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Primes and the Lambert W function

Author

Listed:
  • Matt Visser

    (School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand)

Abstract

The Lambert W function, implicitly defined by W ( x ) e W ( x ) = x , is a relatively “new” special function that has recently been the subject of an extended upsurge in interest and applications. In this note, I point out that the Lambert W function can also be used to gain a new perspective on the distribution of the prime numbers.

Suggested Citation

  • Matt Visser, 2018. "Primes and the Lambert W function," Mathematics, MDPI, vol. 6(4), pages 1-6, April.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:4:p:56-:d:140057
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    Citations

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    Cited by:

    1. Matt Visser, 2019. "Verifying the Firoozbakht, Nicholson, and Farhadian Conjectures up to the 81st Maximal Prime Gap," Mathematics, MDPI, vol. 7(8), pages 1-7, August.
    2. Lóczi, Lajos, 2022. "Guaranteed- and high-precision evaluation of the Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    3. Yuri A. Iriarte & Mário de Castro & Héctor W. Gómez, 2020. "The Lambert- F Distributions Class: An Alternative Family for Positive Data Analysis," Mathematics, MDPI, vol. 8(9), pages 1-17, August.
    4. Pavel Trojovský, 2020. "On the Growth of Some Functions Related to z ( n )," Mathematics, MDPI, vol. 8(6), pages 1-8, June.

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