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Prescribing the binary digits of primes, II

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Abstract

We obtain the expected asymptotic formula for the number of primes p < N = 2n with r prescribed (arbitrary placed) binary digits, provided r < cn for a suitable constant c > 0. This result improves on our earlier result where r was assumed to satisfy \(r < c{\left( {\frac{n}{{\log n}}} \right)^{4/7}}\).

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Authors and Affiliations

  1. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Jean Bourgain

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  1. Jean Bourgain
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Correspondence to Jean Bourgain.

Additional information

This work was partially supported by NSF grants DMS-1301619 and DMS-0835373.

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Bourgain, J. Prescribing the binary digits of primes, II. Isr. J. Math. 206, 165–182 (2015). https://doi.org/10.1007/s11856-014-1129-5

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  • DOI: https://doi.org/10.1007/s11856-014-1129-5

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