Found with PFGW Version 3.7.5

78^58099+77 is 2-PRP! (81.9779s+0.0030s)
78^58099+77 is 3-PRP! (82.7733s+0.0029s)
78^58099+77 is 5-PRP! (82.6555s+0.0030s)
78^58099+77 is 7-PRP! (82.7032s+0.0030s)
78^58099+77 is 11-PRP! (84.1581s+0.0030s)

Primality testing 78^58099+77 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 17, base 3+sqrt(17)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.09% proof)
78^58099+77 is Fermat and Lucas PRP! (594.9009s+0.0038s)

To be completed...