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An explicit version of Chen’s theorem assuming the Generalized Riemann Hypothesis

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Abstract

We prove that assuming the Generalized Riemann Hypothesis every even integer larger than \(\exp (\exp (14))\) can be written as the sum of a prime number and a number that has at most two prime factors.

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An explicit version of Chen’s theorem assuming the Generalized Riemann Hypothesis contains all of the information required to reproduce the datasets generated in the study.

Notes

  1. We can assume \(N > \exp (\exp (10))\) since the final bound for N is higher.

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Acknowledgements

We would like to thank Tim Trudgian, S. supervisor, for his help in developing this paper and his insightful comments. We would also like to thank Daniel Johnston for his helpful suggestions and remarks.

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Authors and Affiliations

  1. Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Matteo Bordignon

  2. UNSW Canberra, School of Science, Canberra, ACT, Australia

    Valeriia Starichkova

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  1. Matteo Bordignon
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  2. Valeriia Starichkova
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The authors contributed equally to this work.

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Correspondence to Valeriia Starichkova.

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M. Bordignon: B. research was supported by OP RDE project No. CZ.\(02.2.69/0.0/0.0/18\_053/0016976\) International mobility of research, technical and administrative staff at Charles University.

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Bordignon, M., Starichkova, V. An explicit version of Chen’s theorem assuming the Generalized Riemann Hypothesis. Ramanujan J (2024). https://doi.org/10.1007/s11139-024-00866-x

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