Found with PFGW Version 3.7.5

7369^8612-8612^7369 is 2-PRP! (21.8119s+0.0016s)
7369^8612-8612^7369 is 3-PRP! (21.9634s+0.0016s)
7369^8612-8612^7369 is 5-PRP! (22.0132s+0.0020s)
7369^8612-8612^7369 is 7-PRP! (21.6065s+0.0015s)
7369^8612-8612^7369 is 11-PRP! (21.7958s+0.0015s)

Primality testing 7369^8612-8612^7369 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 8+sqrt(11)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.13% proof)
7369^8612-8612^7369 is Fermat and Lucas PRP! (106.7465s+0.0023s)

To be completed...