Found with PFGW Version 3.4.6

22^10563+21 is 2-PRP! (7.4554s+0.0137s)
22^10563+21 is 3-PRP! (7.4374s+0.0186s)
22^10563+21 is 5-PRP! (7.4675s+0.0061s)
22^10563+21 is 7-PRP! (7.7270s+0.0038s)
22^10563+21 is 11-PRP! (7.6453s+0.0059s)

Primality testing 22^10563+21 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 3+sqrt(17)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
22^10563+21 is Fermat and Lucas PRP! (103.8765s+0.0093s)

To be completed...