Found with PFGW Version 3.7.5

7226^10367-10367^7226 is 2-PRP! (34.5246s+0.0028s)
7226^10367-10367^7226 is 3-PRP! (34.5644s+0.0028s)
7226^10367-10367^7226 is 5-PRP! (35.3111s+0.0026s)
7226^10367-10367^7226 is 7-PRP! (34.8868s+0.0027s)
7226^10367-10367^7226 is 11-PRP! (34.4998s+0.0026s)

Primality testing 7226^10367-10367^7226 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
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 0.03% (0.13% proof)
7226^10367-10367^7226 is Fermat and Lucas PRP! (207.9739s+0.0027s)

To be completed...