Exercise · ZW-PRIME-NUMBER-THEOREM-004 · ★☆☆ Basic
According to the theorem, what does the ratio π(x)/(x/ln x) tend to as x grows?
Choose one option.
Show answer
- C. 1
Explanation
By the definition of asymptotic equivalence, the ratio tends to 1. Thinking it tends to infinity confuses the growth of π(x) with the adjusted x/ln x.
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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- ZW-PRIME-NUMBER-THEOREM-005 What is the approximate value of π(100)?
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