mersenneforum.org Unorthodox approach to primes
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 2017-01-10, 00:17 #2 Prime95 P90 years forever!     Aug 2002 Yeehaw, FL 7,489 Posts Welcome to the forum. Glad to see you are enjoying exploring the properties of numbers. The process you describe is called "casting out nines": https://en.wikipedia.org/wiki/Casting_out_nines This is a well-known shortcut to see if a number is divisible by 3
2017-01-10, 00:51   #3
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

100000110000002 Posts

Quote:
 Originally Posted by Erkan Hello Interested, I sometimes just play with numbers, write programs in C# for tests and one day I was playing around with Numerology, not to predict anything, just to see how it behaved. Numerology has many different forms and uses. I might have been even unorthodox in that. What I did was reduce/simplify any number to a single digit, 1 to 9, by adding each digit in a number and if the result was larger then 10, repeat the process. A few examples on what I did: 23 = 2+3 = 5. 55 = 5+5 = 10 = 1+0 = 1. 287 = 2+8+7= 17 = 1+7 = 8. Next I wrote down the products of multiplication 0 to 10. And the result was quite amazing. Code: x 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 1 2 0 2 4 6 8 1 3 5 7 9 2 3 0 3 6 9 3 6 9 3 6 9 3 4 0 4 8 3 7 2 6 1 5 9 4 5 0 5 1 6 2 7 3 8 4 9 5 6 0 6 3 9 6 3 9 6 3 9 6 7 0 7 5 3 1 8 6 4 2 9 7 8 0 8 7 6 5 4 3 2 1 9 8 9 0 9 9 9 9 9 9 9 9 9 9 10 0 1 2 3 4 5 6 7 8 9 1 (sorry, I couldn't find any table insert to make it more readable) (It might become clearer by writing them down self then looking at it.) -The first thing, that caught my eye, while writing the numbers down was that the table for 8, neatly counted backwards, 8, 7, 6, 5, 4, 3, 2, 1 (8, 16, 24, 32, 40, 48, 56, 64, (72*, 80)) and that all numeroligical values for the table of 9 were all 9s. -Further I noticed that the 2 and 7 are each others opposite and the 2 returns first the even numbers then the odd numbers and the 7 returns the odd numbers first then the even numbers. 2 => 2,4,6,8,1,3,5,7 7 => 7,5,3,1,8,6,4,2 -The results of the 4 and 5 seems also to be each others opposite while jumping numbers. 4 => 4,8,3,7,2,6,1,5 5 => 5,1,6,2,7,3,8,4 -It looks as if the table flips and then can be folded onto itself at 4 and 5, but the 3 and the 6 prevent this. The 3 returns a repeating sequence of 3,6,9,3,6,9,ect, where the 6 returns 6,3,9,6,3,9,6,3,9,ect (and the 9 only 9s) Here only the 3s and 6s are flipped 6,9,3 and 3,9,6. 3 => 3,6,9,3,6,9,3,6,9,3 6 => 6,3,9,6,3,9,6,3,9,6 *I kept on playing with the numbers and found that the value of 9 and 0 in any number is the same when simplifying a number numerologicly this way: 394 = 3+9+4= 16 = 1+6 = 7 304 = 3+0+4 = 7 5979 = 5+9+7+9 = 30 = 3+0 = 3. 5079 = 5+0+7+9 = 21 = 2+1 = 3. 5070 = 5+0+7+0 = 12 = 1+2 = 3. Then I got interested in primes, as I knew we were searching for the largest prime (possible) and wondered if it could be used in anyway. And what brought me here was Tesla's map for multiplication made by Joey Grether that I stumbled upon by accident on the net. I had made something similar in the past, before I had a pc, a table with numbers and reasoned that no prime other then 2, 3, 5 and 7 would be a product in any math table. I had written down numbers and was looking for an easy way to eliminate all products and have the prime numbers remain. I wrote down horizontally all numbers starting with 0 untill I reached the end of my paper. Then a second row of numbers where below the 1 came the 10 and below the 2 came 11 as 10 = 1+0 =1 and 11 = 1+1 =2, ect. Under the 10 came the 19 and under the 11 came 20 as 1+9 = 10 = 1+0 = 1 and 20 = 2+0 = 2. (this also allowed me to create a negative field of numbers.) I took a ruler and striped away numbers that would be part of any table of x. This was a long time ago but I remember the 3, 6 and 9 were a straight vertical line. 2, 4, 8 were diagonal lines and I believe 5 and 10 were diagonal the other way. The only number that did not create a straight line but was jagged and jumping was the 7. (found it most interested) But I had my all prime numbers, I believe to up to 300. No pc or any books I had to create my own way of finding them quickly I started researching them applying numerology to see if there was any pattern. And I thought I found one, until later I wrote a program in C# and the pattern broke. (if it wasn't a bug btw) But it broke on some very special prime(-like) numbers that I sadly don't remember the name for. My program ran upto a number as large as a computer integer testing for primes numerological. But this was my finding regarding primes: If a potential prime number's numerological value is a 3, 6 or 9, it is not a prime. So a number like 23354749381, that could be a prime, if it's numerological value is not a 3, 6 or 9. 2+3+3+5+4+7+4+9+3+8+1 = 49 = 4+9 = 13 = 1+3 = 4, not a 3, 6 or 9 it could be a prime. Swapping the 9 with a 0 also returns a numerological value of 4. 678453967653679 = 6+7+8+4+5+3+9+6+7+6+5+3+6+7+9 = 91 = 9+1 = 10 = 1+0 = 1, a possible prime. Maybe it can be of any use for any real mathematicians as they can delve deeper in this. Since I am not one myself my researching capabilities are limited. But if there is something about it, I really really would love to know your findings. Hope it helps. Regards, Erkan Karaagacli
code tags or using a TeX table works as might quote tags. the sum of digits repeating until less than 10 you describe is a digit sum in base 10. if you take the remainder on division by 9 you will get the same value. for clarification there is no largest possible prime see the numberphile video:

