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\section{Continue with Primes}  The $21$ section has taught alot about sequences in general. It is no clear that because we did not add one like before, there was always the possibility that the sequence chain divided by its unit, would equal one of the $k$ constants, an integer... thus none of them would be prime. This was clear in the chain unit, $21$'s prime factorisation $3\times7$ being present in each of the factorisations.  In light of this, to generate primes we must break this symmetry of sorts with an addition or more complex change.  We could try an automaton like sequence [this has more chance of not being on OEIS already :) ], and find its prime generating properties.  Setting rules, we may start with a number, say, $93$. then we can say, $9$ now becomes $37$ and $3$ now becomes $1$, on the next iteration we say $1$ becomes, $9$, and $7$ becomes $93$.  More concisely, \begin{equation}  1\to 9 \\  9\to37 \\  3\to1 \\  7 \to 93  \end{equation}  Should be interesting. As you can see I have picked the endings such that many primes are possible. It will though grow something like exponentially.  \begin{equation}  \begin{array}{|c|c|c|c|}  \hline  iter & n & p? & fac \\  \hline  0 & 7 & 1 & 7\\  1 & 93 & 0 & 3×31\\  2 & 371 & 0 & 7×53\\  3 & 1939 & 0 & 7×277 \\  4 & 937137 & 0 & 3×19×41×401\\  5 & 371939193 & 0 & 3^2×19×2175083 \\  6 & 1939371379371 & 0 & 3^2×215485708819 \\ %but 3939371379371 is prime!  7 & 9371371939193371939 & 0 & 13×23×31342381067536361\\  8 & 3719391939371379371193937137 & 3×7×37×83047×57640398964841331823\\  \hline  \end{array}  \end{equation}  7,9,3,1,9,3,1,9,3  -,3,7,9,3,7,9,3,7  -,-,1,3,7,1,3,7,1  -,-,-,9,1,9,9,1,9  -,-,-,-,3,3,3,3,3  -,-,-,-,7,9,7,7,9  -,-,-,-,-,1,1,1,1  -,-,-,-,-,9,3,9,9  -,-,-,-,-,3,7,3,3  %1\to 9 \\  %9\to37 \\  %3\to1 \\  %7 \to 93  \\\\\\\\\\\\\\\\  When producing spaced pairs in this algorith I noticed groupings formed of $1$,$3$,$5$ etc.  the same thing happens in the prime seperations, I considered if there exists an algorithm that can be applied to $N$ base units, where the maximum transform is one unit going to $2$, such that when units are written in singly spaced ordering I.e \\  A \; B \; C \; D \; E \; F \\  GH\; I \; JK\;  The groupings form that of the primes... [Highly Unlikely]