Question 30
Let $S_{n}$ be the sum of the first $n$ prime numbers. For example,
$$
S_{5}=2+3+5+7+11=28 .
$$
Does there exist an integer $k$ such that $S_{2023}\lt k^{2}\lt S_{2024}$ ?
$$
S_{5}=2+3+5+7+11=28 .
$$
Does there exist an integer $k$ such that $S_{2023}\lt k^{2}\lt S_{2024}$ ?