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I find the \mid is a little short, so I alway use \,\big|\, instead of \mid. But I don’t know how to make a longer \nmid. \not\mid or \not | obviously doesn’t produce \nmid, so the what I did for longer \mid doesn’t work. Could you give me some ideas? Thanks!

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    This answer to a slightly different question provides a possible workaround.
    – campa
    Sep 21, 2020 at 12:12

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In the meantime I hope that you excuse me if I reply your question with these links, but I think that they help you to find half answer: Why does \big\mid not work?, \middle too big.

Here my MWE using scalerel package to have a big \nmid. Into \scaleobj{...} you can put a scale factor.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{scalerel}


\begin{document}
\[a\mathbin{\scaleobj{1}{\nmid}} b\]
\[\begin{Vmatrix}
1 & 2 & 3\\
a & b & c
\end{Vmatrix}\mathbin{\scaleobj{2}{\nmid}} \begin{Vmatrix}
7 & 2 & 1\\
a & b & c
\end{Vmatrix}\]

\end{document}

enter image description here

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