6. Probability

• Strassen algorithm for Prim numbers

Wegen Siebformel:

$$N_k=k-\left(\genfrac{}{}{0ex}{}{k}{2}\right)+\left(\genfrac{}{}{0ex}{}{k}{3}\right)-\left(\genfrac{}{}{0ex}{}{k}{4}\right)+\dots \pm \left(\genfrac{}{}{0ex}{}{k}{k}\right)$$

Using binomic formula:

$$(x-y{)}^k=x^k-k\cdot x^{k-1}+\dots$$

for $x=y=1$: $⟹0=N_k-1$ $⟹N_k=1$