Found with PFGW Version 3.4.6

34^6943+33 is 2-PRP! (3.1925s+0.0042s)
34^6943+33 is 3-PRP! (3.0621s+0.0040s)
34^6943+33 is 5-PRP! (3.2760s+0.0036s)
34^6943+33 is 7-PRP! (3.2339s+0.0036s)
34^6943+33 is 11-PRP! (3.2264s+0.0036s)

Primality testing 34^6943+33 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 29, base 3+sqrt(29)
Calling N+1 BLS with factored part 0.20% and helper 0.03% (0.64% proof)
34^6943+33 is Fermat and Lucas PRP! (21.5230s+0.0075s)

To be completed...