There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes less than x approaches p(x) ≈ x / lnx . Use this approximation to estimate the rate (in primes per 100 integers) at which the prime numbers occur when (a) x = 1000. (b) x = 1,000,000. (c) x = 1,000,000,000.
There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes less than x approaches p(x) ≈ x / lnx . Use this approximation to estimate the rate (in primes per 100 integers) at which the prime numbers occur when (a) x = 1000. (b) x = 1,000,000. (c) x = 1,000,000,000.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
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There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes less than x approaches p(x) ≈ x / lnx . Use this approximation to estimate the rate (in primes per 100 integers) at which the prime numbers occur when (a) x = 1000. (b) x = 1,000,000. (c) x = 1,000,000,000.
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