Found with PFGW Version 3.7.5

58^37378-57 is 2-PRP! (53.6257s+0.0053s)
58^37378-57 is 3-PRP! (55.1625s+0.0054s)
58^37378-57 is 5-PRP! (55.9510s+0.0051s)
58^37378-57 is 7-PRP! (54.0904s+0.0054s)
58^37378-57 is 11-PRP! (56.4722s+0.0053s)

Primality testing 58^37378-57 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.06% proof)
58^37378-57 is Fermat and Lucas PRP! (437.4543s+0.0057s)

To be completed...