# What is the history of prime numbers

## On the history of prime numbers

### The fundamental concept of number The fundamental concept of number Literature Ifrah, G .: Universal history of numbers, Campus-Verlag, 1989 Menninger, K .: Number word and number, - A cultural history of numbers, Vandenhoeck & Ruprecht,

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### Didactics of the number range extensions Jürgen Roth Didactics of the number range extensions Module 5: Didactic areas Chapter 5: Real numbers R 5.1 Didactics of the number range extensions 1 Objectives and content 2 Natural numbers N 3 Whole

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### School curriculum mathematics Fachkonferenz Mathematik Schulcurriculum Mathematik School year 5 Textbook: Fundamente der Mathematik 5, Schroedel-Verlag, ISBN 978-3-06-040348-6 The school curriculum is based on the material distribution plan

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### INTRODUCTION TO THE DIDACTICS OF MATHEMATICS HEINZ JÖRG CLAUS INTRODUCTION TO THE DIDACTICS OF MATHEMATICS SCIENTIFIC BOOK SOCIETY DARMSTADT CONTENTS Foreword IX I. What is didactics of mathematics? 1 II. Objectives of mathematics teaching, curriculum

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### Set theory 1-E1. M-1, Lubov Vassilevskaya Set theory 1-E1 M-1, Lubov Vassilevskaya Fig .: Castle (fragment), Fulda 1-E2 M-1, Lubov Vassilevskaya Fig .: Bells, representation of a set Without knowing it, every toddler encounters the principle of

More Table of contents Introduction ... 7 I Objectives of the geometry lesson (H.-G. Weigand) ... 13 1 Learning objectives, competencies and guidelines ... 13 2 General objectives of the geometry lesson ... 17 2.1 Geometry and

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### 3 numbers and arithmetic In this chapter numbers and individual elements from the field of arithmetic are recapitulated. In particular, the real numbers are introduced and some calculation rules such as power calculations and logarithms

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### Algebra in Secondary School Hans-Joachim Vollrath Algebra in Secondary School 2nd Edition Spectrum Akademischer Verlag Heidelberg Berlin Contents Introduction 1 I Algebra in School 5 1 The framework of the course 5 2 On the historical

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### Algebra in Secondary School Hans-Joachim Vollrath Algebra in Secondary School Spectrum Akademischer Verlag Heidelberg Berlin Contents Introduction I. Algebra in School 1 1. The framework of course 1 2. On the historical development

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### Quantities and figures Sets and mappings The set concept average, union, difference set Cartesian product mappings Principle of the smallest natural number Complete induction Sets and mappings

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### 3 quantities and illustrations \$ Id: mengen.tex, v 1.2 2008/11/07 08:11:14 hk Exp hk \$ 3 Sets and Figures 3.1 Sets A set combines a set of mathematical objects into a new object. The classic informal

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### References to the educational standards Differential Calculation Kinga Szűcs FSU Jena Faculty of Mathematics and Computer Science Department Didactics Based on Prof. Dr. Bernd Zimmermann's seminar presentations Contents References to educational standards

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### Prime numbers and pseudoprime numbers 1 Prime Numbers and Pseudoprime Numbers Holger Stephan Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin 20th Day of Mathematics May 9, 2015, Beuth University of Applied Sciences Berlin Prime Numbers

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### Mathematics and its methods I and their methods I m.mt.fwd.1.1 and their methods I and their methods I k.mt.fwd.1.1 In this module, the technical fundamentals for German teaching at lower secondary level are developed.

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### Didactics of geometry for lower secondary level Hans-Georg Weigand / Andreas Filier / Reinhard Hölzl / Sebastian Kuntze / Matthias Ludwig / Jürgen Roth / Barbara Schmidt-Thieme / Gerald Wittmann Didactics of Geometry for Secondary Level I Spectrum

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### Guideline. a is a multiple of d and shortened to write: d a. If d is not a divisor of a, we also write: d a. d divides a or Algebra and Number Theory Lecture Algebra and Number Theory Guide 1 Number Theory in Z Designations: Z: = {..., 3, 2, 1, 0, 1, 2, 3, ...} (whole numbers) and N: = {1 , 2, 3, ...} (natural numbers

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### Mathematics preliminary course 1 Preliminary course in mathematics 1 Introduction to mathematical notation Constants i Complex unit i 2 + 1 = 0 e Euler's number Circle number 2 Introduction to mathematical notation Identifiers prime numbers, numerators

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### Math square root and real numbers Mathematics square roots and real numbers Basic knowledge and exercises a: a a Stefan Gärtner 1999 004 Gr Mathematics elementary algebra Page Contents Table of contents Page Basic knowledge Definition of square root

