Found with PFGW Version 3.7.5

7397^7706-7706^7397 is 2-PRP! (34.8049s+0.0040s)
7397^7706-7706^7397 is 3-PRP! (34.9099s+0.0040s)
7397^7706-7706^7397 is 5-PRP! (32.3318s+0.0033s)
7397^7706-7706^7397 is 7-PRP! (29.7377s+0.0029s)
7397^7706-7706^7397 is 11-PRP! (37.0411s+0.0071s)

Primality testing 7397^7706-7706^7397 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.14% proof)
7397^7706-7706^7397 is Fermat and Lucas PRP! (178.9611s+0.0051s)

To be completed...