Prime Numbers

[kashi]

Let me start by saying that prime numbers have absolutely no practical significance in the working of the universe to my knowledge. In a world filled with everything arbitrary (language, art, law, money etc. are all artificial human constructs), I am fascinated by the idea that prime numbers (and some other very basic mathematical concepts) aren't created by anyone or anything, they just ARE! They are the same no matter what culture, country or galaxy you are from, and no matter what number system you use (eg. binary, hexidecimal). They existed before we did. Why ARE they?

[om@umr.edu]

An interesting subject, Kashi.

More interesting is our inability to write an equation that will predict the occurrence of prime numbers.

For some unknown reason, the universe seems to follow mathematical relationships. Perhaps prime numbers are like the catastrophic, chaotic events that determined so much of the history of our universe.

With kind regards,

Oliver
http://www.umr.edu/~om

[Algenon the mouse]

Prime numbers are cool. I like square numbers as well since they only have an odd number of factors. (sort of like some people I know...) Prime numbers are extremely important when teaching about fractions, Least common multiply and Greatest common factor. If you know how to use prime factorization then you are all set.

[kashi]

Everyone here understands the significance of prime numbers in primary school mathematics, but what I'm interested in is whether they have any bearing on what goes on in the cosmos. From what I'm led to believe, the distribution of prime numbers appears to be random. Isn't that a little...ummm...strange?

[gooodcop]

HI
Numbers HAVE importance in the universe. As the person above pointed out, the universe does seem, for unknown reasons, to be centered around mathematical relationships. Very good. Our human thinking revolves around numbers, relationships between numbers, our concept of time, etc. We are founded on numbers in our thinking and logic.

The number 9, contains intelligence and Im at a loss to explain it fully.

I just finished reading the link to "cosmos: other theory" advertisement, and was sorry to see the author failed to point out, that his thinking comes from Hindu -- about God being relative to the universe and physics. Hindu believes that god IS the sun, plus all the stars, the universe we know. This would include black holes, for which we can SEE and measure the heat with aids, yet we do not generally believe in God since we cant see him. Yet, we believe in black holes? AND Hindu believes, that God lives in every living creature.... He is the HEAT or light inside us - our intelligence and emotions. When the heat goes, we go. Etc. God's half of us is the "conscience" voice we know about, but not everyone responds to it, as we have freedom of choice. We have an animal half that interferes with self gratification and lower pursuits. They also believe, that all atoms are the same substance, and that it is GOD who sets them spinning, and God can change however many neutrons and protons circle the atom to change the substance from one element to another. This jives with the fact that nuclear power on the sun, can change elements ala alchemy by the suns' sheer power. There is no conflict between the two ideas that I see, when Hindus consider God's closest representative to be our local sun. Now onto numbers.

I published myself my own, new theory copyrighted, on symmetry and the number nine. Its more than a theory, its a new science to be figured out. It has not been discovered before and I discovered it. Anyone who would like to take the idea and build upon it must mention my name as the discoverer -- Sally Counihan--. The number 9 IS symmetry, and there is an IQ pattern of logic inside the number 9's multiples and additions in terms of numerology. We've all heard the math trivia, that the 9 times table results add up in digit terms to nine ultimately. 9 x 9 is 81, or 8/1 added is 9, etc. Its only the tip of the iceberg. Here is the new:

ANY symmetrically mirrored pair of numbers boils down to nine. 221 and 122 = difference 99, which is 18 added, or 9 ultimately.... 23456 and 65432...41976, digits add up 27, 2+7 is 9....when you get the difference of the mirrored pair. When you map out the nines times table up to 100 for sake of ease, according to DIGIT plotting, you get a perfect diamond with a midpoint of reflection lying at 49.5. I call this the mirror line. If you continue to map out the 9 times table, you get a string of harlequin diamonds that morphs slightly, with an angle bitten out of the diamond on the right side. This angle at its most symmetrical, midway shape, repeated four times at right angles, is houndstooth pattern. The ancient egyptians MUST have done what I did and knew more about 9s than is preserved today.

9x table when mapped this way is symmetry, but it extends out of nines, into symmetry in general. ALL symmetrically mirrored pairs of numbers are boiled down to a perfect 9. 9 DEFINES symmetry, and that is a brandy new science people. Since when does a number define symmetry?

This is of great importance, as all life is defined by symmetry. From crystals, to plants, snowflakes, molecules and people, we are all symmetrical. We have two matching halves, or 6, etc.

The universe IS god, and god put clues there to show us that our logic, is his logic. At least, this is what I believe and I have a MENSA iq.

When you play with the nines table, other strange things occur. Here is an example: (we're using 9 table up to 100 for this case
0918273645 minus the mirroring half, 5463728190 is 4545454545. You subtracted five places of nine from the next five places of nine, and get the fifth place of 9 (45) five times like you asked. It defines itself in the answer.

