On Fri, Aug 4, 2017 at 10:03 AM, Ian Kelly <ian.g.ke...@gmail.com> wrote: > On Fri, Aug 4, 2017 at 10:00 AM, Ian Kelly <ian.g.ke...@gmail.com> wrote: >> On Fri, Aug 4, 2017 at 9:47 AM, Chris Angelico <ros...@gmail.com> wrote: >>> On Sat, Aug 5, 2017 at 1:44 AM, Chris Angelico <ros...@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.
I modified Chris's code to check every square below 2**52. 4503599761588224 is the smallest example that is at most one off from a perfect square. -- https://mail.python.org/mailman/listinfo/python-list