Claims

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1992_04_01_filaseta_trifonov: Filaseta and Trifonov prove that every interval (x, x + c x^{1/5} log x] contains a squarefree number for large x, so consecutive squarefree numbers differ by at most s_n^{1/5+o(1)}; the first question for every epsilon > 1/5.

1998_01_01_granville: Granville proves that the abc conjecture implies s_{n+1} - s_n is at most a constant times s_n^epsilon for every epsilon > 0; refereed and conditional, so it answers the first question only under an unproved hypothesis.

2024_01_25_pandey: Pandey's preprint shows that for some eta > 0 every interval [X, X + X^{1/5 - eta}] contains a squarefree number for large X, lowering the Filaseta-Trifonov exponent; the first question for epsilon > 1/5 - eta.

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