Found with PFGW Version 3.6.0

55^27370-54 is 2-PRP! (34.5293s+0.0037s)
55^27370-54 is 3-PRP! (35.4146s+0.0042s)
55^27370-54 is 5-PRP! (35.0858s+0.0068s)
55^27370-54 is 7-PRP! (35.1107s+0.0082s)
55^27370-54 is 11-PRP! (34.3516s+0.0033s)

Primality testing 55^27370-54 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 0.07% and helper 0.00% (0.22% proof)
55^27370-54 is Fermat and Lucas PRP! (267.6112s+0.0046s)

To be completed...