3.8.0

8544^12901-12901^8544 is 2-PRP! (49.4823s+0.0083s)
8544^12901-12901^8544 is 3-PRP! (48.1469s+0.0073s)
8544^12901-12901^8544 is 5-PRP! (47.7504s+0.0078s)
8544^12901-12901^8544 is 7-PRP! (47.5623s+0.0078s)
8544^12901-12901^8544 is 11-PRP! (48.2882s+0.0097s)

Primality testing 8544^12901-12901^8544 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N+1 BLS with factored part 0.03% and helper 0.00% (0.11% proof)
8544^12901-12901^8544 is Fermat and Lucas PRP! (295.9164s+0.0088s)

To be completed...