You can shorten each side removing one sum of nine symmetrically, and continue, and the results are 36363636 fourth place four times, 272727 third place 3x, 1818, and 9.
When you insert the midpoint of the "mirror" from the digit plotting, 49.5, to both sides of the equation, ignoring decimals and looking at digits only, you get
091827364549.5 - 49.55463728190, you get 9182736(4499.94)362718(1). The nines table is peeking out again in the answer.

I have more examples of what looks like some kind of algabraic logic in these types of 9s tables differencing using symmetry. In all these examples, one above being all I can muster from memory, 1 always represents self (9), 0 represents how many tens places when it occurs, and the middle info in parenthesis has some kind of logic showing in it.... in the above our parenthesissed info occurs after fourth place of nine showing, and the answer is 4s and 9s in the parentheses, while the (1) occurs always where 9, or the root of the question, should be. Its a logic of some sort.

Hope some mathematician takes it and runs farther with the idea - but remember this is copyrighted and published already so we must name the discoverer.

Sally

[kashi]

You have some very interesting philosophical points.

I learnt most of those arithmetic tricks before I'd heard of your book. How can you copyright mathematical patterns that exist naturally in the universe? I don't think you can.

I challenge you, Mrs. Mensa IQ, to find numbers that behave this way in other number systems (base 9, 11 etc.). "God" didn't tell us we had to do everything in base 10 now did he/she?

[gooodcop]

Hi Kashi
Why would I think there must be other numbers that have the special quality that number nine has? And what relationship does that statement have, with claiming you already heard it? If you heard it, its so, right? So why would you send me on a goosechase to find another number, there must be TWO strange number phenomenons for some reason.....I dont get it! Just wondering, wouldnt that be like trying to find a physics rule that applies in general to everything else its not meant for? Such as, acceleration of a falling penny from 1000 feet in normal gravity, applying to water evaporation?




One copyrights the discovery of an unpublished, undocumented and thoroughly searched subject, to protect their discovery's credit, when they publish it themselves. Its how things are named, Kashi. Do you mean, we should take Sir Isaac Newton's gravity thing and say its public domain, removing him from history and credit?



I challenge you to show me what I just showed you, in print, with a date on it before this month. Seeing that you learned it all already. Cornell hasnt learned it yet, you might enlighten their mathematics department.

[kashi]

http://www.universetoday.com/forum/index.p...?showtopic=1134

[gooodcop]

And Kashi,
Thanks for sharing the comment on the philosophy I presented as being interesting; however, as I noted, it is pure Hindu philosophy and I certainly didnt invent it. If it interests you, perhaps you might delve further into it.

Sally

[Algenon the mouse]

I think that it might be easier for us to use numbers based on ten because that is the number of digits we have on our fingers. I know that music, nature, art etc. have many number bases to them. As for prime numbers...anyone know the largest prime number found yet?

[kashi]

http://www.utm.edu/research/primes/largest.html

Info about the largest known primes. It has 6320430 digits in it!!!!!

[kashi]

And here is the largest prime:

http://mersenne.org/prime6.txt

The text file is of course over 6 megabytes!!!!

[Algenon the mouse]

gads! That was cool! Now I know what to teach tomorrow for math! I plan to ask them to factor a number that is large but is a prime number to see if they can figure it out. Thanks!

[rahuldandekar]

The fact that we have ten hands is the reason that we use base ten for centuries. But that is, I think, purely a matter of luck. If we had three hands and four fingers on each, we might have used base twelve and counted in terms of four rather than five.( You can see 'five' has interesting properties, 5 x 5 = 25, 45^2 = 2025, where 20 = 4 x 5. Maybe it wouldn't have these in other systems, and then we would have wondered why the other numbers have the properties they would .)

[kashi]

I agree, the fact that we have 10 fingers is why we use base 10, but out of the thousands of cultures and civilisations on this planet (now and in the past), surely some place somewhere counts to 9 or 12 or something. It just strikes me as odd.

[damienpaul]

Actually, Kashi, i think there was an ancient culture that was based at 8, I'll see if I can find the info for you..

[Sp1ke]

Base 12 would actually be a more sensible way to count, in some ways. For example, there would be fewer remainders when you do division. The factors of 10 are only 2 and 5 whereas 12 has 2,3,4 and 6.

In the UK, pre-decimalisation, we used base 12 for currency (12 pennies in a shilling). And time and position are measured in base 60 (hours/minutes/seconds; degrees/minutes/seconds).

[kashi]

Time isn't really to base 60, because there are no 60 different symbols to represent the number values. Same with 12 for currency. That's a very good point about the number 12 though.

