On Goldbach numbers in short intervals
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.
Authors
- Andrés Chirre (ORCID: https://orcid.org/0000-0003-1724-7221)
- Markus Valås Hagen
Institutions
- Norwegian University of Science and Technology (NO)
- Pontificia Universidad Católica del Perú (PE)
Publication Details
- Journal
- Research in Number Theory
- Published
- 2026-08-14
- DOI
- https://doi.org/10.1007/s40993-026-00767-6
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- University of Oxford
- Norges Forskningsråd
- Pontificia Universidad Católica del Perú