Found with PFGW Version 3.7.5

1404^5459-5459^1404 is 2-PRP! (10.3463s+0.0686s)
1404^5459-5459^1404 is 3-PRP! (10.7989s+0.0021s)
1404^5459-5459^1404 is 5-PRP! (11.2693s+0.0024s)
1404^5459-5459^1404 is 7-PRP! (10.5220s+0.0021s)
1404^5459-5459^1404 is 11-PRP! (11.0233s+0.0023s)

Primality testing 1404^5459-5459^1404 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
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 0.11% and helper 0.07% (0.41% proof)
1404^5459-5459^1404 is Fermat and Lucas PRP! (62.8088s+0.0043s)

To be completed...