[Algenon the mouse]

I think that if a alien society had 12 or 9 fingers, then they would probably find it easier to base a number system based on the number of their digits. 9 has some unusually qualities to it.

[dshan]

Originally posted by kashi@Apr 23 2004, 03:34 PM
I agree, the fact that we have 10 fingers is why we use base 10, but out of the thousands of cultures and civilisations on this planet (now and in the past), surely some place somewhere counts to 9 or 12 or something. It just strikes me as odd.

Lots of different bases have been used by different civilisations throughout history, base ten is NOT universal.

Ancient Chinese and Japanese abacuses were built around the seximal system (base 6--i.e. the number of fingers on _one_ hand, plus zero). The Babylonians used base 60 (which is where our 360 degree circles, 60 second minutes and 60 minute hours originated). Some inhabitants of the tropics used base 20, being barefoot they used both fingers and toes to count!

[rahuldandekar]

Yeah but majority use base ten. And Some inhabitants of the tropics used base 20 , but the same argument aplies.
By the way, do you think 'e' is the real base to be used in nature?

[kashi]

That doesn't make sense rahuldandekar. How can you have a base that is not a whole number (regardless of what number system you are using)?

[isferno]

Of coarse, the way you count things does influence the outcome of the total.
No doubt most of you have already heard you can actualy count to 1023, using your 10 fingers only.

But more interresting, ask yourself, do the primes differ with any base you would use (base of 10, base of 60, base of 8 etc)?

example, base of 3:
(i've used the #10 instead of 3)

1 , 2 , 10 : 10 is a prime (10 eq 3)
11,12, 20 : 11/2 = 2; 12 = prime; 20/10 = 2
21,22,100 : 21 = prime; 22/2 = 11; 100/10 = 10
101, 102, 110 : 101/12 = 2; 102 = prime; 110/11 = 10
111, 112, 120
121, 122, 200
201, 202, 210
211, 212, 220
221, 222, 1000 : (1000 equals 10 * 10 * 10; or 10 cubed; or 27 on base of 10)
1001, 1002, 1010

[rahuldandekar]

The thing is, that we use whole numbers, so we neglect the countless infinite number of decimals lying in between. That we use decimals does not mean that we should undervalue the importance of the decimals.
A question : Why do we call 'e' natural base (for logarithms).

[kashi]

Originally posted by isferno@Apr 25 2004, 09:10 PM

But more interresting, ask yourself, do the primes differ with any base you would use (base of 10, base of 60, base of 8 etc)?

With respect, I think that is fairly obvious. If you take 9 bags of rice (call it 1001 bags in binary if you want...it makes no difference it's still the same number of bags), you can chop it up into a number of even groups other than 9 and 1 (i.e. 3 groups of 3...11 in binary if you like). It makes no difference what number system you use. You can still divide it up evenly. In fact it is not neccesary to count the bags at all. Think visually. Just look at x number of objects, and try to divide them up into even groups. If it's prime you won't be able to do it.

The moral of the story. We don't even need a numerical system. That's what makes primes so special. They came along before numbers did!



Rahuldandekar when you talk about base I think you mean something completely different. 'e' would still be a natural "base" for logarithms if we were using base a 9 or 12 number system, it would however have a different decimal value (note the word base has two completely different meanings in this sentence).

[Algenon the mouse]

Interesting debate. (I did mean that most civilizations use base ten btw..there is always an exception to the rule).



I still think it is possible that a different alien civilization with, lets say nine digits, could develop an entirely different number system that we have not even thought of.

[MikeJ]

Prime numbers are so .... primal, really, can't be tamed by any equation. They ride wild and free beyond the yoke of theory, and have to be tracked down one by one.

I also love the number 9. I suspect (but have been just too downright lazy to work it out) that the magic of nine is that it is (BASE - 1). Has anyone actually tried it? Does, for instance 7 work the same in base 8, as 9 does in decimal?

[isferno]

Just think of Inches, Feet and Yards and you have some idea what to expect. <_<

Not everything is based on the number of digits an alien might have.
Though calculating with every other base number will seem as easy as base 10, with as much practice as anyone have had.

One of the differences is that 1/3 is a Rational number with base 3 if written in a decimal form: 0.1 and not the Irrational number 0.33... with base 10.

[kashi]

0.33... is not an irrational number because the decimals are repeating. An irrational number is a number with decimals that do NOT repeat (eg. pi or the square root of 2).

MikeJ, I have also wondered whether it is the "Base - 1" thing that gives 9 its interesting properties. I don&#39;t have much time to nut this stuff out at the moment...perhaps there&#39;s something on the internet somewhere.

[fortyseven]

lots of interesting things with the number nine, because it&#39;s the last digit in our base 10 system. The same would occur for 7 in a base 8 system.