Found with PFGW Version 3.4.6

35^7064+34 is 2-PRP! (3.2180s+0.0051s)
35^7064+34 is 3-PRP! (3.2886s+0.0010s)
35^7064+34 is 5-PRP! (3.2998s+0.0010s)
35^7064+34 is 7-PRP! (3.2894s+0.0010s)
35^7064+34 is 11-PRP! (3.4685s+0.0010s)

Primality testing 35^7064+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 0.25% and helper 0.04% (0.78% proof)
35^7064+34 is Fermat and Lucas PRP! (20.5936s+0.0039s)

To be completed...