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Tackling the various ways politicians enter and exit Downing Street, Rodney Brazier gives context and analysis to this comprehensive account of what goes into becoming the leader of the United Kingdom. With historical examples and contemporary evidence, this text explains the rules which govern gaining and losing the British Prime Ministership.
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Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap length between infinite numbers of consecutive primes has been reduced to a tractable finite size. The text is both introductory and complete: the detailed way in which results are proved is fully set out and plenty of background material is included. The reader journeys from selected historical theorems to the latest best result, exploring the contributions of a vast array of mathematicians, including Bombieri, Goldston, Motohashi, Pintz, Yildirim, Zhang, Maynard, Tao and Polymath8. The book is supported by a linked and freely-available package of computer programs. The material is suitable for graduate students and of interest to any mathematician curious about recent breakthroughs in the field.
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Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann hypothesis, which remains one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann hypothesis. Students with a minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann hypothesis.
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Numbers, Prime --- Nombres premiers --- Numbers, Prime. --- Nombres, Théorie des
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La plupart des nombres suivent des règles simples et claires. Les nombres premiers, eux, sont de vrais trouble-fêtes : ils apparaissent où bon leur semble, sans prévenir, de manière apparemment chaotique et sans suivre aucune règle.
Numbers, Prime --- Nombres premiers --- Nombres premiers. --- Numbers, Prime.
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Numbers, Prime. --- Nombres premiers --- Tables
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Prime ministers --- -Chancellors (Prime ministers) --- Chief ministers (Prime ministers) --- First ministers (Prime ministers) --- Premiers (Prime ministers) --- Cabinet officers --- Heads of state --- Fiction --- -Fiction
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