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The density of integers representable as the sum of four prime cubes

Volume 192 / 2020

Christian Elsholtz, Jan-Christoph Schlage-Puchta Acta Arithmetica 192 (2020), 363-369 MSC: Primary 11P32; Secondary 11P05, 11N36. DOI: 10.4064/aa180827-26-2 Published online: 22 November 2019


The set of integers which can be written as the sum of four prime cubes has lower density at least $0.009664$. This improves earlier bounds of $0.003125$ by Ren, and $0.005776$ by Liu.


  • Christian ElsholtzInstitut für Analysis und Zahlentheorie
    Technische Universität Graz
    A-8010 Graz, Austria
  • Jan-Christoph Schlage-PuchtaMathematical Institute
    University of Rostock
    18957 Rostock, Germany

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