Found with PFGW Version 3.7.5

137^35597-136 is 2-PRP! (42.1887s+0.0027s)
137^35597-136 is 3-PRP! (42.2429s+0.0024s)
137^35597-136 is 5-PRP! (42.3542s+0.0025s)
137^35597-136 is 7-PRP! (42.4687s+0.0025s)
137^35597-136 is 11-PRP! (42.5333s+0.0024s)

Primality testing 137^35597-136 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 12+sqrt(13)
Calling N-1 BLS with factored part 0.08% and helper 0.02% (0.27% proof)
137^35597-136 is Fermat and Lucas PRP! (296.7490s+0.0026s)

To be completed...