The Infinitude of the Primes

John W. Dawson
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John W. Dawson: Penn State York

Chapter Chapter 7 in Why Prove it Again?, 2015, pp 51-57 from Springer

Abstract: Abstract Euclid’s proof that the prime numbers are “more than any assigned multitude” (Elements, proposition IX, 20) has long been hailed as a model of elegance and simplicity. Yet, surprisingly, it has also been misrepresented in a great many accounts: The article Hardy and Woodgold (2009) gives a detailed list of sources, including many by eminent number theorists, that either erroneously describe the structure of Euclid’s proof or make false historical claims about it. It is wise, therefore, to begin by quoting Euclid’s argument directly, as it is given in Heath’s translation (Heath 1956, vol. II, p. 412).

Keywords: Arithmetic Progression; Congruence Class; Harmonic Series; Analytic Number Theory; Topological Concept (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-17368-9_7

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