THM0208canonicalv1Twin Density Primorial
Twin prime density positive at each primorial level k≥2 (up to depth 5).
Payload
Twin Density Primorial
Twin prime density positive at each primorial level k≥2 (up to depth 5).
Twin Density Primorial
Summary
Twin prime density positive at each primorial level k≥2 (up to depth 5).
Statement
\label{thm:twin-density}
At each primorial level $k \ge 2$, at least one twin prime pair
exists below $\min(M_k, 500)$.
\textbf{Lean:} \texttt{twin\_density\_primorial\_5}.\quad
\textbf{Registry:} III.T73.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 270 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 247-253
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.TwinPrimeDeep - Name:
twin_density_primorial_5
Dependencies
- Canonical: III.D105
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.T73twin-density-primorialthm:twin-densityRelease 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
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.