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On Fri, Aug 4, 2017 at 9:47 AM, Chris Angelico <rosuav at gmail.com> wrote: > On Sat, Aug 5, 2017 at 1:44 AM, Chris Angelico <rosuav at gmail.com> wrote: >> That gave me this result almost instantaneously: >> >> 4503599761588224 >> >> which has been rounded up instead of down. I don't know if that counts >> as sufficiently wrong? > > Oh, and I forgot to say: I have no actual *proof* that this is the > lowest number for which this will occur. It does not occur with > 4503599761588223 (the next lower integer), but could happen with > something between two squares, for all I know. However, I suspect that > it wouldn't. Your example demonstrates that the "2**53 < M" assumption was wrong, which is interesting. It may be worth checking values less than 2**26 as well.

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