Found with PFGW Version 3.6.0

3812^6007-6007^3812 is 2-PRP! (20.6354s+0.0028s)
3812^6007-6007^3812 is 3-PRP! (20.5630s+0.0026s)
3812^6007-6007^3812 is 5-PRP! (20.5610s+0.0025s)
3812^6007-6007^3812 is 7-PRP! (20.6235s+0.0029s)
3812^6007-6007^3812 is 11-PRP! (20.4928s+0.0025s)

Primality testing 3812^6007-6007^3812 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.08% and helper 0.02% (0.27% proof)
3812^6007-6007^3812 is Fermat and Lucas PRP! (98.5164s+0.0033s)

To be completed...