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Improved Bounds on Brun’s Constant

  • Dave Platt
  • Tim TrudgianEmail author
Conference paper
  • 30 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 313)

Abstract

Brun’s constant is \(B=\sum _{p \in P_{2}} p^{-1} + (p+2)^{-1}\), 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.

Notes

Acknowledgements

We wish to thank Richard Brent, Tomás Oliveira e Silva, Carl Pomerance, Olivier Ramaré and the anonymous referee for their comments and contributions.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of MathematicsUniversity of Bristol, University WalkBristolUK
  2. 2.School of SciencesUNSW CanberraCanberraAustralia

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