The 6k ±1 Composite–Displacement Sieve: A 6–Wheel Eratosthenes Implementation with Least–Prime–Factor Ownership

This note gives a conservative Version 2 formulation of the Composite–Displacement, or Greedy–Ast, sieve. The algorithm works inside the classical 6–wheel carrier A6 = {n∈N : n≡±1 (mod 6)}, where every prime greater than 3 occurs. For each active prime p≥5, the raw multiples of p inside the carrier split into two genuine arithmetic progressions of common difference 6p, p(6t+ 1), p(6t+ 5).

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-06
DOI
https://doi.org/10.5281/zenodo.18518119
Primary Topic
Cryptography and Residue Arithmetic
Type
preprint
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preprint

The 6k ±1 Composite–Displacement Sieve: A 6–Wheel Eratosthenes Implementation with Least–Prime–Factor Ownership

Stephen Steiner
Zenodo (CERN European Organization for Nuclear Research)
Cryptography and Residue Arithmetic
preprint

The 6k ±1 Composite–Displacement Sieve: A 6–Wheel Eratosthenes Implementation with Least–Prime–Factor Ownership

Stephen Steiner
preprint en

Abstract

This note gives a conservative Version 2 formulation of the Composite–Displacement, or Greedy–Ast, sieve. The algorithm works inside the classical 6–wheel carrier A6 = {n∈N : n≡±1 (mod 6)}, where every prime greater than 3 occurs. For each active prime p≥5, the raw multiples of p inside the carrier split into two genuine arithmetic progressions of common difference 6p, p(6t+ 1), p(6t+ 5).

Zenodo (CERN European Organization for Nuclear Research)
Cryptography and Residue Arithmetic
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