Found with PFGW Version 3.6.0

55^24583+54 is 2-PRP! (25.6647s+0.0046s)
55^24583+54 is 3-PRP! (27.0439s+0.0030s)
55^24583+54 is 5-PRP! (26.4414s+0.0046s)
55^24583+54 is 7-PRP! (27.5867s+0.0033s)
55^24583+54 is 11-PRP! (25.5594s+0.0035s)

Primality testing 55^24583+54 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.12% and helper 0.03% (0.38% proof)
55^24583+54 is Fermat and Lucas PRP! (183.3037s+0.0066s)

To be completed...