Found with PFGW Version 3.4.6

35^11397-34 is 2-PRP! (8.5167s+0.0048s)
35^11397-34 is 3-PRP! (8.4517s+0.0050s)
35^11397-34 is 5-PRP! (10.3543s+0.0049s)
35^11397-34 is 7-PRP! (12.2238s+0.0050s)
35^11397-34 is 11-PRP! (9.9666s+0.0049s)

Primality testing 35^11397-34 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 9+sqrt(19)
Calling N-1 BLS with factored part 0.44% and helper 0.03% (1.35% proof)
35^11397-34 is Fermat and Lucas PRP! (129.2235s+0.0132s)

To be completed...