Benedict Irwin edited Introduction.tex  over 9 years ago

Commit id: 9fe683d0286ccafb12b4e52f20fb897255ec0ee7

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\hline  m & N & T(N) & T^2(N) & T^3(N) & T^4(N) & T^5(N) & T^6(N) & T^7(N) & T^8(N) & T^9(N) & T^{10}(N) & T^{11}(N) & T^{12}(N) & T^{13}(N) & T^{14}(N) & T^{15}(N) & T^{16}(N) & T^{17}(N)\\  \hline  0 \infty  & 1 & 1 \\ 0 & 2 & 2 \\  0 & 3 & 3 \\  2 & 4 & 2|2 & 2|11 & 211\\ 

\end{array}  \end{equation}  Where $m$ is the number of transforms needed for the new number to be prime.  It can be seen that some numbers lead to previous numbers and therefore arrive at the same prime number to terminate the sequence. The steps till the resulting number is prime has the sequence $A(n)$=0,0,0,2,0,1,0,13,2,4,0,1,0,5,4,4,0,1,0,15,1,1,0,2,3,4,4,1,0,2,0,2,1,16,3,2,0,2,1,9,0,2,0,9,6,1,0,0,-,2,1,1,0,1,2,3,2,1,0,2,... as the prime numbers require $0$ transforms to be prime.  We could call this measure $A(n)$ the anti-primality of $n$, although, at the moment just because all prime numbers express anti-primality of $0$. But does the index even mean anything like this...