On Goldbach numbers in short intervals
Abstract
Assuming the Riemann Hypothesis, we prove that for all $$x\geqslant 2$$ , 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.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Identities
Benford’s Law and Fraud Detection
Publication details
- Journal / source
- Research in Number Theory
- Volume
- 12
- Issue
- 3
- Publication date
- 14 August 2026
- Language
- EN