Found with PFGW Version 3.8.0

10502^11005-11005^10502 is 2-PRP! (36.4648s+0.0070s)
10502^11005-11005^10502 is 3-PRP! (36.2788s+0.0069s)
10502^11005-11005^10502 is 5-PRP! (36.3036s+0.0070s)
10502^11005-11005^10502 is 7-PRP! (36.4706s+0.0068s)
10502^11005-11005^10502 is 11-PRP! (36.2770s+0.0068s)

Primality testing 10502^11005-11005^10502 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 6+sqrt(7)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
10502^11005-11005^10502 is Fermat and Lucas PRP! (184.9817s+0.0074s)

To be completed...