Found with PFGW Version 3.6.0

1040^3957-3957^1040 is 2-PRP! (5.7091s+0.0015s)
1040^3957-3957^1040 is 3-PRP! (5.7492s+0.0016s)
1040^3957-3957^1040 is 5-PRP! (5.6939s+0.0018s)
1040^3957-3957^1040 is 7-PRP! (5.6193s+0.0017s)
1040^3957-3957^1040 is 11-PRP! (5.8801s+0.0015s)

Primality testing 1040^3957-3957^1040 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.11% and helper 0.02% (0.37% proof)
1040^3957-3957^1040 is Fermat and Lucas PRP! (27.5538s+0.0018s)

To be completed...