Found with PFGW Version 3.7.5

3847^7128-7128^3847 is 2-PRP! (36.4066s+0.0046s)
3847^7128-7128^3847 is 3-PRP! (35.6672s+0.0050s)
3847^7128-7128^3847 is 5-PRP! (35.9622s+0.0050s)
3847^7128-7128^3847 is 7-PRP! (35.8605s+0.0033s)
3847^7128-7128^3847 is 11-PRP! (34.7042s+0.0049s)

Primality testing 3847^7128-7128^3847 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 17
Running N-1 test using base 37
Running N-1 test using base 47
Running N+1 test using discriminant 59, base 5+sqrt(59)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
3847^7128-7128^3847 is Fermat and Lucas PRP! (285.5024s+0.0065s)

To be completed...