Prime numbers , Unified Fields

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Its explained via modular arithmetic which is a standard tool and area of research in number theory.

Generically if x = Np + q where N and p are integers then it is said that x = q mod p, ie x is q more than a multiple of p. For example 7 = 2 mod 5, since 7 = 5*1 + 2, 23 = 7 mod 16 or 23 = 7 mod 8. It easily explains things like why a number which is divisible by 3 also have the sum of its digits divisible by 3.

We use base 10, which is 1 more than a multiple of 3, ie 10 = 1 mod 3. Now consider a number with 2 digits (ie its between 10 and 99 inclusive), which we'll write as XY (for example if we consider 56 then X = 5, Y = 6 or for 93 X = 9 and Y = 3 etc). It follows that XY = 10*X + Y, so for 56 we have 56 = 5*10 = 6 etc. Now consider this in mod 3, where we have 10 = 1 mod 3. Thus we have XY = X*10 + Y = X*(3*3+1) + Y and taking this mod 3 gives XY = X*1 + Y mod 3 = X+Y mod 3. Thus the 2 digit number XY is divisible by 3 if X+Y is. This works for any number of digits because $$10^{N} = 1$$ mod 3 for all whole numbers N.

For instance, consider 5541. Is this divisible by 3? Well 5541 = 5+5+4+1 mod 3 = 15 mod 3. So 5541 is divisible by 3 if 15 is. Obviously it is but we can use the same method again to see it, ie 15 = 1+5 mod 3 = 6 mod 3 and 6 is divisible by 3, so 15 is, so 5541 is. Its clear that you can do this for any sized initial number, repeating it again and again until you get a single digit number which you can easily determine whether its a multiple of 3.

For instance, is 536392004240671 divisible by 3? We add up the digits, 5+3+6+3+9+2+0+0+4+2+4+0+6+7+1 = 52. Now add its digits up, 5+2 = 7. 7 isn't divisible by 3 and thus neither is 536392004240671. Didn't even need a calculator!

Precisely the same applies to mod 9 arithmetic. If you use hexidecimal (base 16) then it works for mod 5, mod 3 and mod 15. If you use base 12 then it works for mod 11 arithmetic.

So yeah all good Great Wizard of OZ land, but the scare crow still has no brain. If it is given in the prime number lines of the 6n form in mod 3 all prime numbers fall in the 2,8,5 or the 1,7,4 then we could order up all the numbers in the line by pairs of 5,7 and 2,4 and 1,8 . given by the mod of 3 then all multiplication of all pairs would be congruent with 8 which would fall on the 2,8,5 line . given that all sq of prime fall on the 1,7,4 line then it is easy to assume that the pairing in this method would be a pregenerator to sq. interruptions of the prime number field, falling half way between the 2 sq. of the pairing, so like if we take 11 and 13 for example and multiply we would get 143 and in the line of 1,7,4 the sq. of 11 and the sq. of 13 would fall equal distance down the line from 143 and up the line from 143 there for my pea brain can imagine the pattern of prime in a step wise fashion , like building stairs so to speak, or would this just be a fancy way of doing the sieve of Eratosthenes?
 
Multiples of 9?

Does 142, 857 perhaps register in the final theory? It is afterall the shadow of the radii
of a circul 22/7 opr 3.142 857. Because 142+857 is 999?


:p
 
Multiples of 9?

Does 142, 857 perhaps register in the final theory? It is afterall the shadow of the radii
of a circul 22/7 opr 3.142 857. Because 142+857 is 999?


:p
Interesting Green What a funny name , Onomastics is my real passion , Green Destiny, We could call you Gd. I hope your feelings would be O.K. with that. I use the color green to keep track of 2s and 6s, six being a light green for yellow is my designated color for 3s. Very Interesting in deed Gd. I don't know ? but I have noticed that 1/7 = .142857142857.................. and you all know Pythagoras thought the answer to the universe was all about 7 so I think you have stumbled on to something vital. If the wizard comes back maybe we can be enlightened Dorthy sorry I mean Gd, If I only had a brain . The circle thing hmmm spiral hummmm circle no no a web no no layers of webs getting progressively larger . Yeah that is it First a tight knit web and then one a little looser round web then a little wider webbing and the primes are the holes in the web and as you cast more webs they knock out more primes, but more primes get generated, but the webbing keeps getting further apart so they keep peaking through cracks in the web. The web is held together at resonance spots . like for example take 5 and 7 and multiply and you have 35 which is congruent to eight mod type of number and now all convergences of 5 and 7 happen at the button spots of 35+35+35+35+35 , or 35,70,105,140,175, and now you can easily see the 8 code for if 8,16,24,32,40,48, is congruent to 8,7,6,5,4,3 then 35,70,105,140........ is congruent too which looks like to me as web ties holding it all together now. A net ! Like a fish net!! yeah!! Good work, Gd you have a brain, a bunch of circular nets, that sounds right.
 
