Found with PFGW Version 3.5.2

66^12734+65 is 2-PRP! (17.0558s+0.0197s)
66^12734+65 is 3-PRP! (17.2039s+0.0055s)
66^12734+65 is 5-PRP! (22.8751s+0.0057s)
66^12734+65 is 7-PRP! (30.0536s+0.0052s)
66^12734+65 is 11-PRP! (38.2878s+0.0069s)

Primality testing 66^12734+65 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 8+sqrt(17)
Calling N+1 BLS with factored part 0.06% and helper 0.03% (0.22% proof)
66^12734+65 is Fermat and Lucas PRP! (376.0358s+0.0178s)

To be completed...