From: Farley Flud <ff@linux.rocks>
Subject: Re: Project Euclid Problem 26 SOLVED!!!
Newsgroups: comp.os.linux.advocacy
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Date: Sun, 10 Mar 2024 07:55:28 +0000
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On Sat, 9 Mar 2024 14:42:56 -0600, Physfitfreak wrote:

> 
> I wish there was a chart I could look up, giving denominator integers 
> (with prime factors other than 2 and 5) as its x axis and max number of 
> repeating decimals as the y axis. With x interval going to about a 
> million or even a billion.
>

Here are plots of the ranges 0-1000 and 0-10000:

https://i.postimg.cc/gkkGbtZj/prob26-1k.png

https://i.postimg.cc/0PxQCcrL/prob26-10k.png

You will need to download these images to view them in an off-line
image viewer that will allow scrolling.

The second image is 10000x1200 resolution and cannot fit within any
monitor.

There is a linear increase across the range.  This is expected
because the Euler totient, which is directly related to the
repeat length, for a prime number p = p - 1.

Thus there will never be a repeat length of greater magnitude
than the number itself.