Found with PFGW Version 3.7.5

1828^7005-7005^1828 is 2-PRP! (17.9671s+0.0023s)
1828^7005-7005^1828 is 3-PRP! (17.7389s+0.0023s)
1828^7005-7005^1828 is 5-PRP! (17.4597s+0.0017s)
1828^7005-7005^1828 is 7-PRP! (19.5004s+0.0018s)
1828^7005-7005^1828 is 11-PRP! (17.0320s+0.0024s)

Primality testing 1828^7005-7005^1828 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
1828^7005-7005^1828 is Fermat and Lucas PRP! (104.3435s+0.0034s)

To be completed...