Paper 6. The Twin Criterion: Six Exception Positions

Osman, Mohamed

Paper 6. The Twin Criterion: Six Exception Positions

A single open cell in a sector is a twin pair unless it sits at one of six named places

Mohamed Osman · ORCID 0009-0004-5912-999X · independent researcher · 2026-10-16

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Abstract. After switching on every line up to M in the sector between M^2 and (M+6)^2, at most six cells can be open without being a twin, and their positions are explicit quadratics in M.

No progress toward the twin-prime conjecture is claimed. Priority is not claimed for any result. Every number printed is regenerated by a script in code/ of the repository. Licence: CC BY 4.0 (text), MIT (code).