Found with PFGW Version 3.6.0

2037^4138-4138^2037 is 2-PRP! (9.1418s+0.0034s)
2037^4138-4138^2037 is 3-PRP! (9.1653s+0.0019s)
2037^4138-4138^2037 is 5-PRP! (9.1627s+0.0033s)
2037^4138-4138^2037 is 7-PRP! (9.2211s+0.0023s)
2037^4138-4138^2037 is 11-PRP! (9.1575s+0.0021s)

Primality testing 2037^4138-4138^2037 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.06% and helper 0.01% (0.19% proof)
2037^4138-4138^2037 is Fermat and Lucas PRP! (42.8661s+0.0019s)

To be completed...