Multiples of 9?

Does 142, 857 perhaps register in the final theory? It is afterall the shadow of the radii
of a circul 22/7 opr 3.142 857. Because 142+857 is 999?


:p
Interesting Green What a funny name , Onomastics is my real passion , Green Destiny, We could call you Gd. I hope your feelings would be O.K. with that. I use the color green to keep track of 2s and 6s, six being a light green for yellow is my designated color for 3s. Very Interesting in deed Gd. I don't know ? but I have noticed that 1/7 = .142857142857.................. and you all know Pythagoras thought the answer to the universe was all about 7 so I think you have stumbled on to something vital. If the wizard comes back maybe we can be enlightened Dorthy sorry I mean Gd, If I only had a brain . The circle thing hmmm spiral hummmm circle no no a web no no layers of webs getting progressively larger . Yeah that is it First a tight knit web and then one a little looser round web then a little wider webbing and the primes are the holes in the web and as you cast more webs they knock out more primes, but more primes get generated, but the webbing keeps getting further apart so they keep peaking through cracks in the web. The web is held together at resonance spots . like for example take 5 and 7 and multiply and you have 35 which is congruent to eight mod type of number and now all convergences of 5 and 7 happen at the button spots of 35+35+35+35+35 , or 35,70,105,140,175, and now you can easily see the 8 code for if 8,16,24,32,40,48, is congruent to 8,7,6,5,4,3 then 35,70,105,140........ is congruent too which looks like to me as web ties holding it all together now. A net ! Like a fish net!! yeah!! Good work, Gd you have a brain, a bunch of circular nets, that sounds right.
 
So yeah all good Great Wizard of OZ land, but the scare crow still has no brain. If it is given in the prime number lines of the 6n form in mod 3 all prime numbers fall in the 2,8,5 or the 1,7,4 then we could order up all the numbers in the line by pairs of 5,7 and 2,4 and 1,8 . given by the mod of 3 then all multiplication of all pairs would be congruent with 8 which would fall on the 2,8,5 line . given that all sq of prime fall on the 1,7,4 line then it is easy to assume that the pairing in this method would be a pregenerator to sq. interruptions of the prime number field, falling half way between the 2 sq. of the pairing, so like if we take 11 and 13 for example and multiply we would get 143 and in the line of 1,7,4 the sq. of 11 and the sq. of 13 would fall equal distance down the line from 143 and up the line from 143 there for my pea brain can imagine the pattern of prime in a step wise fashion , like building stairs so to speak, or would this just be a fancy way of doing the sieve of Eratosthenes?
Now that we have established we are using a standard tool in number theory that is used in all fascists of life ranging from computer science , banking , chemistry to music, I am getting a sense of unification yet the dyslexic carpenter is heading to billings Montana to satisfy the new E.P.A. rules on lead abatement, I will refect on the event horizon as I approach the new charges that will be bestowed on the unsuspecting public. I would hope you all could contemplate this:
4+7=2
8+5=4
3+3=6
7+1=8
2+8=1
6+6=3
1+4=5
5+2=7
9+9=9
the 4 column is multiples of 4 and the 7 column is multiples of 7. The 2 column is multiples of 2 and 11.
Lets look at 11s for verification
11=2
22=4
33=6
44=8
55=1
66=3
77=5
88=7
99=9
 
Modular arithmetic is only one aspect of the prime number "universe".

See if you can spot a correlation between your multiples of 9 idea, and Benford's law which is about the distribution of digits in number bases > 2. Then look at the distribution of primes, which is independent of the base of numbers.

Maybe check out the zeta function and see if you can understand the Riemann hypothesis. Just a suggestion.
 
