Found with PFGW Version 3.7.5

8788^12217+12217^8788 is 2-PRP! (149.8341s+0.0075s)
8788^12217+12217^8788 is 3-PRP! (149.4375s+0.0083s)
8788^12217+12217^8788 is 5-PRP! (147.2519s+0.0101s)
8788^12217+12217^8788 is 7-PRP! (151.2981s+0.0077s)
8788^12217+12217^8788 is 11-PRP! (150.6857s+0.0100s)

Primality testing 8788^12217+12217^8788 [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% (0.07% proof)
8788^12217+12217^8788 is Fermat and Lucas PRP! (749.8426s+0.0073s)

To be completed...