A function $f$ is defined such that $f(0) = 0$ and for all $i \gt 0$, $f(i) = i - (\text{smallest prime factor of i})$. Someone applied $f$ to a number $N$ exactly $K$ times such that the resulting number is exactly $2023$ less than $N$. Find the least $N$ when $K$ is minimized. Note that $f(1)=1$.