View Full Version : Prime Numbers

kashi

2004-Apr-19, 03:01 PM

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

2004-Apr-19, 04:55 PM

An interesting subject, Kashi. :D

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 :D

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

Algenon the mouse

2004-Apr-20, 01:04 AM

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

2004-Apr-20, 02:10 AM

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

2004-Apr-20, 05:19 AM

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

2004-Apr-20, 10:19 AM

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

2004-Apr-20, 11:28 AM

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

2004-Apr-20, 11:53 AM

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

gooodcop

2004-Apr-20, 01:53 PM

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

2004-Apr-21, 04:08 AM

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

2004-Apr-21, 12:59 PM

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

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

kashi

2004-Apr-21, 01:14 PM

And here is the largest prime:

http://mersenne.org/prime6.txt

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

Algenon the mouse

2004-Apr-22, 12:24 AM

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

2004-Apr-23, 09:34 AM

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

2004-Apr-23, 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.

damienpaul

2004-Apr-23, 09:40 PM

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

2004-Apr-23, 10:38 PM

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

2004-Apr-23, 11:42 PM

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

2004-Apr-24, 01:50 AM

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

2004-Apr-24, 09:44 AM

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

2004-Apr-24, 01:53 PM

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

2004-Apr-25, 08:25 AM

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

2004-Apr-25, 10:10 AM

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

2004-Apr-25, 12:23 PM

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

2004-Apr-25, 01:23 PM

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

2004-Apr-25, 09:28 PM

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

2004-Apr-25, 10:57 PM

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

2004-Apr-25, 11:05 PM

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

2004-Apr-26, 06:09 AM

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't have much time to nut this stuff out at the moment...perhaps there's something on the internet somewhere.

fortyseven

2004-Apr-26, 09:26 PM

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

kashi

2004-Apr-26, 11:07 PM

I challenge you to try it!

BAMBI

2004-May-07, 05:06 PM

Id find it odd if you could not do what sally did with 9 and apply something similar to any other number. After all, every number is linked in some way with any other number, allowing us to count.

Just out of interest, what are numbers? are they just symbols that represent some sort of volume or entity?

Sp1ke

2004-May-09, 12:01 AM

what are numbers?

I remember some of this from years ago. It's all a bit hazy but maybe someone else can fill in the gaps.

IIRC all counting and numbers can be derived from set theory. The empty set represents 0. The set containing the empty set represents 1. The set containing the set containing the empty set is 2 and so on. This provides a way to enumerate all the positive integers. There's an infinite number of these (called Aleph 0)

The set of real numbers (1.5, 1.7654 etc) is also infinite but a different infinite set to the integers. That's because you can match every integer to a real number but there's still a load of real numbers left over. This gives a different infinite set (Aleph 1?)

Then the set of irrational numbers like sqrt(2) gives another set of infinite numbers.

Overall numbers are just a set of labels for things. "Three" smiley faces is a label for :) :) :) . But it's handy to perform mathematical operations on the numbers, like addition, division, calculus, algebra, rather than on the things themselves. So 3+2=5 is like :) :) :) + :) :) = :) :) :) :) :) but 324*812=263088 is easier than the equivalent with smiley faces :D

StarLab

2004-May-09, 01:32 AM

Just out of interest, what are numbers? are they just symbols that represent some sort of volume or entity?

IIRC all counting and numbers can be derived from set theory. The empty set represents 0. The set containing the empty set represents 1. The set containing the set containing the empty set is 2 and so on. This provides a way to enumerate all the positive integers. There's an infinite number of these (called Aleph 0

The set of real numbers (1.5, 1.7654 etc) is also infinite but a different infinite set to the integers. That's because you can match every integer to a real number but there's still a load of real numbers left over. This gives a different infinite set (Aleph 1?)

Then the set of irrational numbers like sqrt(2) gives another set of infinite numbers.

Weird, isn't it, how the question asked here is an elementary school question, yet the answer is complex enough to learn in college! :blink:

Here's a paradox for you: is there a way to anwer the above question when a five year old asks it and still be mathematically correct in your response? Because "what are #s?" is such a simle question, and Einstein did say that an answer to such a question can be simplified for a five-year-old. So what is your answer?

kashi

2004-May-09, 10:29 AM

It's the same with pretty much everything you learn at school if you take it to another level. What is Music? Why is music? etc.

rahuldandekar

2004-May-09, 11:59 AM

what are numbers?

