Found with PFGW Version 3.5.2

79^9587-78 is 2-PRP! (11.8043s+0.0302s)
79^9587-78 is 3-PRP! (11.1620s+0.0054s)
79^9587-78 is 5-PRP! (15.5096s+0.0054s)
79^9587-78 is 7-PRP! (19.3020s+0.4037s)
79^9587-78 is 11-PRP! (24.3016s+0.0061s)

Primality testing 79^9587-78 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N-1 BLS with factored part 0.05% and helper 0.00% (0.16% proof)
79^9587-78 is Fermat and Lucas PRP! (92.0950s+0.0063s)

To be completed...