Found with PFGW Version 3.4.8

40^18165+39 is 2-PRP! (55.2975s+0.0117s)
40^18165+39 is 3-PRP! (58.1013s+0.0170s)
40^18165+39 is 5-PRP! (56.7988s+0.0180s)
40^18165+39 is 7-PRP! (54.6838s+0.0098s)
40^18165+39 is 11-PRP! (56.7511s+0.0175s)

Primality testing 40^18165+39 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.09% and helper 0.04% (0.31% proof)
40^18165+39 is Fermat and Lucas PRP! (354.8296s+0.0133s)

To be completed...