I don't know about scientific correctness, but everyone has his particular idea about numbers.

Numbers are supposed to be something invented by the human mind in order to keep statistical track of somethings, like sheep, babies etc. But numbers have been actually discovered, and this is suggested by their independent discovery by different civilisations. The fact that Indians and the Mayas independently discovered zero shows that they are not invented.

Numbers are an intricate property of nature. they are quantities in which things are present in nature. they are existing. They are in the laws of nature.

kashi

2004-May-09, 01:27 PM

It's an interesting discussion. I like the way this thread has evolved. Numbers can be reduced to a philosophical concept almost.

StarLab

2004-May-09, 04:00 PM

Let's keep it that way...

TheThorn

2004-May-09, 04:14 PM

Originally posted by Sp1ke@May 9 2004, 12:01 AM

what are numbers?

I remember some of this from years ago. It's all a bit hazy but maybe someone else can fill in the gaps.

IIRC all counting and numbers can be derived from set theory. The empty set represents 0. The set containing the empty set represents 1. The set containing the set containing the empty set is 2 and so on. This provides a way to enumerate all the positive integers. There's an infinite number of these (called Aleph 0)

The set of real numbers (1.5, 1.7654 etc) is also infinite but a different infinite set to the integers. That's because you can match every integer to a real number but there's still a load of real numbers left over. This gives a different infinite set (Aleph 1?)

Then the set of irrational numbers like sqrt(2) gives another set of infinite numbers.

Overall numbers are just a set of labels for things. "Three" smiley faces is a label for :) :) :) . But it's handy to perform mathematical operations on the numbers, like addition, division, calculus, algebra, rather than on the things themselves. So 3+2=5 is like :) :) :) + :) :) = :) :) :) :) :) but 324*812=263088 is easier than the equivalent with smiley faces :D

There are two types of numbers - cardinal and ordinal. Cardinal numbers are how many of something there are (there are 31 days in May). Ordinal numbers have to do with order (Mother's day is the 9th day of May).

What Sp1ke described are cardinal numbers. The cardinality of the empty set (there's no phi on this keyboard, so let's call it o for now) is 0 because there's nothing in it. The cardinality of the set that contains nothing but the empty set, {o} is 1 (there's one thing in it, the empty set). The cardinality of a set that contains the empty set plus a set that contains the empty set, {o,{o}} is 2, because there are two things in it. Note the minor correction, Sp1ke - it isn't just {{o}} - that has only one thing in it).

The cardinality of {o,{o},{o,{o}}} is three. And so on. We can use this method to construct sets with any cardinality based on nothing but the null set which is nothing <G>. Talk about pulling yourself up by your own bootstraps!

It's just a set theory way of counting, and a mathematician's way of making something as simple as countin complex enough to justify the existence of set theory. <G>.

Now, all those Alephs are another thing, but I'm out of time.

But one more comment - I vote for base 2 (binary) as the natural counting base for the whole universe. Once intelligence evolved to the point where it creates digital computational devices, mechanical, electrical, or whatever, they will naturally have to start using binary. It will be forced on them just like it was forced on us, no mater what their "natural" counting base was.

BAMBI

2004-May-09, 07:02 PM

But one more comment - I vote for base 2 (binary) as the natural counting base for the whole universe.

Interesting point TheThorn. In a way binary is very simple as it just consists of electrical current being switched on and off creating patterns of 1s and 0s which represent different characters. Without binary society would be far behind what it is today.

It’s interesting how the use of binary has made today’s computers and technology possible. In a way using binary almost seems inefficient to me, as a combination of 8, 1s and 0s are needed just to represent one character. Binary seems to have its limits, therefore I wonder what will be used in the future. Can anything else be used? It wouldn't surprise me. :) Maybe its time I invented a successor to binary.

Anyone got any tips?

StarLab

2004-May-09, 08:53 PM

I vote using the E/M spectrum as a counting base...photons have different energies, I think it's fair if smaller wavelengths (like gamma rays) mean higher numbers, larger wavelengths (like radio waves) mean low numbers. After all, binary is computer language, and each 0 and 1 is dependent on photon-electron interactions. B)

Sp1ke

2004-May-10, 10:21 AM

Rather than binary, how about using fuzzy counting? Instead of a switch being on or off, it can have any state between 0 and 1. So 0.5 means its half on and half off; 0.95 means it's almost totally on.

