Found with PFGW Version 3.7.5

3422^9631-9631^3422 is 2-PRP! (22.1818s+0.0013s)
3422^9631-9631^3422 is 3-PRP! (22.2125s+0.0013s)
3422^9631-9631^3422 is 5-PRP! (22.5680s+0.0013s)
3422^9631-9631^3422 is 7-PRP! (22.5606s+0.0014s)
3422^9631-9631^3422 is 11-PRP! (22.1440s+0.0014s)

Primality testing 3422^9631-9631^3422 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 0.05% and helper 0.03% (0.17% proof)
3422^9631-9631^3422 is Fermat and Lucas PRP! (130.3506s+0.0029s)

To be completed...