Found with PFGW Version 3.7.5

88^57416+87 is 2-PRP! (82.5208s+0.0028s)
88^57416+87 is 3-PRP! (82.5487s+0.0031s)
88^57416+87 is 5-PRP! (83.6381s+0.0030s)
88^57416+87 is 7-PRP! (99.7337s+0.0030s)
88^57416+87 is 11-PRP! (95.5623s+0.0030s)

Primality testing 88^57416+87 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
88^57416+87 is Fermat and Lucas PRP! (596.0200s+0.0030s)

To be completed...