Found with PFGW Version 3.4.6

2769^3008-3008^2769 is 2-PRP! (10.6101s+0.0048s)
2769^3008-3008^2769 is 3-PRP! (10.3796s+0.0048s)
2769^3008-3008^2769 is 5-PRP! (10.5720s+0.0042s)
2769^3008-3008^2769 is 7-PRP! (10.2155s+0.0046s)
2769^3008-3008^2769 is 11-PRP! (10.5036s+0.0048s)

Primality testing 2769^3008-3008^2769 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.08% and helper 0.04% (0.29% proof)
2769^3008-3008^2769 is Fermat and Lucas PRP! (54.3354s+0.0088s)

To be completed...