- This is a paper on Prime Numbers and in this paper :
- we shall be taking a look at the interaction between [ prime-numbers ] and [ composite-numbers ] ;
in order to properly interpret the issues affecting :

- the structural integrity within each [ Prime Number System ] .

- we shall be taking a look at the interaction between [ prime-numbers ] and [ composite-numbers ] ;

- CONCEPT ONE :
- [ 1543 ] is a [ prime number ] and [ natural numbers ] up to [ 1543 ] are made-up-of :
- Item 1 --- the number [ 1 ] ,
- Item 2 --- the prime-numbers from [ 2 ] thru [ 1543 ] ,
- Item 3 --- the composite-numbers in-between [ 2 ] and [ 1543 ] .

And the 3 items must necessarily add up to [ 1543 ] and :

- Structural Integrity can only be maintained when this happens .

- [ 1543 ] is a [ prime number ] and [ natural numbers ] up to [ 1543 ] are made-up-of :
- CONCEPT TWO :
- Since Item 1 above is constant ,
- [ prime numbers ] and [ composite numbers ] may be regarded as complimentary towards one-another ,
- within the context of Structural Integrity of any one Prime Number System .

And that-is-to-say :

- anything that affects the [ distribution of prime numbers ] will also affect the [ distribution of composite numbers ] ,
- and vice versa .

Consequently , [ prime numbers ] and [ composite numbers ] must mesh-in simlessly within the [ Prime Number System ] ;

- othewise hovac will occur .

- [ prime numbers ] and [ composite numbers ] may be regarded as complimentary towards one-another ,

We shall be looking at both [ prime numbers ] and [ composite numbers ] in this paper .

- Since Item 1 above is constant ,

- Our paper here shall then consist of the 6 papers as follows :

1st paper | * * |
On Prime Number Systems and Core Structural Pattern Propagations |
---|---|---|

2nd paper | * * |
On Counting Natural Numbers up to [ N = 1543 ] |

3rd paper | * * |
On Counting [ Candidates-for-Primes modulo 30 ] up to [ N =1543 ] |

4th paper | * * |
On Unique-Factorization Combinatorics via the Pascal Triangle |

5th paper | * * |
On the Match-up of Structual Patterns within Prime Number Systems |

6th paper | * * |
On Unique-Factorization Equations within Prime Number Systems |

********** | * | ******************************************************** |

After Thoughts on the Six (6) Paper | |
---|---|

Section AT-1 | The { Frequency of Prime Numbers } in general |

Section AT-2 | The { Frequency-of-Primes } for [ Modulo M ] |

Section AT-3 | Deriving the Formula for the { Candidates-for-Primes } |

Section AT-4 | A Second Look at the { Frequency-of-Primes } |

Section AT-5 | Concluding Remarks |

********** | ********************************* |