Found with PFGW Version 3.8.0

4823^13028-13028^4823 is 2-PRP! (43.7976s+0.0019s)
4823^13028-13028^4823 is 3-PRP! (42.8665s+0.0014s)
4823^13028-13028^4823 is 5-PRP! (45.8515s+0.0012s)
4823^13028-13028^4823 is 7-PRP! (43.0355s+0.0015s)
4823^13028-13028^4823 is 11-PRP! (43.2890s+0.0012s)

Primality testing 4823^13028-13028^4823 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.11% proof)
4823^13028-13028^4823 is Fermat and Lucas PRP! (252.5478s+0.0062s)

To be completed...