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arXiv · 2609.17543

Distinct Consecutive Products

Przemek Chojecki
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Abstract

We prove that there is a density-one set of positive integers for which the products of all distinct consecutive blocks are distinct, answering a question of Erdős and Graham. The construction retains or rejects entire interiors of consecutive-prime gaps and is therefore stable under passage to longer prefixes. Uniform affine-curve estimates control the witnesses with no previous rejected gap, and a scale-contracting forest controls every remaining witness unconditionally.

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Przemek Chojecki. 2026-07-14. Distinct Consecutive Products. https://arxiv.org/abs/2609.17543

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