Found with PFGW Version 3.7.5

4051^12366+12366^4051 is 2-PRP! (108.9094s+0.0062s)
4051^12366+12366^4051 is 3-PRP! (110.6838s+0.0050s)
4051^12366+12366^4051 is 5-PRP! (110.8765s+0.0059s)
4051^12366+12366^4051 is 7-PRP! (94.3818s+0.0046s)
4051^12366+12366^4051 is 11-PRP! (101.0859s+0.0057s)

Primality testing 4051^12366+12366^4051 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 13+sqrt(13)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
4051^12366+12366^4051 is Fermat and Lucas PRP! (514.8017s+0.0067s)

To be completed...