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}