Found with PFGW Version 3.7.5

122^5789-5789^122 is 2-PRP! (4.0664s+0.0016s)
122^5789-5789^122 is 3-PRP! (4.1156s+0.0012s)
122^5789-5789^122 is 5-PRP! (4.1336s+0.0017s)
122^5789-5789^122 is 7-PRP! (4.0605s+0.0017s)
122^5789-5789^122 is 11-PRP! (4.0539s+0.0017s)

Primality testing 122^5789-5789^122 [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 base 13
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 0.10% and helper 0.02% (0.34% proof)
122^5789-5789^122 is Fermat and Lucas PRP! (28.9162s+0.0031s)

To be completed...