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Almost primes in short intervals

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Abstract

In this paper, we prove that the short interval (x − x 101/232, x] contains at least an almost prime P 2 for sufficiently large x, where P 2 denotes an integer having at most two prime factors counted with multiplicity.

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Authors and Affiliations

  1. Institut Elie Cartan Nancy, CNRS, Nancy-Université, INRIA, Boulevard des Aiguillettes, B.P. 239, 54506, VandŒuvre-lès-Nancy, France

    Jie Wu

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  1. Jie Wu
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Correspondence to Jie Wu.

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Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday

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Wu, J. Almost primes in short intervals. Sci. China Math. 53, 2511–2524 (2010). https://doi.org/10.1007/s11425-010-4039-y

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  • DOI: https://doi.org/10.1007/s11425-010-4039-y

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