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How Many Prime Numbers Are There?

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The Little Book of Big Primes

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Abstract

The answer is given by the fundamental theorem:

There exist infinitely many prime numbers.

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References

  1. KUMMER, E.E. Neuer elementarer Beweis, dass die Anzahl aller Primzahlen eine unendliche ist. Monatsber. Akad. d. Wiss., Berlin, 1878/9, 777–778.

    Google Scholar 

  2. STIELTJES, T.J. Sur la théorie des nombres. Etude bibliographique. An. Fac. Sci. Toulouse, 4, 1890, 1–103.

    Google Scholar 

  3. PóLYA, G. & SZEGÖ, G. Aufgaben und Lehrsätze aus der Analysis, 2 vols. Springer-Verlag, Berlin, 1924 (4th edition, 1970 ).

    Book  MATH  Google Scholar 

  4. BELLMAN, R. A note on relatively prime sequences. Bull. Amer. Math. Soc., 53, 1947, 778–779.

    Article  MATH  Google Scholar 

  5. FÜRSTENBERG, H. On the infinitude of primes. Amer. Math. Monthly, 62, 1955, p. 353.

    Article  Google Scholar 

  6. GOLOMB, S.W. A connected topology for the integers. Amer. Math. Monthly, 66, 1959, 663–665.

    Article  MathSciNet  MATH  Google Scholar 

  7. MULLIN, A.A. Recursive function theory (A modern look on an Euclidean idea). Bull. Amer. Math. Soc., 69, 1963, p. 737.

    Article  MathSciNet  Google Scholar 

  8. EDWARDS, A.W.F. Infinite coprime sequences. Math. Gazette, 48, 1964, 416–422.

    Article  MATH  Google Scholar 

  9. SAMUEL, P. Théorie Algébrique des Nombres. Hermann, Paris, 1967. English translation published by Houghton-Mifflin, Boston, 1970.

    Google Scholar 

  10. COX, C.D. & VAN DER POORTEN, A.J. On a sequence of prime numbers. J. Austr. Math. Soc., 1968, 8, 571–574.

    Article  MATH  Google Scholar 

  11. BORNING, A. Some results fork!±1 and 2·3·5... p+ 1. Math. Comp., 26, 1972, 567–570.

    MathSciNet  MATH  Google Scholar 

  12. TEMPLER, M. On the primality ofk!+1 and 2·3... p+1. Math. Comp., 34, 1980, 303–304.

    MathSciNet  MATH  Google Scholar 

  13. WASHINGTON, L.C. The infinitude of primes via commutative algebra. Unpublished manuscript.

    Google Scholar 

  14. BUHLER, J.P., CRANDALL, R.E. & PENK, M.A. Primes of the form n! + 1 and 2·3·5... p + 1. Math. of Comp., 38, 1982, 639–643.

    MathSciNet  MATH  Google Scholar 

  15. ODONI, R.W.K. On the prime divisors of the sequence wn+i = 1 + wiw2... w n. J. London Math. Soc., (2), 32, 1985, 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  16. DUBNER, H. Factorial and primorial primes. J. Recr. Math., 19, 1987, 197–203.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, K7L 3N6, Kingston, Ontario, Canada

    Paulo Ribenboim

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  1. Paulo Ribenboim
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© 1991 Paulo Ribenboim

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Ribenboim, P. (1991). How Many Prime Numbers Are There?. In: The Little Book of Big Primes. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4330-2_2

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  • DOI: https://doi.org/10.1007/978-1-4757-4330-2_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97508-5

  • Online ISBN: 978-1-4757-4330-2

  • eBook Packages: Springer Book Archive

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