Found with PFGW Version 3.6.0

1040^4523-4523^1040 is 2-PRP! (9.2531s+0.0028s)
1040^4523-4523^1040 is 3-PRP! (9.2250s+0.0032s)
1040^4523-4523^1040 is 5-PRP! (9.2126s+0.0030s)
1040^4523-4523^1040 is 7-PRP! (9.2122s+0.0029s)
1040^4523-4523^1040 is 11-PRP! (9.1963s+0.0020s)

Primality testing 1040^4523-4523^1040 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 16+sqrt(7)
Calling N+1 BLS with factored part 0.13% and helper 0.01% (0.40% proof)
1040^4523-4523^1040 is Fermat and Lucas PRP! (42.2973s+0.0029s)

To be completed...