Found with PFGW Version 3.7.5

55^36683-54 is 2-PRP! (45.8614s+0.0039s)
55^36683-54 is 3-PRP! (49.3151s+0.0063s)
55^36683-54 is 5-PRP! (52.6636s+0.0069s)
55^36683-54 is 7-PRP! (52.6779s+0.0066s)
55^36683-54 is 11-PRP! (53.6467s+0.0063s)

Primality testing 55^36683-54 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 6+sqrt(19)
Calling N-1 BLS with factored part 0.02% and helper 0.00% (0.05% proof)
55^36683-54 is Fermat and Lucas PRP! (408.4347s+0.0083s)

To be completed...