Improved bounds on Brun's constant

Autor: Platt, Dave, Trudgian, Tim

Publikováno v: 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, Springer Proceedings in Mathematics and Statistics, vol. 313, Springer-Verlag Berlin, pp. 395-406 . https://doi.org/10.1007/978-3-030-36568-4

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.

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https://research-information.bris.ac.uk/en/publications/e6c3acbe-8271-493a-91d6-4bf49722a3c4