Found with PFGW Version 3.8.0

10901^10970-10970^10901 is 2-PRP! (36.3069s+0.0072s)
10901^10970-10970^10901 is 3-PRP! (36.3114s+0.0135s)
10901^10970-10970^10901 is 5-PRP! (36.3084s+0.0068s)
10901^10970-10970^10901 is 7-PRP! (36.4599s+0.0069s)
10901^10970-10970^10901 is 11-PRP! (36.2987s+0.0072s)

Primality testing 10901^10970-10970^10901 [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 0.02% and helper 0.01% (0.07% proof)
10901^10970-10970^10901 is Fermat and Lucas PRP! (187.8037s+0.0082s)

To be completed...