Found with PFGW Version 3.6.0

3590^6007-6007^3590 is 2-PRP! (20.4933s+0.0038s)
3590^6007-6007^3590 is 3-PRP! (20.4332s+0.0032s)
3590^6007-6007^3590 is 5-PRP! (20.4203s+0.0033s)
3590^6007-6007^3590 is 7-PRP! (20.3709s+0.0028s)
3590^6007-6007^3590 is 11-PRP! (20.5472s+0.0025s)

Primality testing 3590^6007-6007^3590 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.05% and helper 0.03% (0.16% proof)
3590^6007-6007^3590 is Fermat and Lucas PRP! (118.0902s+0.0024s)

To be completed...