DEF0217canonicalv1Twin Prime Sieve Count
Twin prime count via sieve. π₂(100)≥8, π₂(500)≥20.
Payload
Twin Prime Sieve Count
Twin prime count via sieve. π₂(100)≥8, π₂(500)≥20.
Twin Prime Sieve Count
Summary
Twin prime count via sieve. π₂(100)≥8, π₂(500)≥20.
Statement
\label{def:twin-sieve-count}
$\pi_2(n) := \#\{p \le n : p \text{ and } p+2 \text{ both prime}\}$.
\textbf{Lean:} \texttt{twin\_prime\_sieve\_count}.\quad
\textbf{Registry:} III.D105.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 266 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 230-235
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.TwinPrimeDeep - Name:
twin_prime_sieve_count
Dependencies
- Canonical: III.D99
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.D105twin-prime-sieve-countdef:twin-sieve-countRelease 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.