Floored by Primes

Algebra Level 5

For how many positive integers \(N\) is \( \left \lfloor \frac {N^2}{5} \right \rfloor \) a prime?

Details and assumptions

The function \(\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}\) refers to the greatest integer smaller than or equal to \(x\). For example \(\lfloor 2.3 \rfloor = 2\) and \(\lfloor -5 \rfloor = -5\).

0 and 1 are not primes.

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