Improved bounds on Brun's constant

Dave Platt, Timothy Trudgian

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

Abstract

Brun’s constant is B = Pp∈P2p−1 + (p + 2)−1, where the summation is over all twin primes. We improve the unconditional bounds on Brun’s constant to 1.840503 < B < 2.288490, which are about 13% tighter.
Original languageEnglish
Title of host publicationFrom Analysis to Visualization
Subtitle of host publicationA Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017
EditorsDavid H Bailey, Naomi Simone Borwein, Richard P Brent, Regina S Burachik, Judy-anne Heather Osborn, Brailey Sims, Qiji J Zhu
PublisherSpringer-Verlag Berlin
Pages395-406
Volume313
ISBN (Electronic)978-3-030-36568-4
ISBN (Print)978-3-030-36567-7
DOIs
Publication statusPublished - 26 Mar 2020

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume313
ISSN (Print)2194-1009

Keywords

  • Applied Analysis
  • Math Education
  • Experimental Mathematics
  • Financial Mathematics
  • Number Theory
  • Commemorative Jonathan Borwein

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  • Cite this

    Platt, D., & Trudgian, T. (2020). Improved bounds on Brun's constant. In D. H. Bailey, N. S. Borwein, R. P. Brent, R. S. Burachik, J. H. Osborn, B. Sims, & Q. J. Zhu (Eds.), From Analysis to Visualization: A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017 (Vol. 313, pp. 395-406). (Springer Proceedings in Mathematics and Statistics; Vol. 313). Springer-Verlag Berlin. https://doi.org/10.1007/978-3-030-36568-4