## Wednesday, December 26, 2007

### Prime Number Pattern

A Prime Number is a number that is defined as only being divisible by itself and 1. On the surface it would seem that this simple definition should produce a simple, predictable pattern for Prime Numbers but it doesn’t happen. It doesn’t happen because this simple definition is subject to about 4 rules that complicate the location of a Prime Number.

Here are the rules:

1. Numbers that are evenly divisible by 2 aren’t Prime Numbers. These numbers end in 0, 2, 4, 6, 8 in the far right column.

2. Numbers that are evenly divisible by 5 aren’t Prime Numbers. These numbers end in 5 and 0 in the far right column. (25, 40)

3. Numbers ending in 1, 3, 7, 9 may or may not be Prime Numbers. (11, 13, 17, 19) are Prime Numbers since they are only divisible by themselves and 1. (21, 33, 27, 99) are not Prime Numbers because they are divisible by some number having 1, 3, 7, 9 in the far right column

4. Except for the single digit Prime Number 3, any number whose digits total 3 or a multiple of 3 and has 1, 3, 7, 9 in the far right column isn’t a Prime Number ( 69, 6 + 9 = 15, 15 / 3 = 5 ) isn’t a Prime Number

If only the first two rules existed then Prime Numbers always ending in 1, 3, 7, 9 would be evenly distributed. Unfortunately, some numbers ending in 1, 3, 7, 9, in the far right column can be evenly divisible by some other numbers ending in 1, 3, 7, 9. In addition, except for the single digit Prime Number 3, any number having 1, 3, 7, 9 in the far right column and whose digits total 3 or a multiple of 3 isn’t a Prime Number. The 3rd rule is bad enough but the 4th rule really scrambles the Prime Number Pattern.