Found with PFGW Version 3.7.5

265^37614+37614^265 is 2-PRP! (169.2952s+0.0037s)
265^37614+37614^265 is 3-PRP! (161.9292s+0.0036s)
265^37614+37614^265 is 5-PRP! (163.6098s+0.0041s)
265^37614+37614^265 is 7-PRP! (161.2177s+0.0036s)
265^37614+37614^265 is 11-PRP! (163.9727s+0.0038s)

Primality testing 265^37614+37614^265 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 31
Running N-1 test using base 41
Running N+1 test using discriminant 47, base 4+sqrt(47)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.06% proof)
265^37614+37614^265 is Fermat and Lucas PRP! (1115.6687s+0.0037s)

To be completed...