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Prime numbers strange

  1. May 19, 2013 #1
    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)

    Can you please explain this?

    Kind regards Rene
     
  2. jcsd
  3. May 19, 2013 #2
    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.
     
  4. May 19, 2013 #3
    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
     
  5. May 19, 2013 #4

    Borek

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    Staff: Mentor

    What is a prime number?
     
  6. May 19, 2013 #5
    Yes I understand, stupid from me! Thanks!
     
  7. May 19, 2013 #6
    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
  8. May 20, 2013 #7

    Bacle2

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    Science Advisor

    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 .
     
  9. May 20, 2013 #8

    D H

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    Staff Emeritus
    Science Advisor

    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:
    [tex]\operatorname{dr}(n) =
    \begin{cases} 9 & n\equiv 0 \pmod 9 \\ n \bmod 9 & \text{otherwise} \end{cases}[/tex]
    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.
     
  10. May 20, 2013 #9
    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.
     
  11. May 20, 2013 #10

    Borek

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    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.
     
  12. May 20, 2013 #11
    Yes just the gigits 12 45 78 but I find it strange that they form 3 9 6 in this order.
    I don't know about numerology.

    Thanks.
     
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