Exercise · ZW-PRIME-NUMBER-THEOREM-006 · ★★☆ Intermediate
If π(x) ~ x/ln x, what is the approximate estimate of π(1000) using x/ln x?
Choose one option.
Show answer
- A. About 145
Explanation
Compute 1000/ln 1000 ≈ 1000/6.908 ≈ 144.8, close to 145. An estimate of 61 corresponds to dividing by a miscalculated logarithm.
Review the concept: Prime number theorem
The prime number theorem describes the asymptotic behavior of π(x), the number of primes less than or equal to x, as x tends to infinity.
\[\pi(x) \sim \frac{x}{\ln x}\]
More practice problems: prime number theorem
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