Found with PFGW Version 3.7.5

3971^10520-10520^3971 is 2-PRP! (26.5840s+0.0016s)
3971^10520-10520^3971 is 3-PRP! (26.2356s+0.0016s)
3971^10520-10520^3971 is 5-PRP! (26.5745s+0.0016s)
3971^10520-10520^3971 is 7-PRP! (26.2478s+0.0017s)
3971^10520-10520^3971 is 11-PRP! (26.0292s+0.0016s)

Primality testing 3971^10520-10520^3971 [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 0.03% and helper 0.02% (0.12% proof)
3971^10520-10520^3971 is Fermat and Lucas PRP! (150.0955s+0.0026s)

To be completed...