Found with PFGW Version 3.7.5

3794^9371-9371^3794 is 2-PRP! (21.5810s+0.0013s)
3794^9371-9371^3794 is 3-PRP! (21.5736s+0.0014s)
3794^9371-9371^3794 is 5-PRP! (21.5501s+0.0015s)
3794^9371-9371^3794 is 7-PRP! (21.5633s+0.0015s)
3794^9371-9371^3794 is 11-PRP! (21.6137s+0.0015s)

Primality testing 3794^9371-9371^3794 [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 2+sqrt(11)
Calling N+1 BLS with factored part 0.00% and helper 0.00% (0.01% proof)
3794^9371-9371^3794 is Fermat and Lucas PRP! (128.0027s+0.0024s)

To be completed...