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Benedict Irwin added Prime Factors.tex
almost 10 years ago
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\section{Prime Factor Notation}
A more fundamental notation may be that of the prime factors of any number. This stems from the fact that any number which is in the state divisible by 4 must also lead to a number divisible by 2 if one is to disregard the strange non-existant numbers which appeared in the simple divisor notation. This means the states now correspond to the prime numbers $2,3,5,7,11,13...$ where one is now omitted! The states will be bosonic and follow bosonic rules, this is because numbers such as $9$ are divisible by $3$, a prime, in two ways. This then creates a number line of states in the progression \begin{equation}
1 = |0,0,0,0,0,...> \\
2 = |1,0,0,0,0,...> \\
3 = |0,1,0,0,0,...> \\
4 = |2,0,0,0,0,...> \\
5 = |0,0,1,0,0,...> \\
6 = |1,1,0,0,0,...> \\
7 = |0,0,0,1,0,...> \\
8 = |3,0,0,0,0,...> \\
9 = |0,2,0,0,0,...> \\
10= |1,0,1,0,0,...> \\
etc.
\end{equation}
