Found with PFGW Version 3.6.0

114^5836+113 is 2-PRP! (2.1894s+0.0027s)
114^5836+113 is 3-PRP! (2.2291s+0.0030s)
114^5836+113 is 5-PRP! (2.2305s+0.0023s)
114^5836+113 is 7-PRP! (2.2294s+0.0020s)
114^5836+113 is 11-PRP! (2.2204s+0.0019s)

Primality testing 114^5836+113 [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 0.23% and helper 0.03% (0.72% proof)
114^5836+113 is Fermat and Lucas PRP! (15.3214s+0.0032s)

To be completed...