Benedict Irwin edited 9090+3.tex  over 9 years ago

Commit id: fe33ec302ac2c951c68d5e31535e108cc6c5af3b

deletions | additions      

       

(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...