DEF0213canonicalv1Brun Sieve Count
Brun sieve: count integers in [1..n] coprime to first d primes. Inclusion-exclusion at depth d. B(30,3)=8=φ(30).
Payload
Brun Sieve Count
Brun sieve: count integers in [1..n] coprime to first d primes. Inclusion-exclusion at depth d. B(30,3)=8=φ(30).
Brun Sieve Count
Summary
Brun sieve: count integers in [1..n] coprime to first d primes. Inclusion-exclusion at depth d. B(30,3)=8=φ(30).
Statement
\label{def:brun-sieve-count}
$B(n, d) := \#\{k \in [1,n] : \gcd(k, M_d) = 1\}$, the inclusion-exclusion
count of integers coprime to the first~$d$ primes.
\textbf{Lean:} \texttt{brun\_sieve\_count}.\quad
\textbf{Registry:} III.D101.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 253 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 99-105
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.SieveInfrastructure - Name:
brun_sieve_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.D101brun-sieve-countdef:brun-sieve-countRelease 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.