Found with PFGW Version 3.4.6

35^14899-34 is 2-PRP! (13.9672s+0.0054s)
35^14899-34 is 3-PRP! (13.9139s+0.0057s)
35^14899-34 is 5-PRP! (16.8204s+0.0056s)
35^14899-34 is 7-PRP! (20.5796s+0.0058s)
35^14899-34 is 11-PRP! (16.7802s+0.0057s)

Primality testing 35^14899-34 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 23
Running N-1 test using base 29
Running N-1 test using base 37
Running N-1 test using base 41
Running N+1 test using discriminant 47, base 1+sqrt(47)
Calling N-1 BLS with factored part 0.39% and helper 0.00% (1.18% proof)
35^14899-34 is Fermat and Lucas PRP! (274.4433s+0.0152s)

To be completed...