Found with PFGW Version 3.7.5

1171^5484-5484^1171 is 2-PRP! (8.9992s+0.0024s)
1171^5484-5484^1171 is 3-PRP! (10.4319s+0.0020s)
1171^5484-5484^1171 is 5-PRP! (14.3880s+0.0028s)
1171^5484-5484^1171 is 7-PRP! (10.7580s+0.0024s)
1171^5484-5484^1171 is 11-PRP! (10.4757s+0.0022s)

Primality testing 1171^5484-5484^1171 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N+1 BLS with factored part 0.06% and helper 0.01% (0.19% proof)
1171^5484-5484^1171 is Fermat and Lucas PRP! (49.7688s+0.0040s)

To be completed...