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Modular arithmetic is only one aspect of the prime number "universe".

See if you can spot a correlation between your multiples of 9 idea, and Benford's law which is about the distribution of digits in number bases > 2. Then look at the distribution of primes, which is independent of the base of numbers.

Maybe check out the zeta function and see if you can understand the Riemann hypothesis. Just a suggestion.
Trying on the zeta , just learned about it not to long ago. I have lead a sheltered life being a house builder and all. The terminology is difficult for my dyslexic mind. My incite to riot to this point in my life comes from observing 3,5,7 and it was not tell I meet a girl that had the 1,9 that it all made some kind of since. I am going to check out the Benford thing because I have received mental messages about ben for 2 years now. Even while I was driving back from billings. But the funniest thing happened . Oh congates to Me for now I am lead containment certified, but the funny thing is the text in the manual was split up into 8 modules. Yeah instead of 8 chapters. I find that odd that I first learned of modules just before leaving for Billings. I hope it gave me an Idea what modules are. What i got out of it is modules are like different chapters of the same book. The Riemann thing I just can't get my brain around what a nontrivial zero is. I do know I live in base 16 and 12 by my carpentry and I live in base 4 and 8 in music. So before I go check out old Ben boy let Me leave everyone with this which I got from the Idea " Only odd plus even will make an odd:
0+0=0=0
0+1=1=1
1+2=3=3
2+3=5=5
3+4=7=7
4+5=9=9
5+6=11=2
6+7=13=4
7+8=15=6
8+9=17=8
9+10=19=1
10+11=21=3
11+12=23=5
12+13=25=7 O.K. then the funny thing to me is taking 1 to 1 or even 3 to 3 or any interval you wish as long as you don,t leave the extra number in the middle which then in that case would be one half of the sum and moving in from equal distance simultaneously like pairing (3,3) (5,1) (7,8) (6,9) (2,4) and if you look at it the 2,4 in the first set of the patten 11 and 13 then the next set of 2,4 is 29 and 31 , but the next set of 2,4 is 47 and 49 the sq. of 7. Now something tells Me that the mirror effect of squares is related, but I haven't quite pictured the whole thing yet. O.K. off to Ben-O-Rama
 
Me-Ki-Gal, it's obvious that you enjoy noticing patterns in numbers, even if it's hard to interpret what the hell you're talking about (no offense!).

May I suggest that you ditch your obsession with the "law of 9's", as it is merely an artifact of our common base-10 usage, and look into other more universal aspects of number theory such as prime-generating Euler-Rabinowitsch polynomials or, if you're a visual guy, check out the number spiral.
 
Modular arithmetic is only one aspect of the prime number "universe".

See if you can spot a correlation between your multiples of 9 idea, and Benford's law which is about the distribution of digits in number bases > 2. Then look at the distribution of primes, which is independent of the base of numbers.

Maybe check out the zeta function and see if you can understand the Riemann hypothesis. Just a suggestion.
Benford very interesting. One thing I can say is it does not matter the base system with the 1- and the 1+ for it, as far as uniform distribution, it is all about the thickness of the product you are working with and how much you want to divide the space. So what are you using to divided the space with and how thick is it, then the 1- and the 1+ is based upon that very thickness.
 
Benford's law applies to statistically random sets of numbers. It's about the distribution of digits and doesn't apply to base2, because any number in base2 is considered to be a "random" distribution of 1 and 0, so any set of binary numbers is not Benford distributed.
 
The two magic numbers in any numerology big or small is 1/3 and 42. One third always implies the other side holds the other .66(6) so you have to derive two other measurements that allow it to follow the pigeonhole principal. One dimensionally you get three. In two dimensions, it leads to 9. So why 42? Well what's the expected number of throws to a single fair three dimensional die before two sixes show up successively? Uh... 42. Though it could be 54 which is twice the number of boxes in a 3*3*3 cube. Also the number for xenon which CERN used to produce antimatter. Oh but wait the cc/per mol for xenon is what number? 42.9?:bugeye:
 
mban1923l.jpg
 
Benford's law applies to statistically random sets of numbers. It's about the distribution of digits and doesn't apply to base2, because any number in base2 is considered to be a "random" distribution of 1 and 0, so any set of binary numbers is not Benford distributed.

