Found with PFGW Version 3.7.5

1082^7431-7431^1082 is 2-PRP! (20.2959s+0.0021s)
1082^7431-7431^1082 is 3-PRP! (20.6878s+0.0026s)
1082^7431-7431^1082 is 5-PRP! (20.6228s+0.0024s)
1082^7431-7431^1082 is 7-PRP! (20.6734s+0.0026s)
1082^7431-7431^1082 is 11-PRP! (21.0554s+0.0024s)

Primality testing 1082^7431-7431^1082 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N+1 BLS with factored part 0.05% and helper 0.01% (0.17% proof)
1082^7431-7431^1082 is Fermat and Lucas PRP! (108.1837s+0.0041s)

To be completed...