Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Claim. There is a set of positive integers of density one whose increasing enumeration has distinct products on distinct consecutive blocks; the answer to the question is yes.
The result. R. Kielhorn, Distinct consecutive products in a density-one set via prime-gap deletions, preprint published on Zenodo on 10 July 2026 (DOI 10.5281/zenodo.21287065, CC BY 4.0, a PDF with its LaTeX source). Its abstract: a subset of the natural numbers of density one whose increasing enumeration has pairwise distinct finite consecutive products, by a sparse deletion scheme based on prime-gap interiors and connector intervals, a structural analysis of the possible product collisions, integral-point estimates for separated-variable curves, and results on primes in almost all short intervals. The site's curator linked the preprint in the thread on 13 July 2026 among claimed solutions that had not passed moderation, writing that they had not read these attempts in detail and made no claim about their correctness.
Standing. Reviewed by nobody. Pratt's digested proof of 1 September 2026 mentions that other individuals also proposed AI-assisted proofs without naming them. The preprint is not held in this corpus; this page draws on its Zenodo record. The problem's solved standing rests on Chojecki's claim and Sneiderman's claim.
Depends on. No page of this wiki.