Question 57
Find the largest positive integer $n$ such that
$$
\lfloor\sqrt{1}\rfloor + \lfloor\sqrt{2}\rfloor + \lfloor\sqrt{3}\rfloor + \dots + \lfloor\sqrt{n}\rfloor
$$
is a prime ($\lfloor x \rfloor$ denotes the largest integer not exceeding $x$). (Patrik Bak)
$$
\lfloor\sqrt{1}\rfloor + \lfloor\sqrt{2}\rfloor + \lfloor\sqrt{3}\rfloor + \dots + \lfloor\sqrt{n}\rfloor
$$
is a prime ($\lfloor x \rfloor$ denotes the largest integer not exceeding $x$). (Patrik Bak)