THM0203canonicalv1Goldbach Verified to 500
Goldbach verified to 500 via sieve: every even n in [4,500] = p+q with p,q prime.
Payload
Goldbach Verified to 500
Goldbach verified to 500 via sieve: every even n in [4,500] = p+q with p,q prime.
Goldbach Verified to 500
Summary
Goldbach verified to 500 via sieve: every even n in [4,500] = p+q with p,q prime.
Statement
\label{thm:goldbach-500}
Every even $n$ with $4 \le n \le 500$ has a Goldbach representation.
\[
\forall n \in [4, 500],\; 2 \mid n \implies
\exists p, q \text{ prime}: p + q = n.
\]
\textbf{Lean:} \texttt{goldbach\_500}.\quad
\textbf{Registry:} III.T68.\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 260 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 151-161
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.GoldbachDeep - Name:
goldbach_500
Dependencies
- Canonical: III.D102
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.T68goldbach-verified-to-500thm:goldbach-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.