Let ^@ p ^@ be a prime number such that the next larger number i | Math Question and Answer

Answer:

$3$

Step by Step Explanation:

Given, $p$ is a prime number such that the next larger number is a perfect square.
$i.e., p + 1 = n^2$
Rewriting $p + 1 = n^2,$ we get
$\begin{align} & p = n^2 - 1 \\ \implies & p = (n - 1)(n +1) \end{align}$
Since $p$ is a prime number, therefore $n-1$ needs to be equal to $1.$
$\implies n = 2$
Therefore, $p = 3$ is unique.
Hence, the required sum is $3.$

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