DEF0212canonicalv1Sieve Prime Count
π(n): count of primes ≤ n via sieve. π(10)=4, π(30)=10, π(100)=25.
Payload
Sieve Prime Count
π(n): count of primes ≤ n via sieve. π(10)=4, π(30)=10, π(100)=25.
Sieve Prime Count
Summary
π(n): count of primes ≤ n via sieve. π(10)=4, π(30)=10, π(100)=25.
Statement
\label{def:sieve-prime-count}
$\pi(n) := \#\{p \le n : p \text{ prime}\}$, computed via the sieve.
\textbf{Lean:} \texttt{sieve\_prime\_count}.\quad
\textbf{Registry:} III.D100.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 252 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 92-97
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.SieveInfrastructure - Name:
sieve_prime_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.D100sieve-prime-countdef:sieve-prime-countRelease 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.
FTH0807formal theorem
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FTH0808formal theorem
FTH0808formal theorem
FTH0809formal theorem
FTH0809formal 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.