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On a problem of Erdős

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Abstract

Let s≥2 be an integer. Denote by f 1(s) the least integer so that every integer l>f 1(s) is the sum of s distinct primes. Erdős proved that f 1(s)<p 1+p 2+⋯+p s +Cslogs, where p i is the ith prime and C is an absolute constant. In this paper, we prove that f 1(s)=p 1+p 2+⋯+p s +(1+o(1))slogs=p 2+p 3+⋯+p s+1+o(slogs). This answers a question posed by P. Erdős.

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References

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Acknowledgement

We sincerely thank the referee for his/her substantial suggestion.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Information Science & Technology, Nanjing, 210044, P.R. China

    Jin-Hui Fang

  2. School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing, 210046, P.R. China

    Yong-Gao Chen

Authors
  1. Jin-Hui Fang
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  2. Yong-Gao Chen
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Corresponding author

Correspondence to Jin-Hui Fang.

Additional information

The authors are supported by the National Natural Science Foundation of China, Grant Nos. 11126302, 11071121. J.-H. Fang is also supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions, Grant No. 11KJB110006 and the Foundation of Nanjing University of Information Science & Technology No. 20110421.

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Fang, JH., Chen, YG. On a problem of Erdős. Ramanujan J 30, 443–446 (2013). https://doi.org/10.1007/s11139-012-9407-5

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  • DOI: https://doi.org/10.1007/s11139-012-9407-5

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