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The Prime Pages (prime number research, records and resources)

The Prime Pages (prime number research, records and resources)
Related:  MathematicsMATEMATICA

Another Look at Prime Numbers Primes are numeric celebrities: they're used in movies, security codes, puzzles, and are even the subject of forlorn looks from university professors. But mathematicians delight in finding the first 20 billion primes, rather than giving simple examples of why primes are useful and how they relate to what we know. Somebody else can discover the "largest prime" -- today let's share intuitive insights about why primes rock: Primes are building blocks of all numbers. And just like in chemistry, knowing the chemical structure of a material helps understand and predict its properties.Primes have special properties like being difficult to determine (yes, even being difficult can be a positive trait). These properties have applications in cryptography, cycles, and seeing how other numbers multiply together. So what are prime numbers again? A basic tenet of math is that any number can be written as the multiplication of primes. Well, not really. Analogy: Prime Numbers and Chemical Formulas Why? 1.

Nombres, curiosités, théorie et usages: page d'orientation générale Berechnung der Periodenlänge von Dezimalbrüchen Berechnung der Periodenlänge von Dezimalbrüchen Beim Dividieren zweier Zahlen mit dem Taschenrechner oder auf dem Papier erhält man bekanntlicherweise immer dann Kommastellen, wenn sich der Dividend nicht ohne Rest durch den Divisor teilen läßt. Manchmal gibt es nur „wenige“ Kommastellen, besser gesagt: eine begrenzte Zahl von Kommastellen, oftmals aber unendlich viele, die jedoch immer aus einer periodischen Wiederholung derselben Zahlenfolge bestehen. Warum ist ein nichtabbrechender Dezimalbruch automatisch periodisch? Bekanntlicherweise kann man die Kommastellen eines Dezimalbruchs durch das aus der Grundschule bekannte Verfahren des schriftlichen Dividierens mit Resten erhalten. Solange sich kein Rest wiederholt, müssen logischerweise alle Reste unterschiedlich sein. Als nächstes überlegen wir, von was es abhängt, ob überhaupt eine Periode bzw. wann keine Periode entsteht. Wann entsteht keine Periode Welche Nenner lassen sich so erweitern? Die Länge der Periode

History of Mathematics Home Page Every culture on earth has developed some mathematics. In some cases, this mathematics has spread from one culture to another. Now there is one predominant international mathematics, and this mathematics has quite a history. It has roots in ancient Egypt and Babylonia, then grew rapidly in ancient Greece. Mathematics written in ancient Greek was translated into Arabic. There are other places in the world that developed significant mathematics, such as China, southern India, and Japan, and they are interesting to study, but the mathematics of the other regions have not had much influence on current international mathematics. By far, the most significant development in mathematics was giving it firm logical foundations. By the 20th century the edge of that unknown had receded to where only a few could see. Mathematics continues to grow at a phenomenal rate. Regional mathematics | Subjects | Books and other resources | Chronology Maintained by

Stats GIMPS (Prime95) Zipf, Power-law, Pareto - a ranking tutorial Lada A. Adamic Information Dynamics Lab Information Dynamics Lab, HP Labs Palo Alto, CA 94304 A line appears on a log-log plot. One hears shouts of "Zipf!","power-law!" All three terms are used to describe phenomena where large events are rare, but small ones quite common. Zipf's law usually refers to the 'size' y of an occurrence of an event relative to it's rank r. Pareto was interested in the distribution of income. What is usually called a power law distribution tells us not how many people had an income greater than x, but the number of people whose income is exactly x. Although the literature surrounding both the Zipf and Pareto distributions is vast, there are very few direct connections made between Zipf and Pareto, and when they exist, it is by way of a vague reference [1] or an overly complicated mathematical analysis[2,3]. Figure 1a below shows the distribution of AOL users' visits to various sites on a December day in 1997. Acknowledgements References 1. 2. 3. 4. 5. 6. 7. 8. 9.

Every odd integer larger than 1 is the sum of at most five primes I’ve just uploaded to the arXiv my paper “Every odd number greater than 1 is the sum of at most five primes“, submitted to Mathematics of Computation. The main result of the paper is as stated in the title, and is in the spirit of (though significantly weaker than) the even Goldbach conjecture (every even natural number is the sum of at most two primes) and odd Goldbach conjecture (every odd natural number greater than 1 is the sum of at most three primes). It also improves on a result of Ramaré that every even natural number is the sum of at most six primes. The method used is the Hardy-Littlewood circle method, which was for instance also used to prove Vinogradov’s theorem that every sufficiently large odd number is the sum of three primes. , which is mostly supported on the primes. as the sum of three primes, it suffices to obtain a good lower bound for the sum By Fourier analysis, one can rewrite this sum as an integral where and . for various values of . by a rational . is large. . or .

