Found with PFGW Version 3.6.0

117^5373+116 is 2-PRP! (2.1645s+0.0039s)
117^5373+116 is 3-PRP! (2.0818s+0.0018s)
117^5373+116 is 5-PRP! (2.1106s+0.0016s)
117^5373+116 is 7-PRP! (2.0822s+0.0019s)
117^5373+116 is 11-PRP! (2.0740s+0.0016s)

Primality testing 117^5373+116 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.16% and helper 0.14% (0.63% proof)
117^5373+116 is Fermat and Lucas PRP! (13.9582s+0.0034s)

To be completed...