Found with PFGW Version 3.4.6

35^8354+34 is 2-PRP! (4.9839s+0.0043s)
35^8354+34 is 3-PRP! (5.0311s+0.0045s)
35^8354+34 is 5-PRP! (5.1723s+0.0044s)
35^8354+34 is 7-PRP! (5.1655s+0.0046s)
35^8354+34 is 11-PRP! (5.1364s+0.0045s)

Primality testing 35^8354+34 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.13% proof)
35^8354+34 is Fermat and Lucas PRP! (30.8700s+0.0055s)

To be completed...