Acta Mathematica Hungarica

, Volume 112, Issue 1, pp 1–14

A note on Romanov's constant

  • János Pintz

DOI: 10.1007/s10474-006-0060-6

Cite this article as:
Pintz, J. Acta Math Hung (2006) 112: 1. doi:10.1007/s10474-006-0060-6


In 1934 Romanov showed that a positive proportion of the natural numbers can be written as the sum of a prime and a power of two. Yong-Gao Chen and Xue-Gong Sun proved recently that the lower asymptotic density of this set is larger than 0.0868. We improve this bound to 0.09368 and show various connections with the generalized twin prime problem and the Goldbach-Linnik problem.

Goldbach--Linnik problem generalized twin prime problem Romanov's constant 

Copyright information

© Springer-Verlag/Akadémiai Kiadó 2006

Authors and Affiliations

  • János Pintz
    • 1
  1. 1.Rényi Institute of the Hungarian Academy of Sciences