This is harder to implement but it more accurately captures reality. In real life, nothing is ever black and white, all or nothing, true or false. In real life, things are usually within a range - so someone is fairly tall or quite old, not "tall" or "old" in an absolute sense. By forcing all our data into 1s or 0s, you run the risk of, for example, classifying someone as "old" or "not old" and ignore the grey :) area in between when they're quite old but not as old as someone else...

The big problem with binary maths is that it encourages the viewpoint that "I'm right therefore you're wrong", rather than "I'm fairly sure I'm right but that doesn't stop you having a valid viewpoint too, even if it doesn't entirely fit in with my views".

[More philosophy than maths? :unsure: :) ]

GOURDHEAD

2004-May-10, 12:15 PM

Rather than binary, how about using fuzzy counting? Instead of a switch being on or off, it can have any state between 0 and 1. So 0.5 means its half on and half off; 0.95 means it's almost totally on.

We, especially I, already indulge in way too much fuzzy thinking. Let's not encourage this with deliberate fuzzy logic much deliberate fuzzy counting.

I strongly agree with what I perceive your intent to be. We should avoid hyper-infatuation with our own ideas and avoid rejecting out of hand the ideas of others.

kashi

2004-May-10, 12:23 PM

If you like "fuzzy thinking" then you should work with probability and quantum mechanics.

TheThorn

2004-May-10, 04:45 PM

Originally posted by Sp1ke@May 10 2004, 10:21 AM

Rather than binary, how about using fuzzy counting? Instead of a switch being on or off, it can have any state between 0 and 1. So 0.5 means its half on and half off; 0.95 means it's almost totally on.

Analog computers, which came before digital computers, did exactly this. A lot of analog instrumentation still does. Analog to digital conversion is all over the place, (your digital tire gauge for instance) as is digital to analog (in your CD player, for instance).

But we switched from analog to digital for very very good reasons, and I expect that every other intelligence in the universe will follow the same path, because those reasons were universal - they had nothing to do with our situation on this planet.

Even if binary wasn't forced on us by electronics, it makes sense as the base for communications with alien intelligence because it stands out of the crowd as the lowest possible base for a number system.

vertion

2004-Oct-18, 09:27 PM

Originally posted by om@umr.edu@Apr 19 2004, 04:55 PM

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.

Yea right, there is a very linear pattern to prime numbers. You guys are just being so 'negative'. 2 and 3 are the parents of all prime numbers. In a VERY linear way.

Any questions? Email me.... popenergy@aol.com

gavwvin

2004-Oct-19, 09:12 AM

People have gone mad trying to find a formula to link prime numbers- it still eludes us. The only way of finding one is to divide by every integer lower than the square root of it.

ferg.c.

2004-Oct-19, 09:24 AM

There is money to be made in prime numbers!

See the goldberg conjecture!

Google it I don't know if there's a web sit just for this but if you can prove it there's a whole load of cash waiting for you!

I think it runs like this but I'm not sure.

Any prime number is the sum of an other two prime numbers.

Have fun!

Ferg. :)

TheThorn

2004-Oct-19, 01:13 PM

It's Goldbach's conjecture.

It says that any even number greater than 2 is the sum of two primes.

At one point, Faber and Faber (the publishers), as a publicity stunt for a book, offered a $1,000,000 prize for anyone who could prove it, but it had to be claimed before April 2002, and no one did.

Unless someone has recently offered a new prize, I don't think you're going to get rich working on Goldbach's conjecture.

antoniseb

2004-Oct-19, 01:23 PM

Originally posted by ferg.c.@Oct 19 2004, 09:24 AM

Any prime number is the sum of an other two prime numbers.

Hmm, which two primes can be added together to make eleven?

big_j_1019

2004-Oct-19, 03:31 PM

Originally posted by kashi@Apr 21 2004, 01:14 PM

And here is the largest prime:

http://mersenne.org/prime6.txt

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

Please I learned how to calculate that number in preschool.....(lol...yea right :lol: )

vertion

2004-Oct-19, 09:26 PM

Originally posted by gavwvin@Oct 19 2004, 09:12 AM

People have gone mad trying to find a formula to link prime numbers- it still eludes us. The only way of finding one is to divide by every integer lower than the square root of it.

