Found with PFGW Version 3.7.5

124^12623-123 is 2-PRP! (4.4973s+0.0009s)
124^12623-123 is 3-PRP! (4.4940s+0.0009s)
124^12623-123 is 5-PRP! (4.4971s+0.0008s)
124^12623-123 is 7-PRP! (4.4941s+0.0008s)
124^12623-123 is 11-PRP! (4.5018s+0.0008s)

Primality testing 124^12623-123 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 7
Running N-1 test using base 17
Running N-1 test using base 19
Running N+1 test using discriminant 47, base 1+sqrt(47)
Calling N+1 BLS with factored part 0.05% and helper 0.02% (0.17% proof)
124^12623-123 is Fermat and Lucas PRP! (46.0778s+0.0010s)

To be completed...