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arXiv · 2512.23534

On Goldbach numbers in short intervals

Andrés Chirre·Markus Valås Hagen
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Abstract

Assuming the Riemann Hypothesis, we prove that for all $x\geq 2$, there exists at least one even integer within the interval $(x, x+123\log^2x]$, that can be expressed as the sum of two primes. This result is an improvement over the recent work of Cully-Hugill and Dudek, who obtained the constant $9696$ instead of $123$.

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Andrés Chirre, Markus Valås Hagen. 2025-12-29. On Goldbach numbers in short intervals. https://arxiv.org/abs/2512.23534

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