Found with PFGW Version 3.6.0

4122^4355-4355^4122 is 2-PRP! (10.4525s+0.0025s)
4122^4355-4355^4122 is 3-PRP! (10.7305s+0.0023s)
4122^4355-4355^4122 is 5-PRP! (10.8372s+0.0024s)
4122^4355-4355^4122 is 7-PRP! (11.0507s+0.0038s)
4122^4355-4355^4122 is 11-PRP! (11.0944s+0.0032s)

Primality testing 4122^4355-4355^4122 [N-1/N+1, Brillhart-Lehmer-Selfridge]
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 0.06% and helper 0.03% (0.21% proof)
4122^4355-4355^4122 is Fermat and Lucas PRP! (51.0145s+0.0036s)

To be completed...