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This is a treatise on Primal Numbers which results in the solution of long outstanding unsolved problems of the prime numbers. Primal numbers are Nature’s Number System defined herein and are built with a completely new set of criteria. This work builds on and greatly expands the work presented in earlier texts [1]“Calculate Primes” 2007 and [3] “Breaking RSA Codes” 2014. The original release was in a paper submitted to a mathematics journal “Principles of Prime Numbers” 2006. A new number system is developed based on prime numbers and a new visual representation is presented in the form of “Sppn and Rppn Tables”. The understanding of Prime Numbers as a complete system of mathematics continues with visualizations of the results of using the “McCanney Generator Function” which directly calculates prime numbers in groups. The base N modulo number systems (e.g. the most common of which is base 10) are shown to be inadequate to understand the true nature of Prime Numbers, which are the building blocks of all of mathematics. It will be shown that trying to understand prime numbers using base 10 has been the hinderance that has kept solutions since the ancient Greeks first formulated the first unsolved problems (many which exist yet today). The solutions to outstanding unsolved problems have mainly been because the tools were not available to understand the prime numbers as a complete number system in their own right. The research originally intended and found the basis for proofs by Induction since the tables generate future tables. The result is that the prime numbers all belong to families with ancestors and offspring. This leads to the discovery (Calculate Primes 2007) that all prime numbers have an ancestry going back to 0 and 1 and the Peano postulates. They are not simply the numbers missing from the standard multiplication tables or numbers in a sieve process of elimination. They are not derived from brute force factorization calculations (as is done in traditional computer computational mathematics) but are directly calculated in groups from previous groups of Prime Numbers. The definition that prime numbers are those numbers divisible by only themselves and 1 is shown to be lacking in scope and gives no understanding of the true nature of prime numbers or natural occurring number systems. It also leads to ambiguous concepts regarding the numbers 0 and 1.
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