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Infinite partial sumsets in the primes

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Abstract

We show that there exist infinite sets A = (a1, a2, …} and B = {b1, b2, …} of natural numbers such that ai + bj is prime whenever 1 ≤ i < j.

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Acknowledgements

The first author is supported by NSF grant DMS-1764034 and by a Simons Investigator Award. The second author is supported by a grant from the Institute for Advanced Study and by ISF grant 2112/20. Part of this research was conducted at the Institute for Advanced Study. We thank Joel Moreira for discussions leading to Section 5, Vitaly Bergelson for informing us of the reference [8], James Maynard for informing us of the reference [21], Yemon Choi for supplying references on translation-finite sets, Mariusz Lemanczyk for pointing out a gap in a previous version of the proof of Corollary 5.2, Joel David Hamkins for providing an argument allowing us to strengthen that corollary, and Keiju Sono for a correction.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Los Angeles, Los Angeles, CA, 90095-1555, USA

    Terence Tao

  2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Tamar Ziegler

Authors
  1. Terence Tao
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  2. Tamar Ziegler
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Correspondence to Tamar Ziegler.

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To Peter, with admiration

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Tao, T., Ziegler, T. Infinite partial sumsets in the primes. JAMA 151, 375–389 (2023). https://doi.org/10.1007/s11854-023-0323-y

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  • DOI: https://doi.org/10.1007/s11854-023-0323-y

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