I wonder if the following method of arithmetic entropy encoding could work for lossless compression of a binary signal:
For some 24 bit signal: $Sn = \begin{pmatrix}x_{1}\\x_{2}\\ \vdots \\x_{24}\end{pmatrix}\in \{ 0,1\}^{24} $
I'm looking for any sum of primorials $S_{p\#}=\sum_{n\in \mathbb{P}}{p_{n}\#}$, where any primorial $p_{n\#}$ is allowed to appear several times but with the smallest product: $\prod_{n\in\mathbb{P}}p_{n}$, and
such that $S:=\begin{pmatrix}1\\11\\13\\17\\19\\23\\29\\31\\37\\41\\43\\47\end{pmatrix}$, and $S_{A}:=\begin{pmatrix}-1\\1\end{pmatrix}\otimes S +\begin{pmatrix}S_{p\#}+210\\S_{p\#}+210\\S_{p\#}+210\\ \vdots\\S_{p\#}+210\end{pmatrix}_{24}$
For which the indicator function: $\mathbf{1}_{A}:S_{A}\to \{0,1\}^{24}$, defined for $S_{A}:=\begin{pmatrix}s_1\\s_2\\s_3\\\vdots\\s_{24}\end{pmatrix} as$ $\mathbf{1}_{A}(s_{i}):=\biggl\{\begin{matrix}1 \quad if s_{i}\in\mathbb{P}\\0\quad if s_{i}\notin\mathbb{P}\end{matrix}$
To be an efficient compression of the 24 bit signal the used primorials $p_{n\#}$ must fulfill: $\prod_{n\in\mathbb{P}}p_{n}\leq 2^{24}$, while it can be relaxed a little bit by using the optimization rule, that if the largest primorial is used more often than 1 time, it's prime number is used only one time as a factor and for each additional time the prime number $2$ is used as a factor instead and further rules for the prime factors $3,5$ and $7$ can be standardized.
What I would like to know specifically is if there exists any special sequence like used for $S:=\begin{pmatrix}1\\11\\13\\17\\19\\23\\29\\31\\37\\41\\43\\47\end{pmatrix}$,
that would in general more likely match to any arbitrary 24 bit signal.