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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