Found with PFGW Version 3.7.5

3871^7500-7500^3871 is 2-PRP! (30.6261s+0.0042s)
3871^7500-7500^3871 is 3-PRP! (30.6415s+0.0046s)
3871^7500-7500^3871 is 5-PRP! (29.6337s+0.0040s)
3871^7500-7500^3871 is 7-PRP! (29.2713s+0.0038s)
3871^7500-7500^3871 is 11-PRP! (30.4216s+0.0041s)

Primality testing 3871^7500-7500^3871 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N-1 test using base 23
Running N+1 test using discriminant 31, base 10+sqrt(31)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.12% proof)
3871^7500-7500^3871 is Fermat and Lucas PRP! (187.6868s+0.0035s)

To be completed...