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.
Showing posts with label Patterns. Show all posts
Showing posts with label Patterns. Show all posts
Wednesday, December 26, 2007
Sunday, November 18, 2007
Oh, Incidentally, Primes In Patterns!!!
1. A Prime Number is defined as any number that can only be divided evenly by itself and 1. One digit Primes are 1, 2, 3, 5, 7 since they can only be divided evenly by 1 and themselves. .
2. A Prime Number, if it is a Prime Number, has 1, 3, 7, 9 in its’ far right column. (11, 13, 17, 19) are all Primes since they can only be divided by 1 and themselves..
3. Except for single digit prime number 3 ( see 1.), if you add the digits forming a prime number ending in 1, 3, 7, 9, a prime number’s digits will never total 3 or be a multiple of 3. For instance 69 is not a Prime because its’ digits 6 and 9 total 15 which is divisible evenly by 3. ( 69, 6 + 9 = 15, 15 / 3 = 5 ).
More Confusion:
1. Not all numbers having 1, 3, 7, 9 in their far right column are Prime Numbers. ( 21, 33, 27, 39 ) are all divisible by 3 (My lazy example). The rule is divisible by any old number except 1, since 1 never changes the number it’s dividing. The total of their digits ( 3, 6, 9 12 ) are all divisible by 3 ( see 3, last section ).
2.A number which ends in 1, 3, 7, 9 and isn’t a prime, is divisible by a number ending in 1, 3, 7, or 9 in its’ first column ( 469, 469 / 7 = 67, 7909, 7909 / 11 = 719 ).
2. A Prime Number, if it is a Prime Number, has 1, 3, 7, 9 in its’ far right column. (11, 13, 17, 19) are all Primes since they can only be divided by 1 and themselves..
3. Except for single digit prime number 3 ( see 1.), if you add the digits forming a prime number ending in 1, 3, 7, 9, a prime number’s digits will never total 3 or be a multiple of 3. For instance 69 is not a Prime because its’ digits 6 and 9 total 15 which is divisible evenly by 3. ( 69, 6 + 9 = 15, 15 / 3 = 5 ).
More Confusion:
1. Not all numbers having 1, 3, 7, 9 in their far right column are Prime Numbers. ( 21, 33, 27, 39 ) are all divisible by 3 (My lazy example). The rule is divisible by any old number except 1, since 1 never changes the number it’s dividing. The total of their digits ( 3, 6, 9 12 ) are all divisible by 3 ( see 3, last section ).
2.A number which ends in 1, 3, 7, 9 and isn’t a prime, is divisible by a number ending in 1, 3, 7, or 9 in its’ first column ( 469, 469 / 7 = 67, 7909, 7909 / 11 = 719 ).
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