Found with PFGW Version 3.7.5

39^37078-38 is 2-PRP! (27.5563s+0.0046s)
39^37078-38 is 3-PRP! (27.5413s+0.0060s)
39^37078-38 is 5-PRP! (28.7596s+0.0171s)
39^37078-38 is 7-PRP! (30.1394s+0.0102s)
39^37078-38 is 11-PRP! (27.9102s+0.0060s)

Primality testing 39^37078-38 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
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 0.03% and helper 0.01% (0.08% proof)
39^37078-38 is Fermat and Lucas PRP! (259.6924s+0.0051s)

To be completed...