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Benedict Irwin edited 9090+3.tex
over 9 years ago
Commit id: fe33ec302ac2c951c68d5e31535e108cc6c5af3b
deletions | additions
diff --git a/9090+3.tex b/9090+3.tex
index f82caa2..7aec203 100644
--- a/9090+3.tex
+++ b/9090+3.tex
...
(90;;82)-1& 0 & \\
(90;;83)-1& 0 & 11×... \\
(90;;84)-1& 0 & \\
(90;;85)-1& 0 &
79×(11507479861910241657077100;;6)|1150747986191 79×[[(11507479861910241657077100;;6)|1150747986191]] \\
(90;;86)-1& 0 & 23×67×[[5899356970090260161642380980473128429001238864963718954633944900005899356970090260161642380980473128429001238864963718954633944900005899356970090260161642380980473128429]]\\
(90;;87)-1& 0 & \\
(90;;88)-1& 0 & \\
...
(90;;93)-1& 0 & 29×[[31347962382445141065830721003134796238244514106583072100313479623824451410658307210031347962382445141065830721003134796238244514106583072100313479623824451410658307210031347962382445141]]\\
(90;;94)-1& 0 & 11×[[8264462809917355371900826446280991735537190082644628099173553719008264462809917355371900826446280991735537190082644628099173553719008264462809917355371900826446280991735537190082644628099]]\\
(90;;95)-1& 0 & \\
(90;;98)-1& 0 & 79×[[(11507479861910241657077100;;7)|1150747986191]] \\
\hline
\end{array}
\end{equation}
...
\end{equation}
Rule would be \begin{equation}
p_H=3134796238244514106583072100 \\
q_H=31347962382445141 \\
\mathrm{if} \; n-9=14m\in\mathbb{Z^0} \;\; ((90;;n)-1)=29×(p_H;;m)|q_H
\end{equation}
According to "Wikipedia:Twin Prime" the largest twin prime pair found has each $200700$ digits. So we require a $(90;;100351)\pm1$ term or greater. This is still a huge task. We may be a ble to buil a similar algorithm to assess primality (or more strictly rule out non-primes). Together, the two algorithms may then sift out again more numbers, if we refine the search to twin primes, this would give some good numbers to focus on.
Building a similar table to before.
...
\end{array}
\end{equation}
\section{Analysing the 169 digit prime}
We may chop into a $11\times11$ grid \\ \\
1 1 5 0 7 4 7 9 8 6 1 9 1 \\
0 2 4 1 6 5 7 0 7 7 1 0 0 \\
1 1 5 0 7 4 7 9 8 6 1 9 1 \\
0 2 4 1 6 5 7 0 7 7 1 0 0 \\
1 1 5 0 7 4 7 9 8 6 1 9 1 \\
0 2 4 1 6 5 7 0 7 7 1 0 0 \\
1 1 5 0 7 4 7 9 8 6 1 9 1 \\
0 2 4 1 6 5 7 0 7 7 1 0 0 \\
1 1 5 0 7 4 7 9 8 6 1 9 1 \\
0 2 4 1 6 5 7 0 7 7 1 0 0 \\
1 1 5 0 7 4 7 9 8 6 1 9 1 \\
0 2 4 1 6 5 7 0 7 7 1 0 0 \\
1 1 5 0 7 4 7 9 8 6 1 9 1 \\
\\
We can now see $11$ vertical period $2$ substrings. \\
10...,12...,54...,01...,76...,77...,90...,87...,67...,11...,90...,10...