Found with PFGW Version 3.8.0

9384^11059-11059^9384 is 2-PRP! (37.2165s+0.0064s)
9384^11059-11059^9384 is 3-PRP! (37.1911s+0.0074s)
9384^11059-11059^9384 is 5-PRP! (37.2159s+0.0065s)
9384^11059-11059^9384 is 7-PRP! (39.2037s+0.0071s)
9384^11059-11059^9384 is 11-PRP! (37.4977s+0.0068s)

Primality testing 9384^11059-11059^9384 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.05% proof)
9384^11059-11059^9384 is Fermat and Lucas PRP! (186.4120s+0.0177s)

To be completed...