### 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 language | English |
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Title of host publication | From Analysis to Visualization |

Subtitle of host publication | A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017 |

Editors | David H Bailey, Naomi Simone Borwein, Richard P Brent, Regina S Burachik, Judy-anne Heather Osborn, Brailey Sims, Qiji J Zhu |

Publisher | Springer-Verlag Berlin |

Pages | 395-406 |

Volume | 313 |

ISBN (Electronic) | 978-3-030-36568-4 |

ISBN (Print) | 978-3-030-36567-7 |

DOIs | |

Publication status | Published - 26 Mar 2020 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 313 |

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