Found with PFGW Version 3.7.5

39^44718+38 is 2-PRP! (42.5905s+0.0041s)
39^44718+38 is 3-PRP! (42.6128s+0.0038s)
39^44718+38 is 5-PRP! (44.2356s+0.0047s)
39^44718+38 is 7-PRP! (46.6697s+0.0042s)
39^44718+38 is 11-PRP! (43.0326s+0.0042s)

Primality testing 39^44718+38 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
39^44718+38 is Fermat and Lucas PRP! (346.6680s+0.0058s)

To be completed...