Center wide longtable (not tabular or tabularx)

The key is to suitably set the lengths \LTleft and \LTright that longtable uses for the horizontal placement of the table.

\documentclass[a4paper]{article}
\usepackage{longtable}
\usepackage{lipsum}
\begin{document}
\lipsum[2]
\begingroup
\setlength{\LTleft}{-20cm plus -1fill}
\setlength{\LTright}{\LTleft}
\begin{longtable}{|*{13}{p{1cm}}|}
01 & 02 & 03 & 04 & 05 & 06 & 07 & 08 & 09 & 10 & 11 & 12 & 13 \\
01 & 02 & 03 & 04 & 05 & 06 & 07 & 08 & 09 & 10 & 11 & 12 & 13 \\
01 & 02 & 03 & 04 & 05 & 06 & 07 & 08 & 09 & 10 & 11 & 12 & 13 \\
01 & 02 & 03 & 04 & 05 & 06 & 07 & 08 & 09 & 10 & 11 & 12 & 13 \\
\end{longtable}
\endgroup
\lipsum[2]
\end{document}