Noether formula ($c_1^2+c_2=12\chi ({\mathcal{O}}_X)$)

For a smooth compact complex surface, the degree-four part of its Todd class is $(c_1^2+c_2)/12$. Applying Riemann–Roch to its structure sheaf gives the formula. For a K3 surface, $c_1=0$ and $\chi ({\mathcal{O}}_X)=2$, so its topological Euler characteristic is $c_2=24$.