Found with PFGW Version 3.7.5
7406^12879+12879^7406 is 2-PRP! (46.9514s+0.0023s)
7406^12879+12879^7406 is 3-PRP! (46.9086s+0.0022s)
7406^12879+12879^7406 is 5-PRP! (46.9685s+0.0020s)
7406^12879+12879^7406 is 7-PRP! (46.8136s+0.0021s)
7406^12879+12879^7406 is 11-PRP! (46.9242s+0.0020s)
Primality testing 7406^12879+12879^7406 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
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 0.04% and helper 0.01% (0.15% proof)
7406^12879+12879^7406 is Fermat and Lucas PRP! (319.5357s+0.0033s)
To be completed...