A note on Romanov's constant

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• 作者：János Pintz
• 关键词：Goldbach ; Linnik problem ; generalized twin prime problem ; Romanov's constant
• 刊名：Acta Mathematica Hungarica
• 出版年：2006
• 出版时间：July, 2006
• 年：2006
• 卷：112
• 期：1-2
• 页码：1-14
• 全文大小：211 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Sciences
  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2632

文摘

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.