Found with PFGW Version 3.8.0

8501^13400-13400^8501 is 2-PRP! (55.0958s+0.0097s)
8501^13400-13400^8501 is 3-PRP! (55.2778s+0.0097s)
8501^13400-13400^8501 is 5-PRP! (53.9621s+0.0094s)
8501^13400-13400^8501 is 7-PRP! (57.1328s+0.0111s)
8501^13400-13400^8501 is 11-PRP! (55.7075s+0.0099s)

Primality testing 8501^13400-13400^8501 [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 0.01% and helper 0.00% (0.03% proof)
8501^13400-13400^8501 is Fermat and Lucas PRP! (272.6030s+0.0102s)

To be completed...