Found with PFGW Version 3.6.0

1638^3905-3905^1638 is 2-PRP! (6.0119s+0.0016s)
1638^3905-3905^1638 is 3-PRP! (6.6171s+0.0045s)
1638^3905-3905^1638 is 5-PRP! (6.0282s+0.0024s)
1638^3905-3905^1638 is 7-PRP! (5.9514s+0.0019s)
1638^3905-3905^1638 is 11-PRP! (5.8907s+0.0019s)

Primality testing 1638^3905-3905^1638 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 0.11% and helper 0.06% (0.39% proof)
1638^3905-3905^1638 is Fermat and Lucas PRP! (28.6986s+0.0031s)

To be completed...