Find the largest possible $n$ such that $\big\lfloor \sqrt{1} \big\rfloor + \big\lfloor \sqrt{2} \big\rfloor + \big\lfloor \sqrt{3} \big\rfloor + \cdots + \big\lfloor \sqrt{n} \big\rfloor$is a prime number.

**Clarification:** $\lfloor x \rfloor$ returns the largest integer less than or equal to $x$.

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