Abstract
As we go to larger and larger integers, primes become rarer and rarer. Is there a largest prime after which all whole numbers are composite? This sounds counter-intuitive and, in fact, it isn’t true, as Euclid demonstrated a long time ago. Actually, he did it without demonstrating any primes — he just showed that assuming a finite number of primes leads to a neat contradiction.
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References
C. Pomerance: The search for prime numbers. Sci. Am. 247, No. 6, 136–147 (1982)
W. H. Mills: A prime representing function. Bull. Am. Math. Soc. 53, 604 (1947)
T. Nagell: Introduction to Number Theory (Wiley, New York 1951)
D. Slowinski: Searching for the 27th Mersenne prime. J. Recreational Math. 11, 258–261 (1978–79)
D. B. Gillies: Three new Mersenne primes and a statistical theory. Math. Comp. 18, 93–97 (1963)
G. H. Hardy, E. M. Wright: An Introduction to the Theory of Numbers, 5th ed., Sect. 2.5 (Clarendon, Oxford 1984)
W. Kaufmann-Bühler: Gauss. A Biographical Study (Springer, Berlin, Heidelberg, New York 1981)
C. Chant, J. Fauvel (eds.): Science and Belief (Longman, Essex 1981)
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© 1997 Springer-Verlag Berlin Heidelberg
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Schroeder, M.R. (1997). Primes. In: Number Theory in Science and Communication. Springer Series in Information Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03430-9_3
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DOI: https://doi.org/10.1007/978-3-662-03430-9_3
Publisher Name: Springer, Berlin, Heidelberg
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