Found with PFGW Version 3.7.5

12356^12885+12885^12356 is 2-PRP! (54.6996s+0.0026s)
12356^12885+12885^12356 is 3-PRP! (54.6337s+0.0026s)
12356^12885+12885^12356 is 5-PRP! (55.1024s+0.0027s)
12356^12885+12885^12356 is 7-PRP! (55.3012s+0.0025s)
12356^12885+12885^12356 is 11-PRP! (55.0618s+0.0026s)

Primality testing 12356^12885+12885^12356 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
12356^12885+12885^12356 is Fermat and Lucas PRP! (270.0858s+0.0026s)

To be completed...