TakenItSeriously

Continuing on with the Prime Factor Harmonic Matrix. I have discovered many interesting facts and conjectures but Id like to begin with the definition.

• Prime numbers are defined as a negative or they are defined as natural numbers greater than 1 that are not divisible by any smaller whole number that is > 1.

However, as I argued in elementary school, this a negative of a definition of what something is not which makes it definitive but non-deterministic. And if youn can't look at a large odd numbr and cant just say its prime with much certainty, 

Therefore In order to define it as the positive, we need to define composite numbers, not prime numbers..

• Composite numbers are defined as natural numbers greater than 1 that are evenly divisible by a smaller prime factor such that:

1 < SPF < P²

where the SPF ≡ Smallest Prime Factor of the number.

Finally we can redifine prime numbers as:

• Prime numbers are All Natural numbers that are > 1 and are not a composite number.

Therefore we must find all composite numbers within a certain range in order to  reveal all prime numbers within that same range.

Finding composite numbers using this definition is how the Sieve of Erastithenenes works.

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