Found with PFGW Version 3.8.0

565^27318+27318^565 is 2-PRP! (106.0583s+0.0090s)
565^27318+27318^565 is 3-PRP! (106.2494s+0.0165s)
565^27318+27318^565 is 5-PRP! (110.2074s+0.0082s)
565^27318+27318^565 is 7-PRP! (106.0449s+0.0091s)
565^27318+27318^565 is 11-PRP! (106.9317s+0.0092s)

Primality testing 565^27318+27318^565 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.03% proof)
565^27318+27318^565 is Fermat and Lucas PRP! (607.6813s+0.0095s)

To be completed...