Found with PFGW Version 3.4.8

34^19874+33 is 2-PRP! (25.0971s+0.0057s)
34^19874+33 is 3-PRP! (51.2567s+0.0061s)
34^19874+33 is 5-PRP! (60.8352s+0.0164s)
34^19874+33 is 7-PRP! (62.7654s+0.0156s)
34^19874+33 is 11-PRP! (62.1567s+0.0142s)

Primality testing 34^19874+33 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 13+sqrt(13)
Calling N+1 BLS with factored part 0.19% and helper 0.01% (0.58% proof)
34^19874+33 is Fermat and Lucas PRP! (423.2281s+0.0174s)

To be completed...