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### Basics of arithmetic and number theory Fundamentals of arithmetic and number theory 1.0 Divisibility In this section we will study the whole numbers themselves and especially important numbers, the prime numbers

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### 1. Rules in the irregular 1. Rules in the irregular 1.1. Prime numbers Natural numbers are the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, ... A natural number n> 1 is called prime if it has no factors other than 1 and n. Examples: the

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### Argue / communicate 4 weeks of geometry capturing basic terms, circular area, circular line, radius, center point, diameter, knowing, naming and differentiating names for angles, vertices, inscriptions next to, vertices,

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### Examination for the partial academic examination, module 2, PH Heidelberg, Subject Mathematics Examination for the academic partial examination, module, GHPO I from 7.003, RPO from 4.08.003 Introduction to Geometry Winter semester 1/13, February 1, 013 Examination for the ATP, module, introduction

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### Amrei Naujoks and Marei Böttcher Amrei Naujoks and Marei Böttcher Mathematics is the only subject in the school that has a strong hierarchical structure. if you miss something at the beginning, you can no longer follow. In primary school

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### Educational standards for mathematics, 8th grade Educational standards for mathematics, 8th grade 1 Educational standards for mathematics, 8th grade The educational standards for mathematics, 8th grade, define concrete learning outcomes. These learning outcomes

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### An intellectual tool for mathematics Günther Fuchs Intellectual tools for mathematics Verlag Dr. Kovac Hamburg 2015 IX 1 table of contents 1. What is mathematics? 2. The abstract universe of mathematics 3 2.1. The mathematical universe

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### Prime numbers from Euclid to today Mathematical Institute University of Cologne [email protected] November 5, 2004 Pythagoras of Samos (approx. 570-480 BC) Euclid of Alexandria (approx. 325-265 BC) Divisibility theorem of Euclid

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### Mathematics I fall semester 2014 Mathematics I Fall Semester 2014 www.math.ethz.ch/education/bachelor/lectures/hs2014/other/mathematik1 BIOL Prof. Dr. Erich Walter Farkas http://www.math.ethz.ch/ farkas 1/32 1 Continuity limit value of a

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### Elementary methods of proof Elementary proof methods Christian Hensel 404015 Table of contents Lecture on the subject of elementary proof methods as part of the introductory seminar Mathematical Problem Solving 1 Introduction and important terms

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### Higher faster further! Student Circle Mathematics Faculty of Mathematics. University of Regensburg Higher, Faster, Further! The extremal principle The extremal principle is a versatile solution technique for mathematical

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### Set theory - short version Set theory - short version 1st chapter from my ALGEBRA - course language profile / WR profile - intermediate level KSOe Ronald Balestra CH - 8046 Zurich www.ronaldbalestra.ch Last name: First name: August 18, 2014 Table of contents

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### Mathematics for users I Prof. Dr. H. Brenner Osnabrück WS 2011/2012 Mathematics for Users I Lecture 17 Power Series Definition 17.1. Let (c n) n N be a sequence of real numbers and let x be another real number. Then is called

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### texts on mathematical research and teaching texts on mathematical research and teaching 50 texts on mathematical research and teaching 50 Andreas Marx student ideas about infinite processes Verlag Franzbecker Bibliographical Information

More Contents: Volume 1 0. Introduction 15 1. Initial situation 17 1.1 Situation of the German education system 17 1.2 Imbalance "in mathematics lessons 19 1.2.1 Results of German schoolchildren

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### Topic assignment. Technical tasks (1) Page 1 of 5 GS Rethen Competence Orientation Subject: Mathematics Competences to be acquired at the end of year 3: The pupils - use introduced mathematical terms appropriately. - describe

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### Numbers 25 = = 0.08 2. Numbers Number ranges known to us so far: N Z Q R (C). } {{} later notation of rational / real numbers as infinite decimal fractions = decimal expansion. Example (rational numbers) 1 10

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### Basic math Chapter 2 Fundamentals of Mathematics (Prof. Udo Hebisch) 2.1 Logic In mathematics, a statement is understood to be a sentence formulated in a natural or formal language that is unambiguous

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### De Morgan rules De Morgan's rules By evaluating the truth table we find that is universal; also (p q) p q (p q) p q. These two tautologies are called De Morgan's rules,

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### Basic knowledge of number theory Kristina Reiss Gerald Schmieder Basic Knowledge of Number Theory An Introduction to Numbers and Number Ranges Second Edition With 43 Figures ^ y Springer Table of Contents 1 Basics and Requirements 1.1

More Equation solving reloaded Karl Josef FUCHS, Alfred DOMINIK, University of Salzburg 0. Prologue As authors, we would first like to say a few words about the genesis of the provocative title of our contribution.