DEF0218canonicalv1Hardy-Littlewood Constant
Hardy-Littlewood twin constant C₂(k) = ∏ p(p-2)/(p-1)² for p≥3. C₂(2)=3/4, C₂(3)=45/64. Decreasing toward C₂≈1.3203.
Payload
Hardy-Littlewood Constant
Hardy-Littlewood twin constant C₂(k) = ∏ p(p-2)/(p-1)² for p≥3. C₂(2)=3/4, C₂(3)=45/64. Decreasing toward C₂≈1.3203.
Hardy-Littlewood Constant
Summary
Hardy-Littlewood twin constant C₂(k) = ∏ p(p-2)/(p-1)² for p≥3. C₂(2)=3/4, C₂(3)=45/64. Decreasing toward C₂≈1.3203.
Statement
\label{def:hl-constant}
The twin prime constant truncated at depth~$k$:
\[
C_2(k) = \prod_{\substack{i=2 \\ p_i \ge 3}}^{k}
\frac{p_i(p_i - 2)}{(p_i - 1)^2}.
\]
Computed as a rational (numerator, denominator).
$C_2(2) = 3/4$, $C_2(3) = 45/64$.
\textbf{Lean:} \texttt{hl\_twin\_constant\_approx}.\quad
\textbf{Registry:} III.D106.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 267 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 255-266
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.TwinPrimeDeep - Name:
hl_twin_constant_approx
Dependencies
- Canonical: (none)
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
III.D106hardy-littlewood-constantdef:hl-constantRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (1)
Appears in (1)
Downstream uses (computed) (2)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
Sources
Version & History
Status disclaimer
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