Rechnen mit Quadratwurzeln 5. Rechnen mit Quadratwurzeln Einführung 1) Der schon häufig verwendete Begriff der „Wurzel“ soll zunächst noch einmal genauer betrachtet werden: Ö9 ist diejenige positive Zahl, die mit sich selbst multipliziert 9 ergibt. Ö9 = 3, denn 32 = 9. Es gibt aber noch eine weitere Zahl, die mit sich selbst multipliziert 9 ergibt, nämlich -3: Es ist jedoch falsch, daraus zu schließen, dass Ö9 auch -3 sein könnte, denn gemäß der Definition ist die Wurzel einer Zahl eine nicht-negative Zahl. Entsprechend gilt: Ö36 = 6 , denn 62 = 36 und 6 > 0 ; Ö0,16 = 0,4 , denn 0,42 = 0,16 und 0,4 > 0 ; Ö2,56 = 1,6 , denn 1,62 = 2,56 und 1,6 > 0. Vergleicht man mit , so erkennt man: Hätte man sich bei der Definition der Wurzel dagegen auf die negativen Zahlen, deren Quadrat den Radikanden ergibt, festgelegt, so würde hier gelten: 2) Besonders einfach lässt sich die Wurzel aus dem Quadrat einer Zahl ziehen: Allgemein gilt: oder kurz: 3) Die beiden Gleichungen haben nicht die gleiche Lösungsmenge. Da auch in Allgemein: . . also:

» Matematica Open Source GIMPS Home 8 math talks to blow your mind Mathematics gets down to work in these talks, breathing life and logic into everyday problems. Prepare for math puzzlers both solved and unsolvable, and even some still waiting for solutions. Ron Eglash: The fractals at the heart of African designs When Ron Eglash first saw an aerial photo of an African village, he couldn’t rest until he knew — were the fractals in the layout of the village a coincidence, or were the forces of mathematics and culture colliding in unexpected ways? Here, he tells of his travels around the continent in search of an answer. How big is infinity? Arthur Benjamin does “Mathemagic” A whole team of calculators is no match for Arthur Benjamin, as he does astounding mental math in the blink of an eye. Scott Rickard: The beautiful math behind the ugliest music What makes a piece of music beautiful? Benoit Mandelbrot: Fractals and the art of roughness The world is based on roughness, explains legendary mathematician Benoit Mandelbrot.

In Their Prime: Mathematicians Come Closer to Solving Goldbach's Weak Conjecture One of the oldest unsolved problems in mathematics is also among the easiest to grasp. The weak Goldbach conjecture says that you can break up any odd number into the sum of, at most, three prime numbers (num­bers that cannot be evenly divided by any other num­ber except themselves or 1). For example: 35 = 19 + 13 + 3 or 77 = 53 + 13 + 11 Mathematician Terence Tao of the University of California, Los Angeles, has now inched toward a proof. The weak Goldbach conjecture was proposed by 18th-century mathematician Christian Goldbach. Mathematicians have checked the validity of both statements by computer for all numbers up to 19 digits, and they have never found an exception. Next, Tao hopes to extend his approach and show that three primes suffice in all cases.

Zahlen und Kalender der Maya Sie sind hier: Sekundarstufen > Mathematik > Unterrichtseinheiten Mathematik > Algebra > Zahlen und Kalender der Maya Dynamische Arbeitsblätter mit interaktiven Übungen und 3D-Animationen veranschaulichen mit Zahnradmodellen, wie das Zahlen- und Kalendersystem der Maya "tickt". Dabei ist das kleinste gemeinsame Vielfache von Zahlen von zentraler Bedeutung. Am 21. Kompetenzen Die Schülerinnen und Schüler sollen im Lernbereich "Natürliche Zahlen" die Begriffe Teilbarkeit, Vielfache und Teiler sowie Mengen kennen (Klasse 5).im Wahlpflichtbereich "Wie die Menschen Zählen und Rechnen lernten" Einblick gewinnen in das Zählen und in die Schreibweisen von Zahlen in einem anderen Kulturkreis (Klasse 5).sich im Rahmen der Prüfungsvorbereitung mit den Begriffen Teiler- und Vielfachmengen sowie mit Stellenwertsystemen auseinandersetzen (Klasse 10). Kurzinformation zum Unterrichtsmaterial Didaktisch-methodischer Kommentar Inhalte der LernumgebungSchülerinnen und Schüler lernen die Maya-Ziffern kennen.

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