Re: Project Euclid Problem 26 SOLVED!!!

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.