# Prime numbers strange

1. May 19, 2013

### Teragabaga

I took the prime numbers from this link:
http://nl.wikibooks.org/wiki/Wiskunde/Getallen/Lijst_priemgetallen

I did take the first three lines
I did the following with the numbers
The prime 11 = 1+1 = 2
The prime 13 = 1+3 = 4
The prime 17 = 1+7 = 8 and so on

This is the result for the three rows"
2 3 5 7 2 4 8 1 5 2 4 1 5 7 2 8 5 7 4 8 1 7 2 8 7 2 4 8 1 5 1 5 2 4 5 7 4 1 5 2 8 1 2 4 8
1 4 7 2 4 8 5 7 8 5 2 8 1 7 2 4 5 1 5 7 2 7 4 5 7 2 8 7 4 1 5 2 1 5 4 5 7 8 1 7 2 8 7 2 4
8 2 1 5 4 8 5 8 1 1 7 8 5 2 4 1 2 8 5 7 4 1 5 7 1 2 4 8 5 2 4 7 2 8 7 8 7 8 7 4 1 5 4 1 5

There is only once the number 3 and never again does it come up
( I did the same for larger primes)

The numbers 3 6 9 never show when I use this method

The numbers 124578 only show, Funny is
1+2=3 4+5=9 7+8=15=1+5=6 (396)(124578)

Kind regards Rene

2. May 19, 2013

### micromass

Staff Emeritus
A number is divisible by 3 if and only if the sum of its digits is divisible by 3. So 1431 is divisible by 3 because 1 + 4 + 3 +1 = 9 is divisible by 3. This explains your observations.

3. May 19, 2013

### Teragabaga

Yes I understand but when using my method do the numbers 3 6 9 never show?
And why only the numbers 124578 ? Wich is 12=3 45=9 78=15=6?

Thank you

4. May 19, 2013

### Staff: Mentor

What is a prime number?

5. May 19, 2013

### Teragabaga

Yes I understand, stupid from me! Thanks!

6. May 19, 2013

### Teragabaga

Hi all.

But what me makes wonder is, the numbers 3 6 9 do not appear for Obvious reasons.

Only the numbers (124578) But these numbers make up the "missing" numbers 3-6-9?
1+2=3 4+5=9 7+8=15=1+5=6 (396)(124578)

Why is this so?

Thanks, Rene

Last edited: May 19, 2013
7. May 20, 2013

### Bacle2

I'm not sure I understand your method. What do you do with, e.g., 19? 1+9=0 . What if you have larger primes , like 967. You add 9+6+7 ? Then you get 22 .

8. May 20, 2013

### D H

Staff Emeritus
19 -> 1+9=10 -> 1+0=1
967 -> 9+6+7=22 -> 2+2=4

Teragabaga is finding the digital roots of the prime numbers. The digital root of a positive integer n is 9 if n is a multiple of 9, n mod 9 otherwise:
$$\operatorname{dr}(n) = \begin{cases} 9 & n\equiv 0 \pmod 9 \\ n \bmod 9 & \text{otherwise} \end{cases}$$
The reason 9 never shows up is simple. A number with a digital root of 9 means the number is a multiple of 9. Since 9 isn't prime, all positive multiples of 9 aren't prime. Alternatively, a prime cannot have a digital root of 9.

The reason 6 never shows up is almost as simple. A number with a digital root of 6 means the number is an even multiple of 3 but not a multiple of 9. Once again, this means the number is composite (not prime) because the number is a product of two integers, both of which are greater than one. Alternatively, a prime cannot have a digital root of 6.

Finally, 3 shows up once because a number with a digital root of 3 means the number is an odd multiple of 3 but not a multiple of 9. There's only one odd multiple of 3 that is prime (3 itself), so 3 shows up exactly once.

9. May 20, 2013

### Teragabaga

I understand, the only digital roots you can find are 1 2 4 5 7 8. But the funny thing is
1+2=3
4+5=9
7+8=15=1+5=6.

So 124578 = 396

I'm just curious why this is so.

Thanks.

10. May 20, 2013

### Staff: Mentor

124578 was not a number you got, these were separate digits, which you combined into a number without any particular reason, then you applied the summation in an incomplete way (why 369 and not 3+6+9=1+8=9?). You did two random things and you expect a logical explanation to the final result. I believe this is starting to be numerology.

11. May 20, 2013

### Teragabaga

Yes just the gigits 12 45 78 but I find it strange that they form 3 9 6 in this order.