Found with PFGW Version 3.8.0

38^56123-56123^38 is 2-PRP! (164.1607s+0.0031s)
38^56123-56123^38 is 3-PRP! (163.3209s+0.0017s)
38^56123-56123^38 is 5-PRP! (158.9064s+0.0017s)
38^56123-56123^38 is 7-PRP! (157.2504s+0.0018s)
38^56123-56123^38 is 11-PRP! (156.8057s+0.0020s)

Primality testing 38^56123-56123^38 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
38^56123-56123^38 is Fermat and Lucas PRP! (896.6864s+0.0062s)

To be completed...