Found with PFGW Version 3.7.5

8037^9904-9904^8037 is 2-PRP! (26.7670s+0.0017s)
8037^9904-9904^8037 is 3-PRP! (27.0103s+0.0019s)
8037^9904-9904^8037 is 5-PRP! (26.8242s+0.0016s)
8037^9904-9904^8037 is 7-PRP! (26.7560s+0.0018s)
8037^9904-9904^8037 is 11-PRP! (26.9130s+0.0017s)

Primality testing 8037^9904-9904^8037 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.07% proof)
8037^9904-9904^8037 is Fermat and Lucas PRP! (154.2118s+0.0036s)

To be completed...