Theorems about prime numbers | Theorems in analytic number theory | Logarithms
In mathematics, 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 (the number of primes less than or equal to N) 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). (Wikipedia).
The Prime Number Theorem, an introduction ← Number Theory
An introduction to the meaning and history of the prime number theorem - a fundamental result from analytic number theory. Narrated by Cissy Jones Artwork by Kim Parkhurst, Katrina de Dios and Olga Reukova Written & Produced by Michael Harrison & Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways t
From playlist Number Theory
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In this video, I introduce the idea of the prime number theorem and how one might go about proving it. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Number Theory
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A simple number theory proof problem regarding prime number distribution: Prove that there is a prime number between n and n! Please Like, Share and Subscribe!
From playlist Elementary Number Theory
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From playlist Prime Numbers
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This tutorial explains how to determine whether or not a number is a prime number. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)
From playlist Basic Math
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From playlist Mathematics General Interest
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Check out the blog to follow the series! Let us know if you want to see other proofs for #MathChops! https://centerofmathematics.blogspot.com/2017/08/episode-10-prime-number-theorem.html
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From playlist Summer of Math Exposition Youtube Videos
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Joint IAS/Princeton University Number Theory Seminar Topic: Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions Speaker: Florian Richter Affiliation: Northwestern University Date: June 4, 2020 For more video please visit http://vi
From playlist Mathematics
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Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 2) - by Keith Conrad
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From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
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What are prime numbers? Learn how to find the prime factors of a number and write it as a product of prime factors. ❤️ ❤️ ❤️ Support the channel ❤️ ❤️ ❤️ https://www.youtube.com/channel/UCf89Gd0FuNUdWv8FlSS7lqQ/join
From playlist Number
Structure and randomness in the prime numbers - Terence Tao
Speaker : Terence Tao ( Department of Mathematics, UCLA ) Venue : AG 66, TIFR, Mumbai Date and Time : 23 Feb 12, 16:00 "God may not play dice with the universe, but something strange is going on with the prime numbers" - Paul Erdos The prime numbers are a fascinating blend of both struc
From playlist Public Lectures
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 1) - by Keith Conrad
This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
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Video on coprime numbers mod n: https://youtu.be/SslPWR2N5jA Video on the cancellation rule for modular arithmetic: https://youtu.be/UvnVghpIjwk Euler's theorem relates to modular exponentiation. Fermat's little theorem is a special case for prime modulus. Here we go through an explanatio
From playlist Modular Arithmetic
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From playlist MathBits
Arithmetic Statistics - Lecture 1/4 by Álvaro Lozano Robledo [CTNT 2018]
Full playlist: https://www.youtube.com/playlist?list=PLJUSzeW191Qwpyp4wKvuoyQrZmfnmEWCT Notes: https://ctnt-summer.math.uconn.edu/wp-content/uploads/sites/1632/2018/06/CTNT-2018-Arithmetic-Statistics-Lecture-1.pdf Mini-course B: “Arithmetic Statistics” by Álvaro Lozano-Robledo (UConn).
From playlist Number Theory
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From playlist Prime Numbers, HCF and LCM - GCSE 9-1 Maths
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The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Sieves (by Brandon Alberts)