Claims

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2026_04_30_chojecki: A note deducing from the Matomäki–Radziwiłł short-interval theorem that for every epsilon the upper density of n with no large prime factor among n, ..., n+k tends to zero as k grows; it answers the precise Statement, pending.

2026_05_01_chojecki: Gives, under an unproven hypothesis it names LPD, the natural-density variant (a natural density at least 1 - eta) only for epsilon below one half, and through it the precise Statement (a lower density at least 1 - eta) only in that range, which the unconditional claim already covers, so it does not count toward the problem's standing. The note claims that the n with no large prime factor among n, ..., n+h-1 have natural density rho(1/alpha)^h.

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