Found with PFGW Version 3.6.0

57^25311-56 is 2-PRP! (35.5462s+0.0044s)
57^25311-56 is 3-PRP! (32.8634s+0.0033s)
57^25311-56 is 5-PRP! (33.8334s+0.0034s)
57^25311-56 is 7-PRP! (34.0831s+0.0046s)
57^25311-56 is 11-PRP! (32.1667s+0.0048s)

Primality testing 57^25311-56 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 43, base 12+sqrt(43)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.17% proof)
57^25311-56 is Fermat and Lucas PRP! (213.6317s+0.0042s)

To be completed...