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Primes to One Trillion by Don Kostuch is an essay on prime numbers and programming commands. Kostuch carefully explains the prime numbers in a variety of zip files and goes on to discuss the characteristics of C++ programs. Excerpt: "became interested in prime numbers after hearing about Goldbach's Conjecture, "Every even integer greater than 2 can be expressed as the sum of two primes". Verifying this requires a source of primes. Shortlists (or programs to generate them) are widely available. Long lists are scarce, except for primos.mat.br..."
This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes, Morris, I'm from Brazil, but my book will contain numbers different from ·one.''' He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name) and consists of about 16 million decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records.
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.
The first book in an all-new space adventure!
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
The Great Financial Crisis that began in 2007-2008 reminds us with devastating force that financial instability and crises are endemic to capitalist economies. This Handbook describes the theoretical, institutional, and historical factors that can help us understand the forces that create financial crises.
She reveals how conviction-style politicians have appeared in the U.S. and U.K. at the same time: individuals who articulated similar ideas that adapted liberal ideology to shifting circumstances and who achieved fundamental change at critical moments in their nations' histories.".
Is it possible to take a set of particle masses and then work backwards to find a hidden symmetry? Does the Higgs Boson have a partner particle and might that particle solve the mystery of dark matter? Can the tiny masses of neutrinos be predicted? Prime Symmetry and Particle Physics begins with the understanding that the constant π does not have to be measured in spacetime: it can be calculated from a set of real numbers. Former PhD student, George Brewer explores the idea that if this is true of π, why not of other constants? A standard model of physics predicts interactions between quantum fields when particles scatter, but 26 numbers, dimensionless constants for force strengths and the masses of elementary particles, still need to be put into that model. Brewer proposes that many of those constants can actually be calculated from a single equation and a set of integer parameters – a theory that he calls the prime symmetry model. Comparing a set of measured constants against their calculated counterparts provides good evidence for the model's validity. Brewer opens the door for readers to join a select group with information that theorists and experimentalists at the Large Hadron Collider (LHC) are yet to consider, offering them the opportunity to verify the model’s deceptively simple mathematics for themselves, simply by using an online scientific calculator. Inspired by Albert Einstein, Stephen Hawking and Sean Carroll, Prime Symmetry and Particle Physics is an essential read for all particle physics enthusiasts. The book will also appeal to readers interested in the Higgs boson events at the LHC.