THM0207canonicalv1Twin Primes to 500
At least 20 twin prime pairs below 500. Extended from 30 (Wave M9).
Payload
Twin Primes to 500
At least 20 twin prime pairs below 500. Extended from 30 (Wave M9).
Twin Primes to 500
Summary
At least 20 twin prime pairs below 500. Extended from 30 (Wave M9).
Statement
\label{thm:twin-500}
$\pi_2(500) \ge 20$. The twin prime pairs below~500 include
$(3,5)$, $(5,7)$, $(11,13)$, $(17,19)$, $(29,31)$, $(41,43)$,
$(59,61)$, $(71,73)$, \ldots
\textbf{Lean:} \texttt{twin\_primes\_500}.\quad
\textbf{Registry:} III.T72.\quad
\textbf{Scope:} $\tau$-effective.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 269 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 237-245
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.TwinPrimeDeep - Name:
twin_primes_500
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.T72twin-primes-to-500thm:twin-500Release 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.