Last fiddled with by science_man_88 on 2017-01-10 at 00:56

2017-01-10, 01:56   #4
Erkan

Jan 2017

3 Posts

@Science_man_88
Thanks for the TeX table.
I'll edit my post later if I have more time.

It looks like digit sum.

Quote:
 From Wikipedia, the free encyclopedia In mathematics, the digit sum of a given integer is the sum of all its digits (e.g. the digit sum of 84001 is calculated as 8+4+0+0+1 = 13). Digit sums are most often computed using the decimal representation of the given number, but they may be calculated in any other base. Different bases give different digit sums, with the digit sums for binary being on average smaller than those for any other base.
But I don't stop at 13.
8+4+0+0+1 = 13 = 1+3 = 4 (not 13)

@Prime95
Quote:
 I kept on playing with the numbers and found that the value of 9 and 0 in any number is the same when simplifying a number numerologicly this way: 394 = 3+9+4= 16 = 1+6 = 7 304 = 3+0+4 = 7 5979 = 5+9+7+9 = 30 = 3+0 = 3. 5079 = 5+0+7+9 = 21 = 2+1 = 3. 5070 = 5+0+7+0 = 12 = 1+2 = 3.
Would be casting out nines, where I only discovered that the 0 and 9 have the same value and can be changed in a number without changing it's 'numerological' value.
But how I use it wouldn't be true for prime numbers that end on a 9 (and would change that to a 0).

3539 is a prime number.
3530 isn't a prime number.
3539 = 3+5+3+9 = 20 = 2+0 = 2.
3530 = 3+5+3+0 = 11 = 1+1 = 2.

[in general]
It is about telling if a number is a prime number by adding all digits and continuing adding the digits of the result if the result is 10 or larger until 1 digit is left.
Hope you understand it is not about the known digit sum and casting out nines, though very similar yes.

Last fiddled with by Erkan on 2017-01-10 at 02:22

 2017-01-10, 02:22 #5 CRGreathouse     Aug 2006 135418 Posts It's the digital root, which is related but not identical to the digital sum. The digital root is just a stone's throw away from being the residue (mod 9) and has most of its properties in common with it.
2017-01-10, 02:24   #6
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by Erkan @Science_man_88 Thanks for the TeX table. I'll edit my post later if I have more time. I had never heard of digit sum, just read about it in wiki. It looks like digit sum. But I don't stop at 13. 8+4+0+0+1 = 13 = 1+3 = 4 (not 13)
it was actually the code tags I used (# symbol in the symbols shown) that's why it has the small Code: before it. the TeX table version would look something like:

