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So, what's to know about Prime Numbers?

*They are numbers that have 1 and the number itself as the only multiples.

          7 is a Prime Numbers because its multiples are only 1 and 7.

         So that you have 1 group of 7          *******

                                          or 7 groups of 1.     *    *    *    *    *    *    *    * 

 

         Where as with 12 you can have:

 1 group of 12     ++++++++++++

12 groups of 1   +    +     +     +     +     +     +     +     +     +     +     +

2 groups of 6   ++++++        ++++++

6 groups of 2    ++     ++     ++     ++     ++     ++

3 groups of 4    ++++     ++++     ++++     

4 groups of 3    +++     +++     +++     +++     +++

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           These are also called "factors"... 

           which are the numbers that you can

           multiply to get a certain number. 

12 = 1 x 12

12 = 12 x 1

12 = 2 x 6

12 = 6 x 2

12 = 3 x 4

12 = 4 x 3

So, 1, 2, 3, 4, 6, and 12

are all factors of 12

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* The number 1 is not a Prime Number because it only has one multiple and that multiple is 1.

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*There is an on going connection with 6 and Prime Numbers:

        - The Product (2 x 3 ) of the First two Prime Number equals 6 and

        - Every Prime Number more than 2 and 3 are multiples of 6 + or - 1

        - AND Multiplying any Prime Number 5 and above by 6 and adding that 

           product to that Prime Number and each following sum creates a

           Table that has 2 Columns of Composite Numbers that work as a

           sieve for all the Possible Prime Numbers formed by 6n + or - 1

         - 6 is also the difference between the numbers in the 2 sequences of

            Possible Prime Numbers, those being:

          5  11  17  23  29  35  41  47  53  59  65  71  77  83  89  95  103  109  115  123... and 

          7  13  19  25  31  37  43  49  55  61  67  73  79  85  91  97  105   111   117   125...

 

Prime Number Tables

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All the Prime Numbers greater than 3 up to 100 are in this list but not all the numbers are Prime Numbers. We will use Prime Number Tables to show us which numbers are Composite (non-prime) Numbers.

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Each Prime Number Table is unique. Each Table creates 2 Columns of Composite That identifies the Composite Numbers on the Potential Prime Number list. Once these are eliminated from that list, the next Prime Number Table can identify more composite numbers on the list.

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Here is a closer look at the difference between the Two Types of Prime Number Tables.

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How it works
The Prime Number Tables create a method to cross-multiply the Potential Prime Numbers and identify all the Composite Numbers. Let's look at the way it does this.
We have two sequences of Possible Prime Numbers:
(Sequence A) 6n - 1 and (Sequence B) 9n + 1. 
 
Sequence A: 5  11  17  23  29  35  41  47  53  59  65  71  77  83  89  95  101...
Sequence B: 7  13  19  25  31  37  43  49  55  61  67  73  79  85  91  97   
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So, The Prime Number Tables of 6n - 1 multiply:
         A x B in the first Column of Composite Numbers and
         A x A in the second Column of Composite Numbers
And The Prime Number Tables of 6n + 1 multiply:
        B x B in the first Column of Composite Numbers and
        B x A in the second Column of Composite Numbers
This Column can be discarded because all of its calculations are duplicates.
The Table below shows you how this works.
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