Found with PFGW Version 3.7.5

2769^9344-9344^2769 is 2-PRP! (17.9875s+0.0012s)
2769^9344-9344^2769 is 3-PRP! (18.0022s+0.0013s)
2769^9344-9344^2769 is 5-PRP! (17.8809s+0.0014s)
2769^9344-9344^2769 is 7-PRP! (17.8685s+0.0014s)
2769^9344-9344^2769 is 11-PRP! (17.9425s+0.0014s)

Primality testing 2769^9344-9344^2769 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 8+sqrt(17)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.15% proof)
2769^9344-9344^2769 is Fermat and Lucas PRP! (146.5372s+0.0025s)

To be completed...