Brun's Constant

81a

Upper bound, last-listed row: | 2.1594 | [D2025] | **Conditional on the Generalised Riemann Hypothesis**, and the best conditional bound known. Theorem 1.1: "Assume GRH. Then, $B < 2.1594$." Dunn describes this as "the first mathematically rigorous upper bound on $B$ assuming GRH", the earlier [K2007] bound being unpublished and resting on numerical integration. |value changed 2026-08-23
Lower bound, last-listed row: | 1.840503 | [PT2018] | Unconditional, and the value carried in the README table. |text edited 2026-08-23 — bound unchanged

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Bounds Ledger — Brun's Constant (81a)
upper bound: 2.1594 (value changed 2026-08-23)
lower bound: 1.840503 (text edited 2026-08-23 — bound unchanged)
Mirrored from teorth/optimizationproblems@2c1968c. These are the last-listed rows of that constant's bounds table — a listing position, not a statement that this bound is the strongest or most recent. A snapshot at that sha, not a live read.
https://u00dxk2.github.io/bounds-ledger/c/81a.html