$
\begin{tabular}{ l | c | r | l | c| r | l | c | r | l | c | r| l|}
x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 1 \\ \hline
2 & 0 & 2 & 4 & 6 & 8 & 1 & 3 & 5 & 7 & 9 & 2 \\ \hline
3 & 0 & 3 & 6 & 9 & 3 & 6 & 9 & 3 & 6 & 9 & 3 \\ \hline
4 & 0 & 4 & 8 & 3 & 7 & 2 & 6 & 1 & 5 & 9 & 4 \\ \hline
5 & 0 & 5 & 1 & 6 & 2 & 7 & 3 & 8 & 4 & 9 & 5 \\ \hline
6 & 0 & 6 & 3 & 9 & 6 & 3 & 9 & 6 & 3 & 9 & 6 \\ \hline
7 & 0 & 7 & 5 & 3 & 1 & 8 & 6 & 4 & 2 & 9 & 7 \\ \hline
8 & 0 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 9 & 8 \\ \hline
9 & 0 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 \\ \hline
10 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 1 \\ \hline
\end{tabular}$

Tried to add color to showcase a few other properties but didn't get it to work. Thanks to CRG for the correction to the name.

Last fiddled with by science_man_88 on 2017-01-10 at 02:29

 2017-01-10, 02:52 #7 Erkan   Jan 2017 3 Posts [on a side note and Off Topic and thanks for the table btw :) ] Something interesting happens if you add the 'digit sum' results of the products [digit sum results of the products of the multiplication tables 0 to 10] $ \begin{tabular}{ l | c | r | l | c| r | l | c | r | l | c | r| l|} x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline 1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 1 \\ \hline 2 & 0 & 2 & 4 & 6 & 8 & 1 & 3 & 5 & 7 & 9 & 2 \\ \hline 3 & 0 & 3 & 6 & 9 & 3 & 6 & 9 & 3 & 6 & 9 & 3 \\ \hline 4 & 0 & 4 & 8 & 3 & 7 & 2 & 6 & 1 & 5 & 9 & 4 \\ \hline 5 & 0 & 5 & 1 & 6 & 2 & 7 & 3 & 8 & 4 & 9 & 5 \\ \hline 6 & 0 & 6 & 3 & 9 & 6 & 3 & 9 & 6 & 3 & 9 & 6 \\ \hline 7 & 0 & 7 & 5 & 3 & 1 & 8 & 6 & 4 & 2 & 9 & 7 \\ \hline 8 & 0 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 9 & 8 \\ \hline 9 & 0 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 \\ \hline 10 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 1 \\ \hline \end{tabular}$ 1+2+3+4+5+6+7+8+9+1 = 46 = 4+6 = 10 = 1 2+4+6+8+1+3+5+7+9+2 = 47 = 4+7 = 11 = 2 3+6+9+3+6+9+3+6+9+3 = 48 = 4+8 = 12 = 3 4+8+3+7+2+6+1+5+9+4 = 49 = 4+9 = 13 = 4 (corrected this one, sorry) 5+1+6+2+7+3+8+4+9+5 = 50 = _______ = 5 6+3+9+6+3+9+6+3+9+6 = 60 = _______ = 6 7+5+3+1+8+6+4+2+9+7 = 52 = _______ = 7 8+7+6+5+4+3+2+1+9+8 = 53 = _______ = 8 9+9+9+9+9+9+9+9+9+9 = 81 = _______ = 9 1+2+3+4+5+6+7+8+9+1= 46 = 4+6 = 10 = 1+0 =1 I made some numbers bold as to hint. And with all and the above, it's all very similar but not quite. Just let what you have learned go for a minute. I added unorthodox for a reason. It's not the math you learn at school. :) (hope I didn't make any other mistakes it's late here :) ) Last fiddled with by Erkan on 2017-01-10 at 03:01
2017-01-10, 03:34   #8
CRGreathouse

Aug 2006

32×5×7×19 Posts

Quote:
 Originally Posted by Erkan And with all and the above, it's all very similar but not quite. Just let what you have learned go for a minute. I added unorthodox for a reason. It's not the math you learn at school. :)
I would have thought that digital roots would be used as an introduction to modular arithmetic in many schools...

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