## Riffs and Rotes • 59281

Re: Persiflage59281

### Numberfile • What’s Special About 59,281?

If $p$ is prime then the decimal expansion of $1/p$ repeats, so it makes sense to talk about the “average” of the digits of $1/p.$  The average can be bigger than $4.5,$ equal to $4.5,$ or less than $4.5.$  Which is most likely?  Which is least likely?  Click to find out.

$\textsc{Challenge Problem.}$  Is there any prime for which the digit average is bigger than it is for $p = 59281?$

I can’t imagine this will help with the problem, it’s just a thing I do with interesting numbers I encounter …

See Riffs and Rotes for the basic idea.

Here is the Riff for 59281

Here is the Rote for 59281

One peculiar property of this number I notice is its being “square-free all the way down”.  Once again, I have no clue whether that has anything to do with the problem at hand.

### Resources

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