Found with PFGW Version 3.4.8

58^11516+57 is 2-PRP! (13.9199s+0.2025s)
58^11516+57 is 3-PRP! (24.2322s+0.0398s)
58^11516+57 is 5-PRP! (14.3616s+0.0050s)
58^11516+57 is 7-PRP! (23.9716s+0.0295s)
58^11516+57 is 11-PRP! (28.0845s+0.0111s)

Primality testing 58^11516+57 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 12+sqrt(13)
Calling N+1 BLS with factored part 0.30% and helper 0.05% (0.95% proof)
58^11516+57 is Fermat and Lucas PRP! (222.2429s+0.0149s)

To be completed...