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\section{The 21 Thing}  So surely there are... many of these relationships. And as a whole they would perhaps reveal the nature of numbers...  Really we would want a way of quantifying $(d_1d_2\cdots d_N;n)$, for anything...  Just want to see if $21$ does anything interesting.  Find $(21;;n)$ primality, \begin{equation}  \begin{array}{|c|c|c|}  \hline  n & prime? & fact \\  \hline  (21;;1) & 0 & 3×7 \\  (21;;2) & 0 & 3×7×101 \\  (21;;3) & 0 & 3^2×7^2×13×37 \\  (21;;4) & 0 & 3×7×73×101×137 \\  (21;;5) & 0 & 3×7×41×271×9091 \\  (21;;6) & 0 & 3^2×7^2×13×37×101×9901 \\  (21;;7) & 0 & 3×7×239×4649×909091 \\  (21;;8) & 0 & 3×7×17×73×101×137×5882353 \\  (21;;9) & 0 & 3^3×7^2×13×19×37×52579×333667 \\  \hline  \end{array}  \end{equation}  Each sequence seems individual and fascinating. Everything seems to have a factor of $3$,$7$. However our old friends $9091$ and $9901$ appear very soon into the sequence at $n=5,6$, funnily enough begin $10,12$ divided by two, which were the $11...$ sequences positions. Also $5882353$ makes an appearence at $8$ which is $16$ by two, $16$ begin the $111...$ sequence counterpart.