Challenge: find the first value where two functions differ

[Ian Kelly]

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.