Found with PFGW Version 3.7.5

79^55009+78 is 2-PRP! (60.6532s+0.0039s)
79^55009+78 is 3-PRP! (60.1296s+0.0033s)
79^55009+78 is 5-PRP! (60.2922s+0.0036s)
79^55009+78 is 7-PRP! (59.9913s+0.0035s)
79^55009+78 is 11-PRP! (60.7423s+0.0035s)

Primality testing 79^55009+78 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
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 0.04% and helper 0.01% (0.14% proof)
79^55009+78 is Fermat and Lucas PRP! (515.7847s+0.0033s)

To be completed...