Found with PFGW Version 3.7.5

2758^12179+12179^2758 is 2-PRP! (125.2604s+0.0084s)
2758^12179+12179^2758 is 3-PRP! (126.1463s+0.0089s)
2758^12179+12179^2758 is 5-PRP! (124.1347s+0.0078s)
2758^12179+12179^2758 is 7-PRP! (122.2643s+0.0108s)
2758^12179+12179^2758 is 11-PRP! (120.9090s+0.0081s)

Primality testing 2758^12179+12179^2758 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
2758^12179+12179^2758 is Fermat and Lucas PRP! (582.5830s+0.0092s)

To be completed...