Prime Numbers

[TriLogic]

Can you elaborate on this just a little more? I am not sure I understand the phrase "digital root".

I am checking odd numbers ending with 1, 3, 7, and 9. I am using a loop division to check each number in steps of 2.

The problem with checking numbers with terminating digits of 1,3,7 and 9 is that they will include multiples of 3 such as 9,(15),21, 27, 33, 39,...,just keep adding 6 to these numbers and the pattern repeats.(includes terminating digit 5) as 1,7,3,9,5,1,7,3,9,5,...,None of these numbers in this sequence towards infinity are prime.

Calculating Digital Roots is a method of summing individual digits of any number to a single digit number between 1 and 9.

http://en.wikipedia.org/wiki/Digital_root.

9 = 9
21 = 2 + 1 = 3
27 = 2 + 7 = 9
33 = 3 + 3 = 6
39 = 3 + 9 = 12 = 1 + 2 = 3

31 = 3 + 1 = 4
37 = 3 + 7 = 10 = 1
43 = 4 + 3 = 7



Any numbers with Digital Root of 3, 6 or 9 will not be a prime number. So calculating digital roots is useful method of 'rooting out' odd numbers which terminate with 1,3,7,9, that have digital roots of 1,4,7 and 2,5,8 but not 3,6 or 9.

ODD Numbers with digital roots 1,4,7 are found in sequence 1 + 6 = 7 + 6 = 13 + 6 = 19 + 6 = 25 + 6 = 31You can add 12 to terminating digit 9 to eliminate 5's

So 6n + 1 = digital root of 1, 4 or 7
And 6n - 1 = digital root of 2, 5, or 8.

The results of these calculations will give either Prime Number or a prime > 3 multiplied by a prime/primes > 3. This is significant because all other prime factors for all other numbers are based on 2^n and/or 3^n

Primes emerge within two streams: One emerging from the number 1 + multiples of 6 towards infinity. And the other stream emerging from the number 5 + multiples of 6 towards infinity.

The odd numbers to check are within:

1, 7, 13, 19, (25), 31,...stream containing digital roots 1, 4, or 7

or

5, 11, 17, 23, 29, (35), 41....,stream containing digital roots 2, 5 or 8

Sorry if this sounds too confusing to be of any use