• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
(1) M=TT - American Mathematical Society
(1) M=TT - American Mathematical Society

Assessment Task TI-30XB MultiView™:Factors in their Prime
Assessment Task TI-30XB MultiView™:Factors in their Prime

How_to_find_GCF_and_LCM_u sing_the_slide[1]
How_to_find_GCF_and_LCM_u sing_the_slide[1]

PDF
PDF

5th grade Number and Operation Multiplication
5th grade Number and Operation Multiplication

Factors of Numbers, and Prime Numbers
Factors of Numbers, and Prime Numbers

product of primes
product of primes

As easy as PIE - Indian Statistical Institute, Bangalore
As easy as PIE - Indian Statistical Institute, Bangalore

UNITARY DIVISOR PROBLEMS
UNITARY DIVISOR PROBLEMS

How to Express Counting Numbers as a Product of Primes
How to Express Counting Numbers as a Product of Primes

Does Ten Have a Friend?
Does Ten Have a Friend?

... For a positive integer n, the sum of the positive divisors of n is denoted σ(n); the ratio σ(n) n is known as the abundancy ratio or abundancy index of n, denoted I(n). A perfect number is a positive integer n satisfying I(n) = 2. Considering the millenia-old interest in perfect numbers and the (at ...
Relationships and Algorithm in order to achieve the Largest Primes
Relationships and Algorithm in order to achieve the Largest Primes

A proof of Bertrand`s postulate
A proof of Bertrand`s postulate

Vocabulary. Examples. Check Understanding. 1 Prime Factorization
Vocabulary. Examples. Check Understanding. 1 Prime Factorization

1811 Solution to POJ1811
1811 Solution to POJ1811

PlanetMath: good hash table
PlanetMath: good hash table

Prime Numbers - School of Computer Science, University of
Prime Numbers - School of Computer Science, University of

Small gaps between prime numbers - KITP Online
Small gaps between prime numbers - KITP Online

2 Primes Numbers
2 Primes Numbers

Prime Factorisation
Prime Factorisation

UNIT 3: DIVISIBILITY 1. Prime numbers
UNIT 3: DIVISIBILITY 1. Prime numbers

... Here are some quick and easy checks to see if one number will divide exactly. Divisible by 2. A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8. Example: 2346 is divisible by 2 since the last digit is 6. Divisible by 3. A number is divisible by 3 if the sum of the digits is divisible b ...
Homework 5 - SchoolNova
Homework 5 - SchoolNova

of an Odd Perfect Number - American Mathematical Society
of an Odd Perfect Number - American Mathematical Society

Revision session 1: Prime factorisation
Revision session 1: Prime factorisation

Homework #3 - You should not be here.
Homework #3 - You should not be here.

< 1 ... 3 4 5 6 7 8 9 10 11 >

Prime number theorem



In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée-Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function).The first such distribution found is π(N) ~ N / log(N), where π(N) is the prime-counting function and log(N) is the natural logarithm of N. This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N). Consequently, a random integer with at most 2n digits (for large enough n) is about half as likely to be prime as a random integer with at most n digits. For example, among the positive integers of at most 1000 digits, about one in 2300 is prime (log(101000) ≈ 2302.6), whereas among positive integers of at most 2000 digits, about one in 4600 is prime (log(102000) ≈ 4605.2). In other words, the average gap between consecutive prime numbers among the first N integers is roughly log(N).
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report