Found with PFGW Version 3.6.0

3714^3835-3835^3714 is 2-PRP! (8.8768s+0.0023s)
3714^3835-3835^3714 is 3-PRP! (9.1504s+0.0034s)
3714^3835-3835^3714 is 5-PRP! (9.2017s+0.0022s)
3714^3835-3835^3714 is 7-PRP! (9.2283s+0.0024s)
3714^3835-3835^3714 is 11-PRP! (9.2039s+0.0022s)

Primality testing 3714^3835-3835^3714 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 23
Running N+1 test using discriminant 43, base 1+sqrt(43)
Calling N-1 BLS with factored part 0.09% and helper 0.03% (0.29% proof)
3714^3835-3835^3714 is Fermat and Lucas PRP! (42.9082s+0.0020s)

To be completed...