Found with PFGW Version 3.7.5

10821^12968+12968^10821 is 2-PRP! (53.8272s+0.0031s)
10821^12968+12968^10821 is 3-PRP! (53.8067s+0.0030s)
10821^12968+12968^10821 is 5-PRP! (53.8128s+0.0034s)
10821^12968+12968^10821 is 7-PRP! (53.8401s+0.0032s)
10821^12968+12968^10821 is 11-PRP! (54.6122s+0.0033s)

Primality testing 10821^12968+12968^10821 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.08% proof)
10821^12968+12968^10821 is Fermat and Lucas PRP! (263.8858s+0.0032s)

To be completed...