## The Internal Structure of Natural Numbers and the Sets of Odd Numbers that Are not Primes and Even Numbers that Are not Powers of Two.

**Authors:** Emmanuil Manousos

Natural numbers have a strictly defined internal structure that is being revealed in the present article. This structure is inherent of the natural numbers and is not derived through the introduction of any axioms for the set of natural numbers. In the present article, we prove the fundamental theorems that determine this structure. As a consequence of this structure, a mathematical expression for the set of odd numbers that are not primes is derived. Given the set of odd numbers, we can identify the set of prime numbers. Additionally, a new method for expressing odd composite numbers as the product of powers of prime numbers is derived.

**Comments:** 29 Pages.

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### Submission history

[v1] 2017-07-20 13:09:45

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