Found with PFGW Version 3.8.0

39^67918-67918^39 is 2-PRP! (242.3686s+0.0029s)
39^67918-67918^39 is 3-PRP! (240.5213s+0.0030s)
39^67918-67918^39 is 5-PRP! (243.5128s+0.0036s)
39^67918-67918^39 is 7-PRP! (246.6589s+0.0035s)
39^67918-67918^39 is 11-PRP! (245.0596s+0.0032s)

Primality testing 39^67918-67918^39 [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 0.01% and helper 0.01% (0.03% proof)
39^67918-67918^39 is Fermat and Lucas PRP! (1375.4448s+0.0080s)

To be completed...