I have found a way to link the primes just sitting there looking at Eratosthenes's Sieve. But I didn't know I was looking at Eratosthenes's Sieve at the time... I was staring at a calendar when I figured it out. 2 and 3 are the parents of all prime numbers...they 'produce' the center of all prime numbers. When you make this transform...all intervals become linear. I am working on the formula now...the distribution is not at all random, just the interference(intervals) and incrementing intervals work together.

gavwvin

2004-Oct-19, 09:33 PM

Sounds interesting, vertion- I'd like to know if you make any progress. But don't go mad over it!

Going back to ferg.c's comment- Goldbach's conjecture (any even number is the sum of two primes) intrigued me. I've quickly put together a page that checks this conjecture for all even numbers in a given range. It outputs every even number between the two you specify and two primes that add up to it. If you get a red message that means you've disproved Goldbach's conjecture (assuming the page works perfectly!) try it out:

http://www.astronomyforbeginners.com/testi...tart=4&end=1000 (http://www.astronomyforbeginners.com/testing/prime.php?start=4&end=1000)

Change the start= and end= numbers to change the range it checks they must be positive even integers greater than 2 (it only seems to be able to handle about 3,000 at a time).

Let me know if you find an exception!

vertion

2004-Oct-20, 01:35 AM

I would like to report that in addition to a linear pattern, I have found a fractal (subdivisional) pattern in the nature of prime numbers.

gavwvin

2004-Oct-20, 10:03 AM

I had the very same thought, that fractals may have something to do with it. Not an idea that I have developed though.

Could you explain a little more about how the intervals become linear? This has got me interested now.

wstevenbrown

2004-Oct-20, 03:35 PM

Guys, there is an explicit formula for the nth prime number; however, it isn't a polynomial, and it uses number-theoretic functions that aren't on ordinary calculators. I just looked at wolfram.com , a really good math infosite, and didn't find it My vague memory is that the refereed article was acknowledged to be correct, but was disallowed as a solution of the related Hilbert problem. Wish I could be more helpful, S. :(

vertion

2004-Oct-20, 07:24 PM

Originally posted by gavwvin@Oct 20 2004, 10:03 AM

I had the very same thought, that fractals may have something to do with it. Not an idea that I have developed though.

Could you explain a little more about how the intervals become linear? This has got me interested now.

I would love to explain it, just give me a couple days first to see if I can develop a subdivisional algorithm to generate the requirement for the EFF prime challenge. If I can't do it, I'll cough it up right away. If anyone has formulas or methods pertaining to locating a primes in a quick manner that might help my thinking... like a billion digits in size.. please let me know(it would probably need to be subdivisional).

gavwvin

2004-Oct-20, 08:05 PM

I looked up wolfram as wstevenbrown said and heres an article about known prime number formulae:

http://mathworld.wolfram.com/PrimeFormulas.html

You might find it helpful

vertion

2004-Oct-20, 08:37 PM

Thank you :) It's interesting, and a bit deviating from what I have found.

wstevenbrown

2004-Oct-24, 08:22 PM

The formula I found yaears ago in some moldy old journal at UVa library was not a useful one. It was amishmash of recursion, invoking totient functions, Legendre symbols and so forth. The upshot of it was that while it did demonstrably deliver every prime in sequence, it was more computation-intensive than the Sieve of Eratosthenes by a geometrically increasing factor. Sorry for the distraction-- Steve

vertion

2004-Oct-25, 05:01 AM

Interesting... although I'm trying to create mine so that the calculations do not move up exponentially each recursion... any hint as to where to find the algorithm? (Which journal, etc...)

wstevenbrown

2004-Oct-27, 12:59 AM

An arxiv search did not find the original article, but the new & improved version. Look at http://arxiv.org/math/papers/0406/0406001.pdf .This is a paper by a chap named Sebastian Martin Ruiz, and very representative of the type of paper I was remembering. I also checked the guy's reference list. Do you really want to know about Smarandache functions or fuzzy logic as applied to semigroups? I didn't. Best of luck--Steve

vertion

2004-Oct-29, 06:20 PM

Originally posted by vertion@Oct 20 2004, 01:35 AM

I would like to report that in addition to a linear pattern, I have found a fractal (subdivisional) pattern in the nature of prime numbers.

Doh! The fractal pattern is self referential! I have found that any pattern I have looked using the function still requires a collection of iterations to find primes, just like looking for primes the ordinary way--but on a higher level. *Brain ache*

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