Theorems about prime numbers | Article proofs | Prime numbers | Factorial and binomial topics

Proof of Bertrand's postulate

In mathematics, Bertrand's postulate (actually a theorem) states that for each there is a prime such that . It was first proven by Chebyshev, and a short but advanced proof was given by Ramanujan. The following elementary proof was published by Paul Erdős in 1932, as one of his earliest mathematical publications. The basic idea is to show that the central binomial coefficients need to have a prime factor within the interval in order to be large enough. This is achieved through analysis of the factorization of the central binomial coefficients. The main steps of the proof are as follows. First, show that the contribution of every prime power factor in the prime decomposition of the central binomial coefficient is at most . Then show that every prime larger than appears at most once. The next step is to prove that has no prime factors in the interval . As a consequence of these bounds, the contribution to the size of coming from the prime factors that are at most grows asymptotically as for some . Since the asymptotic growth of the central binomial coefficient is at least , the conclusion is that, by contradiction and for large enough , the binomial coefficient must have another prime factor, which can only lie between and . The argument given is valid for all . The remaining values of are by direct inspection, which completes the proof. (Wikipedia).

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AN ELEMENTARY PROOF OF BERTRAND'S POSTULATE! Special #SoMe1

I love when a deep result in mathematics is provable only with elementary techniques, like basic knowledge of combinatorics and arithmetic. In this video I will present the queen of this proofs, namely the Erdős' proof of the Bertrand's postulate, which states that it is always possible to

From playlist Summer of Math Exposition Youtube Videos

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Geometry - Ch. 2: Reasoning and Proofs (21 of 46) What is a Postulate?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a postulate. A postulate, or axium, is a proposition that is not proved or demonstrated but considered to be self evident. It is a “truth” that is accepted. A postulate serves as a sta

From playlist GEOMETRY CH 2 PROOFS & REASONING

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Geometry - Ch. 2: Reasoning and Proofs (29 of 46) Postulate 8: The Plane Postulate

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain Postulate 8: The Plane Postulate – Through any 3 non-collinear points, exists exactly one plane. Next video in this series can be seen at: https://youtu.be/NuiTMuNaUdA

From playlist GEOMETRY CH 2 PROOFS & REASONING

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Geometry - Ch. 3: Proofs (5 of 17) Postulates Needed for Proofs

Visit http://ilectureonline.com for more math and science lectures! In this video I will define what is a postulate, and review some of the basic postulates needed for geometry proofs: linear pair, ruler, segment addition, protractor, angle addition, line intersecting lines, and plane. T

From playlist GEOMETRY CH 3 PROOFS

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Geometry - Ch. 2: Reasoning and Proofs (22 of 46) Postulate 1: Ruler (Numberline)

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain Postulate 1:The Ruler, or Number Line, Postulate – points on a line have corresponding points on a number line such that they can have “x-values” called “coordinates” of the points (x1, x2, x3

From playlist GEOMETRY CH 2 PROOFS & REASONING

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Geometry - Ch. 2: Reasoning and Proofs (34 of 46) Evaluating 3 Postulates

Visit http://ilectureonline.com for more math and science lectures! In this video I will evaluate 3 postulates: Postulate 6: At Least 2 Points Postulate, Postulate 7: Line Intersection Postulate, Postulate 8: The Plane Postulate; given 2 intersecting lines and point F on plane Q. Next vi

From playlist GEOMETRY CH 2 PROOFS & REASONING

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Geometry: Ch 5 - Proofs in Geometry (5 of 58) How to Proof Proofs

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is and how to proof proofs in geometry. Next video in this series can be seen at: https://youtu.be/xuWliQ6CHpw

From playlist GEOMETRY 5 - PROOFS IN GEOMETRY

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The Role of Mathematics in Philosophy | 2012

Prof. Douglas Kindschi of Grand Valley State University speaks on "The Role of Mathematics in Philosophy: Plato to Russell". This talk was part of the GVSU Math Department seminar series and was given in February 2012. https://archive.org/details/The_Role_Of_Mathematics_In_Philosophy_

From playlist Mathematics

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Arguing God with Analytic Philosophy | Episode 903 | Closer To Truth

I desire God to be real, so I know that the easiest person to fool is myself. That's why I favor rational arguments for, and against, the existence of a Supreme Creator. Featuring interview with Richard Swinburne, Philip Clayton, and Bede Rundle. Season 9, Episode 3 - #CloserToTruth ▶Reg

From playlist Big Questions About God - Closer To Truth - Core Topic

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an irrational sum.

🌟Support the channel🌟 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn 🟢 Discord: https://discord.gg/Ta6PTGtKBm 🌟my other channels🌟 Course videos: https://www.youtube

From playlist Interesting Sums

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4 - Kick-off afternoon : Xavier Leroy, Proof assistants in computer science research

J'ai créé cette vidéo à l'aide de l'application de montage de vidéos YouTube (http://www.youtube.com/editor).

From playlist T2-2014 : Semantics of proofs and certified mathematics

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Type theory and formalization of mathematics - Anders Mörtberg

Short Talks by Postdoctoral Members Anders Mörtberg - September 28, 2015 http://www.math.ias.edu/calendar/event/88254/1443464100/1443465000 More videos on http://video.ias.edu

From playlist Short Talks by Postdoctoral Members

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Basics of Mathematical Logic -- How to do Mathematical Proofs (PART 3)

This is the first main video on a series of videos: How to do mathematical proofs. This video focuses on the basics of mathematical logic, specifically, the distinction between deductive and inductive reasoning, and examples of premises, propositions, and whatnot. The course is structured

From playlist How to do Mathematical Proofs

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More Postulates & Theorems Points, Lines, & Planes

I introduce 5 more postulates relating to points, lines, and planes. These postulates are then used to prove the first three theorems in Geometry. Theorem 1, If 2 lines intersect, then they intersect in exactly one point. Theorem 2, Through a line and a point not in the line there is ex

From playlist Geometry

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2.920050977316 - Numberphile

Dr James Grime is discussing a new prime-generating constant. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Extra footage from this interview: https://youtu.be/yXPhq-36Eq4 More James G

From playlist James Grime on Numberphile

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Geometry - Ch. 2: Reasoning and Proofs (27 of 46) Postulate 6: At Least 2 Points

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain Postulate 6: At Least 2 Points Postulate – A line contains at least 2 points. (A line contains an infinite number of points.) Next video in this series can be seen at: https://youtu.be/3apliy

From playlist GEOMETRY CH 2 PROOFS & REASONING

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Proof by Counter Example: Prove a Converse is False

This video provides an example of a proof by counter example. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

Related pages

Central binomial coefficient | Logarithm | Theorem | Mathematical proof | Lemma (mathematics) | Asymptotic analysis | Mizar system | Counterexample | Primorial | Proof by contradiction | Concave function | Binomial theorem | Natural number | Mathematics | Integer | Bertrand's postulate | Real number | Mathematical induction | Elementary proof | Prime power | Prime number | Parity (mathematics) | Interval (mathematics) | Paul Erdős | Legendre's formula