# Divide by Prime

Calculus Level 3

A sequence of real numbers $$\{ a _n \}$$ is defined using the following recurrence relation

$a _{ n + 1} = \frac{ a_{n } } { p_{ n } }$

for all $$n \geq 1$$. If $$p_{n}$$ denotes the $$n^\text{th}$$ prime number, what is $$\displaystyle \lim _{ n \to \infty } a_{n}$$?

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