this is for holding javascript data
Benedict Irwin deleted file Next.tex
about 10 years ago
Commit id: 98732f92a0d6c80798ae08174f706cac7a035bba
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\section{Next}
The next picture is from the program, red lines that make it to the bottom line are prime.
The number associated with the pixels at the top is $(p+1)/2$ so the red line originating from the 3rd pixel along relates to the primality of $2$.
The data map is therefore the sum of the discreet points\begin{equation}
M=\sum_{i=0}^{\infty}\sum_{n=1}^{\infty} ( (2n-1)(i+1), i+1) =1
\end{equation}
If one were to sum across the diagonals $v=\sum M$ then for any $v_i=2$, $i$ is prime.
For a given number, to check it's primality we have \begin{equation}
N=1=M_{1 1} \\
N=2=M_{2 2} +M_{1 3} \\
N=3=M_{3 3} +M_{2 4} +M_{1 5} \\
N=N=M_{N N} +M_{N-1 N+1} +M_{N-2 N+2} + ... + M_{1 2N-1}
\end{equation}
So we create a measure $P(N)$ to collect these arguments \begin{equation}
P(N) = \sum_{i=0}^{N-1} M_{N-i N+i}
\end{equation}
We then have the knowledge that \begin{equation}
\forall N: P(N)=2, N \in \{Primes\}
\end{equation}