deletions | additions       diff --git a/Dirac notation.tex b/Dirac notation.tex  index 2b6076d..9337338 100644  --- a/Dirac notation.tex  +++ b/Dirac notation.tex 
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\end{equation}  An example being \begin{equation}  [\ketbra{3}{2}+\ketbra{5}{3}+\ketbra{7}{5}]\ket{5}=\ket{7}  \end{equation}  Which although it sounds rediculous. When interpreted as \begin{equation}  \frac{6+15+35}{5}=7  \end{equation}  It is clear there is something to this concept! However, it breaks  \begin{equation}  [\ketbra{3}{2}+\ketbra{5}{3}]\ket{3}=\ket{7} \ne \ket{5} \;...  \end{equation}  We have then \begin{equation}  \ketbra{3}{2} \ketbra{5}{3} = \ketbra{7}{3}  \end{equation}  We have not noticed the link between primes seperated by more than one!  We have the following picture in the matrices...  \begin{equation}  \begin{bmatrix}  0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix}  \begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \end{bmatrix}  =\begin{bmatrix} 0 \\ 0 \\ 1 \\ 0 \end{bmatrix} \\  \begin{bmatrix}  0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix}  \begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \end{bmatrix}  =\begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \end{bmatrix} \\  \end{equation}  The next version \begin{equation}  [\ketbra{3}{2}+\ketbra{5}{3}+\ketbra{7}{5}+\ketbra{11}{7}]\ket{7}=\ket{19}  \end{equation}  Which is also prime. But...  The next version \begin{equation}  [\ketbra{3}{2}+\ketbra{5}{3}+\ketbra{7}{5}+\ketbra{11}{7}+\ketbra{13}{11}]\ket{11}=2\otimes2\otimes2\otimes2=16  \end{equation}  \\  \\  \\  \\  In fact there should exist an algorithm to find the next prime using this method.  But not with the broken form...  \\  \\  \\  \\  However the short comings of this notation are that they do not express higher dimensional terms. How does one express a cubic array, i.e a number with three prime factors?