How I work the prime problem,and cannot complete the solution

Do the math on the indices.
Take a collection of things, and index them with integers k, counting up.
Then compute all the combinations of these things that are separable. Index these combinations with the integers j.
Now find out how the integers k and the integers j vary each time you add a new combination. As you go up, find a small error in the 'flatness' of indices i that cause them to align with indices j.  That variation in flatness, changing as you go up, are the primes. That is what Zeta function does.

I use formala that tell me how many digits, in integers, i,  I need for a new group, (n+1)*n, which is the sum of the previous set counters.  And how many integers,j, do I need to represent the size of the combination.  That is why the previous post on strong divisibility caught my eye. It uses the number of n things taken r ways, that is, taking the previous number of groups, adding another counting axis, and get the size of the  new group.

Minimum redundancy says the two integer sets will be used maximally. I can do the Shannon, which I always do, 100% of the time. So I want to make an SNR composed of the number of digits i needed and the number of digits j needed and solve for the biggest twos integer which is not reached.  Then 2^n - 1 tells me all those lower digits count out, they are used maximally.

The solution is the twos set which counts to the largest prime and carries fractions to the smallest divisibility between i and j you need.

Problem

I have to use the integer system of the previous combination to compute the SNR for the next.  Hence, I have my twos binary system built up as hierarchical powers, the one digits system using the previous as a logarithmic base.  But the powers of power should grow as a minimal spanning tree, as Dlog(D) where D is the number of digits systems.  This is where we need a Pro, someone who spends their time doing this stuff. If we solve it, it would be the miracle of the ages, a single method to compute the group boundaries available for any number of N things. It will organize our world.