On Romanoff's constant

DOI10.1016/j.jnt.2003.11.009zbMath1049.11106OpenAlexW2010462498MaRDI QIDQ1434325

Xue-Gong Sun, Yong-Gao Chen

Publication date: 4 August 2004

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2003.11.009

zbMATH Keywords

distribution of primescovering systemstwin primesRomanoff's theoremsums of prime powers

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Congruences; primitive roots; residue systems (11A07) Arithmetic progressions (11B25)

Related Items (20)

On the sum of a Fibonacci number and a prime ⋮ On a problem of Romanoff type ⋮ DENSITY OF TWO SQUARES OF PRIMES AND POWERS OF 2 ⋮ Sums of primes and quadratic linear recurrence sequences ⋮ On integers of the forms \(k\pm 2^{n}\) and \(k2^{n}\pm 1\) ⋮ An effective version of the Bombieri-Vinogradov theorem, and applications to Chen's theorem and to sums of primes and powers of two ⋮ Romanoff theorem in a sparse set ⋮ On computing the density of integers of the form $2^n+p$ ⋮ On integers of the form \(p + 2^{k_1^{r_1}} + \cdots + 2^{k_t^{r_t}}\) ⋮ On Romanov's constant ⋮ Five consecutive positive odd numbers none of which can be expressed as a sum of two prime powers. II ⋮ Variant of a theorem of Erdős on the sum-of-proper-divisors function ⋮ On a conjecture of Erdős ⋮ On the density of integers of the form \(2^k + p\) in arithmetic progressions ⋮ ON THE DENSITY OF INTEGERS OF THE FORM (p−1)2⁻ⁿ IN ARITHMETIC PROGRESSIONS ⋮ An explicit polynomial analogue of Romanoff's theorem ⋮ ALMOST-PRIMES REPRESENTED BY p + a^m ⋮ The sum of a prime and a Fibonacci number ⋮ Unnamed Item ⋮ Romanoff's theorem for polynomials over finite fields revisited

Cites Work

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• A binary additive problem of Erdős and the order of \(2 \bmod {p^2}\)
• On integers of the forms \(k-2^n\) and \(k2^n+1\)
• On integers of the forms \(k^r-2^n\) and \(k^r2^n+1\).
• On the sum of a prime and of two powers of two
• Evaluation of Artin's Constant and the Twin-Prime Constant
• Not Every Number is the Sum or Difference of Two Prime Powers
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2
• On integers of the form 𝑘2ⁿ+1
• On integers of the form $2^k\pm p^{\alpha _1}_1p^{\alpha _2}_2\dotsb p^{\alpha _r}_r$

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