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Prime simplicity. (English) Zbl 1196.11004

The authors study the different versions of Euclid’s proof of the infinitude of primes given in more than 100 textbooks written in English. Some of the claims made in textbooks are almost entertaining: Euclid “introduced factorials” [C. M. Grinstead and J. L. Snell, Introduction to probability. 2nd rev. ed. Providence, RI: American Mathematical Society (AMS) (1997; Zbl 0914.60004)] and used them to prove “some quite useless facts about prime numbers” [L. Hogben, Mathematics for the million. London: George Allen & Unwin (1937; JFM 63.0840.08)]. The ridiculous claim, however, that W. Narkiewicz [The development of prime number theory. Springer Monographs in Mathematics. Berlin: Springer. (2000; Zbl 0942.11002)] called Euclid’s proof “fallacious”, since it only shows that lists of three primes can always be enlarged, is incorrect: Narkiewicz was talking about a gap in Euclid’s proof of his lemma that primes dividing a product must divide one of the factors.

MSC:

11-03 History of number theory
11A41 Primes
97A30 History in mathematics education

Keywords:

prime numbers
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Full Text: DOI

References:

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