Found with PFGW Version 3.7.5

114^40495+40495^114 is 2-PRP! (137.8281s+0.0022s)
114^40495+40495^114 is 3-PRP! (137.8261s+0.0023s)
114^40495+40495^114 is 5-PRP! (138.4223s+0.0022s)
114^40495+40495^114 is 7-PRP! (137.7523s+0.0025s)
114^40495+40495^114 is 11-PRP! (138.0322s+0.0022s)

Primality testing 114^40495+40495^114 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N+1 test using discriminant 31, base 17+sqrt(31)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.08% proof)
114^40495+40495^114 is Fermat and Lucas PRP! (684.7526s+0.0031s)

To be completed...