Why do the digits 12, 45, and 78 form the numbers 3, 9, and 6 in this order?

AI Thread Summary
The discussion centers on the observation that the digits 12, 45, and 78 correspond to the numbers 3, 9, and 6 when summed. Participants explain that a number's divisibility by 3 is determined by the sum of its digits, which clarifies why the numbers 3, 6, and 9 do not appear frequently among prime numbers. The digital roots of prime numbers are discussed, revealing that only certain roots (1, 2, 4, 5, 7, 8) are possible, while roots 3, 6, and 9 are excluded due to their composite nature. The conversation touches on the curious relationship between the digits and their sums, leading to questions about the underlying logic. Ultimately, the discussion hints at a numerological interpretation of these patterns.
Teragabaga
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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
 
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Teragabaga said:
There is only once the number 3 and never again does it come up
( I did the same for larger primes)

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.
 
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micromass said:
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.

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
 
Teragabaga said:
Yes I understand but when using my method do the numbers 3 6 9 never show?

What is a prime number?
 
micromass said:
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.
Yes I understand, stupid from me! Thanks!
 
micromass said:
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.
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
 
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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 .
 
Bacle2 said:
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 .
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) =<br /> \begin{cases} 9 &amp; n\equiv 0 \pmod 9 \\ n \bmod 9 &amp; \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.
 
D H said:
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) =<br /> \begin{cases} 9 &amp; n\equiv 0 \pmod 9 \\ n \bmod 9 &amp; \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.

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
Teragabaga said:
1+2=3
4+5=9
7+8=15=1+5=6.

So 124578 = 396

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
Borek said:
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.

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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