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\section{Primality}  We can try an establish a check for primality in this more tractable notation for large numbers, take $1;n$, we can check the primality for varying $n$.  \begin{equation}  \begin{array}{|c|c|c|}  \hline  & prime & rep \\  \hline  1;1=1 & 0 & 1 \\  1;2=11 & 1 & 11 \\  1;3=111 & 0 & 3×37 \\  1;4 & 0 & 11×101 \\  1;5 & 0 & 41×271 \\  1;6 & 0 & 3×7×11×13×37 \\  1;7 & 0 & 239×4649 \\  1;8 & 0 & 11×73×101×137 \\  1;9 & 0 & 3^2×37×333667 \\  1;10 & 0 & 11×41×271×9091 \\  1;11 & 0 & 21649×513239 \\  1;12 & 0 & 3×7×11×13×37×101×9901 \\  1;13 & 0 & 53×79×265371653 \\  1;14 & 0 & 11×239×4649×909091 \\  1;15 & 0 & 3×31×37×41×271×2906161 \\  1;16 & 0 & 11×17×73×101×137×5882353 \\  \end{array}  \end{equation}  We can observe a potential pattern that evey other $1;2n\in\mathbb{Z}$ string of ones is divisible by $11$,