Found with PFGW Version 3.7.5

3825^8402-8402^3825 is 2-PRP! (16.5239s+0.0010s)
3825^8402-8402^3825 is 3-PRP! (16.1149s+0.0008s)
3825^8402-8402^3825 is 5-PRP! (16.4835s+0.0007s)
3825^8402-8402^3825 is 7-PRP! (15.8439s+0.0010s)
3825^8402-8402^3825 is 11-PRP! (15.8514s+0.0007s)

Primality testing 3825^8402-8402^3825 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.09% proof)
3825^8402-8402^3825 is Fermat and Lucas PRP! (81.9205s+0.0015s)

To be completed...