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

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

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

Nov 28, 2020