Found with PFGW Version 3.7.5

12174^12937+12937^12174 is 2-PRP! (54.4585s+0.0027s)
12174^12937+12937^12174 is 3-PRP! (54.3996s+0.0029s)
12174^12937+12937^12174 is 5-PRP! (54.3977s+0.0027s)
12174^12937+12937^12174 is 7-PRP! (54.3758s+0.0028s)
12174^12937+12937^12174 is 11-PRP! (55.5395s+0.0026s)

Primality testing 12174^12937+12937^12174 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
12174^12937+12937^12174 is Fermat and Lucas PRP! (267.9011s+0.0035s)

To be completed...