Claims

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1976_08_01_eggleton_selfridge: Eggleton and Selfridge give, for every epsilon, infinitely many runs of five consecutive integers n to n plus 4 each n to the epsilon smooth, which settles the question and the site's first reading for k at most 5.

1998_04_01_balog_wooley: Balog and Wooley prove that for every fixed u above 1 infinitely many n are followed by about log log log log n consecutive n^(1/u)-smooth integers: the wording and the first reading, the second for infinitely many n only.

2017_10_05_bober_fretwell_martin_wooley: Theorem 2.1 of Bober, Fretwell, Martin and Wooley gives, for every epsilon and k and all large n, k consecutive n to the epsilon smooth integers in the interval from n minus n to the theta to n for some theta below one.

2026_03_26_yang: Yang shows that for every epsilon and k and all large N the upper half of 1 to N holds k consecutive integers each smooth to its own epsilon power, the site's second strengthening, accepted on the forum by the site's curator.

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