Let $p_0, p_1, p_2, \dots \in \mathbb{N}$ be the D4180: Prime integer sequence.

Then $$\begin{equation} \forall \, n \in \mathbb{N} : \sqrt{p_{n + 1}} - \sqrt{p_n} < 1 \end{equation}$$

Let $p_0, p_1, p_2, \dots \in \mathbb{N}$ be the D4180: Prime integer sequence.
Let $n \in \mathbb{N}$ be a D996: Natural number.

Then $$\begin{equation} \sqrt{p_{n + 1}} - \sqrt{p_n} < 1 \end{equation}$$