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Improved bounds on Brun's constant

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

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
Publisher or commissioning bodySpringer-Verlag Berlin
ISBN (Electronic)978-3-030-36568-4
ISBN (Print)978-3-030-36567-7
DateAccepted/In press - 4 Jul 2018
DatePublished (current) - 26 Mar 2020

Publication series

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


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.

    Research areas

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



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    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Springer at . Please refer to any applicable terms of use of the publisher.

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    Embargo ends: 26/03/21

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