# Basics: How accurate is the prime number theorem for "small" values?

Number Theory Level pending

The prime number theorem states that: $\text{The }n\text{-th prime}\approx n\ln n$ and this approximation gets better and better as $$n\rightarrow\infty$$.

But how accurate is the prime number theorem for small values? Your mission is to find the difference between the exact value of the 3435-th prime and the value obtained using the prime number theorem. (it must be positive)

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