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On Fri, Aug 4, 2017 at 10:00 AM, Ian Kelly <ian.g.kelly at gmail.com> wrote: > 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. Less than (2**26)**2, I mean.

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