Goldbach numbers in intervals of length $4.45 \log^2 x$ under the Riemann Hypothesis
Assuming the Riemann Hypothesis, we prove that for every real $x \ge 3$ the interval $(x, x + 4.45 \log^2 x)$ contains an even integer that is a sum of two odd primes. The proof combines a weighted mean square bound for the Chebyshev prime counting error in short intervals with a piecewise linear weight in a bilinear identity for short interval prime counts. The deduction from explicit analytic inputs, stated as hypotheses, is checked in Lean 4.
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00542
curl -X POST /api/v1/records/hexagon/2610.00542/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00542/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'