Duke Mathematical Journal

A density version of the Vinogradov three primes theorem

Xuancheng Shao

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We prove that if A is a subset of the primes, and the lower density of A in the primes is larger than 5/8, then all sufficiently large odd positive integers can be written as the sum of three primes in A. The constant 5/8 in this statement is the best possible.

Article information

Duke Math. J., Volume 163, Number 3 (2014), 489-512.

First available in Project Euclid: 11 February 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11P32: Goldbach-type theorems; other additive questions involving primes
Secondary: 11D85: Representation problems [See also 11P55]


Shao, Xuancheng. A density version of the Vinogradov three primes theorem. Duke Math. J. 163 (2014), no. 3, 489--512. doi:10.1215/00127094-2410176. https://projecteuclid.org/euclid.dmj/1392128876

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