DEF0314canonicalv1Eratosthenes Sieve
Sieve of Eratosthenes: computable primality predicate via trial division. Foundation for all three conjecture tracks.
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Eratosthenes Sieve
Sieve of Eratosthenes: computable primality predicate via trial division. Foundation for all three conjecture tracks.
Eratosthenes Sieve
Summary
Sieve of Eratosthenes: computable primality predicate via trial division. Foundation for all three conjecture tracks.
Statement
\label{def:eratosthenes-sieve}
The \emph{sieve of Eratosthenes} at bound~$n$ is a computable function
$\mathrm{sieve}(n) : \{0, \ldots, n\} \to \{\mathrm{true}, \mathrm{false}\}$
such that $\mathrm{sieve}(k) = \mathrm{true}$ if and only if $k$ is prime.
\textbf{Lean:} \texttt{eratosthenes\_sieve} in
\texttt{SieveInfrastructure.lean}.\qquad
\textbf{Registry:} III.D99.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 251 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 82-90
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.SieveInfrastructure - Name:
eratosthenes_sieve
Dependencies
- Canonical: I.T09
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.D99eratosthenes-sievedef:eratosthenes-sieveRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
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.