On Romanov's constant

Christian Elsholtz, Jan-Christoph Schlage-Puchta*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show that the lower density of integers representable as a sum of a prime and a power of two is at least 0.107. We also prove that the set of integers with exactly one representation of the form p+2k has positive density. Previous results of this kind needed “at most 15” in place of “exactly one”. To achieve these results we introduce a new method. In particular we make use of uneven distribution of sums of a power of two and a reduced residue class.
Original languageEnglish
Pages (from-to)713-724
JournalMathematische Zeitschrift
Publication statusPublished - 2018

ASJC Scopus subject areas

  • General Mathematics
  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing


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