# Are primes differentiable?

Calculus Level 4

A function $$f_p(x) = \lfloor n+p \sin{x} \rfloor$$ for $$x \in (0, \pi)$$, $$n \in \mathbb{Z}$$ & $$p$$ is a prime number. $$N_p$$ is the number of points where $$f_p(x)$$ is not differentiable. Find the last three digits of $$N_{17497}$$.

Fun fact:

$$17497$$ is the $$2014$$th prime.

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