Found with PFGW Version 3.7.5

39^37749+38 is 2-PRP! (28.1757s+0.0037s)
39^37749+38 is 3-PRP! (28.2029s+0.0036s)
39^37749+38 is 5-PRP! (29.2867s+0.0038s)
39^37749+38 is 7-PRP! (29.5328s+0.0035s)
39^37749+38 is 11-PRP! (28.8144s+0.0038s)

Primality testing 39^37749+38 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
39^37749+38 is Fermat and Lucas PRP! (232.8063s+0.0051s)

To be completed...