How large must $N$ be in order for

$S_N={\displaystyle \underset{k=1}{\overset{N}{}}}\frac{1}{k}$

to exceed $4?$ Note: Computer calculations show that for $S_N$ to exceed $20,N=272,400,600$ and for $S_N$ to exceed $100,N$~~$1\mathrm{.}5{10}^{43}.$

Answer: $N=$