Download or read book Prime Numbers written by David Wells and published by Wiley. This book was released on 2005-05-20 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The "Primes is in P" algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more

Download or read book Prime Obsession written by John Derbyshire and published by Joseph Henry Press. This book was released on 2003-04-15 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.

Download or read book Prime Numbers and the Riemann Hypothesis written by Barry Mazur and published by Cambridge University Press. This book was released on 2016-04-11 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

Download or read book Prime Numbers The Holy Grail Of Mathematics written by Thamer Naouech and published by Thamer Naouech. This book was released on 2020-10-20 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is undeniable how prime numbers are one of the most beautiful and fascinating topics in mathematics. But what are prime numbers? Are they only numbers that are divisible by 1 and themselves, or do they have another interesting hidden face?Throughout history, the mystery of prime numbers has challenged the greatest minds in mathematics starting from Euclid of Alexandria to Fermat, Euler, Gauss, and Erdős,… who attempted to solve the puzzling problem of primes. The achievements they realized and the secrets they revealed can only assert how deep the concept of prime numbers is. Starting from how prime numbers exist in nature, and how they are of great use in modern cryptography on which our daily life completely depends, the author travels in the holy kingdom of primes diving into some conjectures involving those special numbers. From the Riemann Hypothesis and the well-known zeta function, he explains how a note in the margin turned to be Fermat’s Last Theorem, one of the most important problems in the history of mathematics. From Mersenne Primes, he gets to the twin primes, those shining little stars in the blue sky of primes. And from Euclid’s proof of the infinite number of primes he gets to a hidden pattern in the distribution of primes discovered by Stanisław Ulam and called the Ulam Spiral. After this little trip, you will know, dear reader, why prime numbers deserve to be called "the holy grail of mathematics".

Download or read book The Riemann Hypothesis written by Peter B. Borwein and published by Springer Science & Business Media. This book was released on 2008 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.

Download or read book Stalking The Riemann Hypothesis written by Daniel Nahum Rockmore and published by Random House. This book was released on 2011-06-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Professor Bernhard Riemann, it proposes a simple law which Riemann believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scattered without end throughout a boundless numerical universe. Just eight years later, at the tender age of thirty-nine Riemann would be dead from tuberculosis, cheated of the opportunity to settle his conjecture. For over a century, the Riemann Hypothesis has stumped the greatest of mathematical minds, but these days frustration has begun to give way to excitement. This unassuming comment is revealing astounding connections among nuclear physics, chaos and number theory, creating a frenzy of intellectual excitement amplified by the recent promise of a one million dollar bounty. The story of the quest to settle the Riemann Hypothesis is one of scientific exploration. It is peopled with solitary hermits and gregarious cheerleaders, cool calculators and wild-eyed visionaries, Nobel Prize-winners and Fields Medalists. To delve into the Riemann Hypothesis is to gain a window into the world of modern mathematics and the nature of mathematics research. Stalking the Riemann Hypothesis will open wide this window so that all may gaze through it in amazement.

Download or read book The World s Smallest Prime Number written by Michael Perusse and published by . This book was released on 2019-05-21 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the World's Smallest Prime Number. Nothing more, nothing less. Please do not buy it.

Download or read book An Adventurer s Guide to Number Theory written by Richard Friedberg and published by Courier Corporation. This book was released on 2012-07-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.

Download or read book Number Theory written by George E. Andrews and published by Courier Corporation. This book was released on 2012-04-30 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Download or read book The Music of the Primes Why an unsolved problem in mathematics matters Text Only written by Marcus du Sautoy and published by HarperCollins UK. This book was released on 2012-05-31 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: (This ebook contains a limited number of illustrations.) The ebook of the critically-acclaimed popular science book by a writer who is fast becoming a celebrity mathematician.

Download or read book The Great Mathematical Problems written by Ian Stewart and published by Profile Books. This book was released on 2013-03-07 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincaré Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Download or read book The Solitude of Prime Numbers written by Paolo Giordano and published by Penguin. This book was released on 2010-03-18 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the author of Heaven and Earth, a sensational novel about whether a "prime number" can ever truly connect with someone else A prime number is inherently a solitary thing: it can only be divided by itself, or by one: it never truly fits with another. Alice and Mattia, too, move on their own axis, alone with their personal tragedies. As a child, Alice’s overbearing father drove her first to a terrible skiing accident, and then to anorexia. When she meets Mattia she recognizes a kindred, tortured spirit, and Mattia reveals to Alice his terrible secret: that as a boy he abandoned his mentally-disabled twin sister in a park to go to a party, and when he returned, she was nowhere to be found. These two irreversible episodes mark Alice and Mattia’s lives for ever, and as they grow into adulthood their destinies seem intertwined: they are divisible only by themselves and each other. But the shadow of the lost twin haunts their relationship, until a chance sighting by Alice of a woman who could be Mattia’s sister forces a lifetime of secret emotion to the surface. A meditation on loneliness and love, The Solitude of Prime Numbers asks, can we ever truly be whole when we’re in love with another? And when Mattia is asked to choose between human love and his professional love — of mathematics — which will make him more complete?

Download or read book Closing the Gap written by Vicky Neale and published by Oxford University Press. This book was released on 2017-09-29 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2013, a little known mathematician in his late 50s stunned the mathematical community with a breakthrough on an age-old problem about prime numbers. Since then, there has been further dramatic progress on the problem, thanks to the efforts of a large-scale online collaborative effort of a type that would have been unthinkable in mathematics a couple of decades ago, and the insight and creativity of a young mathematician at the start of his career. Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can appreciate their beauty, and yet mathematicians' difficulty with answering some seemingly simple questions about them reveals the depth and subtlety of prime numbers. Vicky Neale charts the recent progress towards proving the famous Twin Primes Conjecture, and the very different ways in which the breakthroughs have been made: a solo mathematician working in isolation and obscurity, and a large collaboration that is more public than any previous collaborative effort in mathematics and that reveals much about how mathematicians go about their work. Interleaved with this story are highlights from a significantly older tale, going back two thousand years and more, of mathematicians' efforts to comprehend the beauty and unlock the mysteries of the prime numbers.

Download or read book Fermat s Last Theorem written by Simon Singh and published by Fourth Estate. This book was released on 2022-05-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing the Collins Modern Classics, a series featuring some of the most significant books of recent times, books that shed light on the human experience - classics which will endure for generations to come.

Download or read book Proof Patterns written by Mark Joshi and published by Springer. This book was released on 2015-03-17 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

Download or read book Number Theory written by Robin Wilson and published by Oxford University Press, USA. This book was released on 2020 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory is the branch of mathematics primarily concerned with the counting numbers, especially primes. It dates back to the ancient Greeks, but today it has great practical importance in cryptography, from credit card security to national defence. This book introduces the main areas of number theory, and some of its most interesting problems.

Download or read book Mind Tools written by Rudy Rucker and published by Courier Corporation. This book was released on 2013-11-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Boston: Houghton Mifflin, 1987.