PRP0112canonicalv1Twin Admissibility Fraction
At each odd prime p≥3, exactly (p-2)/p fraction of residues are twin-admissible. Only r≡0 and r≡p-2 excluded.
Payload
Twin Admissibility Fraction
At each odd prime p≥3, exactly (p-2)/p fraction of residues are twin-admissible. Only r≡0 and r≡p-2 excluded.
Twin Admissibility Fraction
Summary
At each odd prime p≥3, exactly (p-2)/p fraction of residues are twin-admissible. Only r≡0 and r≡p-2 excluded.
Statement
\label{prop:twin-admissibility}
At each odd prime $p \ge 3$, exactly $(p-2)$ out of $p$ residue classes
are twin-admissible: only $r \equiv 0$ and $r \equiv p - 2$ are excluded.
\textbf{Lean:} \texttt{twin\_admissibility\_fraction\_5}.\quad
\textbf{Registry:} III.P45.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 273 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 294-300
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.TwinPrimeDeep - Name:
twin_admissibility_fraction_5
Dependencies
- Canonical: III.D107
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.P45twin-admissibility-fractionprop:twin-admissibilityRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (4)
Appears in (1)
Downstream uses (computed) (8)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
FTH0827formal theorem
FTH0827formal theorem
FTH0832formal theorem
FTH0832formal theorem
FTH0833formal theorem
FTH0833formal theorem
FTH0834formal theorem
FTH0834formal theoremSources
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.