O.K. consider this : is 46 52 58 64 76 82 88 94 just as random as 11 17 23 29 41 47 53 59 that is if you don't consider multiples of 2
 
Look at the first digits of each set of numbers.

You have: 4 5 5 6 7 8 8 9 and 1 1 2 2 4 4 5 5. Not very statistical so far.
 
Look at the first digits of each set of numbers.

You have: 4 5 5 6 7 8 8 9 and 1 1 2 2 4 4 5 5. Not very statistical so far.

Arfa you are a blessing. I have to say it " I like you. Now I think I get base numbering. That is a big step for Me. O.K. base six 6 is ten then 11 is 15, but 12 is 20. That jump to 20 my mind just did not want to see it even spaced from fifteen. Now I do and my statement of thickness and dividing space stands.
 
Arfa you are a blessing. I have to say it " I like you. Now I think I get base numbering. That is a big step for Me. O.K. base six 6 is ten then 11 is 15, but 12 is 20. That jump to 20 my mind just did not want to see it even spaced from fifteen. Now I do and my statement of thickness and dividing space stands.

I just wanted to comment on beery's statement on artifacts. I am an artifact by nature. My D.N.A. is from before the last mutation of my genetic line. This is true . To give you an example my great uncle Lucien was a General in the civil war and died at the truop Hurt house just before the taken of Atlanta. My 3rd Cousin who was my Grand Fathers first cousin was ambassador to japan and then top adviser to the King of Korea , His Queen was Queen Min who was said to have been raped and killed by Japaneses Ninjas in broad day light in the palace courtyard. My other 3rd cousin was one of the cooper Kings of Montana who was partners with Randolf Hearst. O.K. my First cousin who just died last year found Clovis man in New Mexico. O.K. I got one My 1st cousin Worked for Walt Disney in the beginning days and drew the first illustrations of Mikey Mouse. I have traced the mutation in the genetic line and can pinpoint what generation mutated. So maybe even a cave man can do it after all. Every one of these statements is true as blue. Except the caveman thing, now that is still to be determined. Now how old do you think I am?
 
Another observation.

2 is the only even prime, and base2 isn't a candidate for a Benford distribution of numbers (this is easy to prove).

All primes > 2 belong in another set of primes, because numbers with prime bases > 2 have Benford distributions which are statistical for one, and the distinction separates the primes into two sets (the same number as the only even prime, a kind of self referential property); all primes are like singular numbers that don't depend on the base used to represent them.

For instance, every number is represented in base2 in the computers we use, but they are transformed into base10 usually. Just some factoids to think about.
 
Another observation.

2 is the only even prime, and base2 isn't a candidate for a Benford distribution of numbers (this is easy to prove).

All primes > 2 belong in another set of primes, because numbers with prime bases > 2 have Benford distributions which are statistical for one, and the distinction separates the primes into two sets (the same number as the only even prime, a kind of self referential property); all primes are like singular numbers that don't depend on the base used to represent them.

For instance, every number is represented in base2 in the computers we use, but they are transformed into base10 usually. Just some factoids to think about.
Could you think of prime as the great originals, or parents of all other numbers by the marriage of 2 singles getting together? You are opening my mind Arf. I am still contemplating the whole Benford Law. It will take some more analysis for Me of what is being said and sorting out the fiction part of it and I don't mean you , but some of the things on the internet about it all are pretty cheesy. You are in my mind a valuable resource.
 
Could you think of prime as the great originals, or parents of all other numbers by the marriage of 2 singles getting together? You are opening my mind Arf. I am still contemplating the whole Benford Law. It will take some more analysis for Me of what is being said and sorting out the fiction part of it and I don't mean you , but some of the things on the internet about it all are pretty cheesy. You are in my mind a valuable resource.

Not to beat a dead horse, but is it common knowledge that in base 10 that 2 is related in form to 11,20,29,38,47,56,65,74,83,92,101............................
 
Not to beat a dead horse, but is it common knowledge that in base 10 that 2 is related in form to 11,20,29,38,47,56,65,74,83,92,101............................

or if you take 1,10,19,28,37.46,55,64,73,82,91,100........ and factor them out they will be identical by the law of nine, and if you look at it the factorization of 11 will always be half way between the zeros of ( like 10 and 100) but in the previous example it will fall on the half mirror image of the 56 and 65 and all this alternates in a stepwise fashion.
 
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