Found with PFGW Version 3.6.0

1939^4062-4062^1939 is 2-PRP! (10.2973s+0.0029s)
1939^4062-4062^1939 is 3-PRP! (10.2415s+0.0018s)
1939^4062-4062^1939 is 5-PRP! (10.2513s+0.0020s)
1939^4062-4062^1939 is 7-PRP! (10.2862s+0.0025s)
1939^4062-4062^1939 is 11-PRP! (10.2811s+0.0020s)

Primality testing 1939^4062-4062^1939 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 13+sqrt(13)
Calling N+1 BLS with factored part 0.07% and helper 0.04% (0.25% proof)
1939^4062-4062^1939 is Fermat and Lucas PRP! (45.4359s+0.0020s)

To be completed...