THM0201canonicalv1Sieve Correctness
Sieve agrees with trial division up to 200. π(10)=4, π(30)=10, π(100)=25 verified.
Payload
Sieve Correctness
Sieve agrees with trial division up to 200. π(10)=4, π(30)=10, π(100)=25 verified.
Sieve Correctness
Summary
Sieve agrees with trial division up to 200. π(10)=4, π(30)=10, π(100)=25 verified.
Statement
\label{thm:sieve-correct}
The sieve agrees with trial-division primality testing for all $n \le 200$.
Moreover, $\pi(10)=4$, $\pi(30)=10$, $\pi(100)=25$.
\textbf{Lean:} \texttt{sieve\_correct\_200}, \texttt{pi\_10},
\texttt{pi\_30}, \texttt{pi\_100}.\quad
\textbf{Registry:} III.T66.\quad
\textbf{Scope:} established.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 254 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 107-115
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.SieveInfrastructure - Name:
sieve_correct_200
Dependencies
- Canonical: III.D99, III.D100
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.T66sieve-correctnessthm:sieve-correctRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (3)
Appears in (1)
Downstream uses (computed) (6)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
FTH0801formal theorem
FTH0801formal theorem
FTH0802formal theorem
FTH0802formal theorem
FTH0803formal theorem
FTH0803formal 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.