Found with PFGW Version 3.6.0

3426^3763-3763^3426 is 2-PRP! (6.8767s+0.0034s)
3426^3763-3763^3426 is 3-PRP! (6.9538s+0.0034s)
3426^3763-3763^3426 is 5-PRP! (6.9829s+0.0036s)
3426^3763-3763^3426 is 7-PRP! (6.8956s+0.0034s)
3426^3763-3763^3426 is 11-PRP! (6.8818s+0.0039s)

Primality testing 3426^3763-3763^3426 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N+1 BLS with factored part 0.07% and helper 0.02% (0.23% proof)
3426^3763-3763^3426 is Fermat and Lucas PRP! (39.0156s+0.0019s)

To be completed...