The Prime Number Theorem describes the asymptotic distribution of prime numbers among the positive integers, stating that the number of primes less than a given number n approximates n/log(n). This theorem highlights the idea that primes become less frequent as numbers grow larger, yet they follow a predictable pattern in their distribution.

Prime Number Theorem

Asymptotic distribution refers to the probability distribution that a statistic approaches as the sample size becomes infinitely large, providing a way to make inferences about population parameters based on large samples. It is fundamental in statistical theory, particularly in deriving approximate distributions for hypothesis testing and confidence intervals when exact distributions are difficult to obtain.

asymptotic distribution

Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves, serving as the building blocks of number theory. They play a crucial role in various fields, including cryptography, due to their properties and distribution patterns.

prime numbers

positive integers

number of primes

given number

N/log(n)

primes become less frequent

predictable pattern

The distribution of prime numbers is a fundamental topic in number theory, revealing how primes become less frequent as numbers grow larger but never completely vanish. This distribution is intricately linked to the Riemann Hypothesis, which suggests a profound connection between the zeros of the Riemann zeta function and the spacing of prime numbers.

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