Theoretical proof demonstrates the existence of Goldbach numbers in short intervals under the Riemann Hypothesis, establishing a reduced constant bound of 123.
Assuming the Riemann Hypothesis, we prove that for all x 2 , there exists at least one even integer within the interval (x, x+123log 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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Chirre et al. (2026) studied this question.
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