Floored by Primes

Algebra Level 5

For how many positive integers NN is N25 \left \lfloor \frac {N^2}{5} \right \rfloor a prime?

Details and assumptions

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

0 and 1 are not primes.

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