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Question help pls

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Let $$p(x)$$ be defined on $$2 \le x \le 10$$ such that where

$$p(x) = \begin{cases} x + 1 &\quad \lfloor x \rfloor\text{ is prime} \\ p(y) + (x + 1 - \lfloor x \rfloor) &\quad \text{otherwise} \end{cases}$$

is the greatest prime factor of $$\lfloor x\rfloor$$ Express the range of $$p$$ in interval notation.

I've tried to do this problem and I think it's [3,10) but i'm not sure... can someone comfirm this maybe?

Feb 26, 2021