Found with PFGW Version 3.8.0

1584^11083-11083^1584 is 2-PRP! (23.3075s+0.0056s)
1584^11083-11083^1584 is 3-PRP! (23.2166s+0.0064s)
1584^11083-11083^1584 is 5-PRP! (23.2717s+0.0056s)
1584^11083-11083^1584 is 7-PRP! (24.1431s+0.0057s)
1584^11083-11083^1584 is 11-PRP! (23.2362s+0.0063s)

Primality testing 1584^11083-11083^1584 [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 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
1584^11083-11083^1584 is Fermat and Lucas PRP! (143.5198s+0.0049s)

To be completed...