Small gaps between Goldbach primes

2025/08/04 by Akeno, Mizuki
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.02769

Abstract

We study small gaps between Goldbach primes ℙ ∩ (N-ℙ) using the Bombieri-Davenport method and the Maynard-Tao method, and compare the two. We show that for almost all even integers N, the smallest gap in ℙ ∩ (N-ℙ) is at most 0.765… times the average gap, using the Bombieri-Davenport method. This improves a recent result of Tsuda. We also demonstrate that a straightforward application of the Maynard-Tao method is insufficient to improve this bound. However, it allows us to establish the existence of bounded gaps between Goldbach primes with bounded error for almost all even integers N.

Citations

• On the exponents of distribution of primes and smooth numbers
• Primes in arithmetic progressions to large moduli II: Well-factorable estimates
• Primes in Tuples I
• An Overview of the Sieve Method and its History
• Restriction theory of the Selberg sieve, with applications

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