12-28-2021 Justin Coslor
Base 2 Prime Connection Stacks

Think about organizing primes between powers of 2 (see Primes Between Powers of 2 by Coslor, Justin 2021) ... as a way of organizing their positions, configurations, and use. Powers of 2 are mirrored pairs of objects when the number 2 is multiplied by itself a whole number of times (see Energy Grid by Coslor, Justin 2010, but with objects that exist it is important to think in terms of Natural Numbers instead of Integers). Primes are the most finite, whole, and unique numbers of all beyond the number one, and all whole composite non-prime numbers are made of prime numbers multiplied together: comparable to a sum of ones in any whole object base. Consider composites of primes between powers of 2 and prime numbers between powers of 2. Odd numbers, even numbers, and center objects often exist between powers of 2 and often between prime numbers. Think about when there are Center Objects in base 10 arithmatic. There are only Center Objects when there is an odd number of objects. Every equidistant set of Natural Numbers is such that the sum of the two outer numbers minus the middle number equals the middle number when there is an odd number of objects in a sequence. (Philosophy Of Natural Mathematics by Coslor, Justin 2021).

I wonder how exponential powers of non-even prime bases relate to exponential powers of 2 that they are between? For example (and this is not the best example due to skipping over two of the powers of 2), the Center Object between two to the first and two to the fourth is three squared because two plus sixteen minus nine equals nine. This is similar to when two numbers added together are then divided in half to equal the center of their sum. Some Center Objects are composites of different primes. There is often more than one prime multiplied by itself recursively between two outer numbers. There is only a Natural Number Center Object when there are an odd number of objects, and that Center Object is sometimes even and is sometimes odd.

Prime Connection Stacks are whole number balance units like a placeholder system for representing the prime factors of Natural Numbers. Exponential powers of primes are Prime Connection Stacks when they are multiplied together to represent Natural Numbers. (Prime Connection Stacks by Coslor, Justin 2021; related to Prime Triangles on the numberline by Coslor, Justin 2013, related to Upper And Lower Right Angle Prime Triangles On A Numberline With Parallel Sides by Coslor, Justin 2015) 

I wonder how in the Natural Number System, a base ten non-binary whole number system of counting, how the increments of two multiplied by itself when multiplied by non-even Prime Connection Stacks relate at each of those increments? In other words how in the Natural Numbers does two to the Nth exponential power relate at each Nth step to another exponentialized number when they are all multiplied together? Prime Connection Stacks of the number two on their own are the number two multiplied by itself one or more times as in pairs of pairs of pairs of objects, etc, as in two times two times two equals eight objects. Base 5 Prime Connection stacks on their own are the number five multiplied by itself one or more times as in five fives of fives equal to one-hundred-and-twenty-five objects such as in a row or plate of rows or stack of plates of rows of five objects that together can be arranged as a larger block or other shaped volume, or when their exponents are larger the total number of objects exist as higher exponent expansions of individual objects recursively. For example, One-thousand objects equals the multiplicative product of the prime connection stack two times two times two as objects multiplied by the prime connection stack five times five times five as objects, and is visualizable in Higher Dimensional Math (see Higher Dimensional Math by Coslor, Justin 2021). My purpose in this paper is to explain these concepts in ways that are visualizable to people who do not have a lot of mathematical experience.