Is Two a Pseudo Prime?

Originally posted by nablator
I agree but did you read the rest of my post ? 17 is also unique for the same reason. Or 113. It's a general property of all primes, that no other prime is a multiple of them. Nothing special with 2 or 3. It is not an exception it is a rule. By definition all primes share this property.

I understand what you're saying but I think you're missing my point.

Out of ALL the primes .... billions and trillions and gazillions ... on to infinity (and beyond ! ), NO OTHER PRIME has the property of EVENESS. So if there is some deep underlying and hidden universal "prime making machine" that spits out an infinity of ODD primes, where does 2 fit into this scheme ?
Could it be that even though 2 apparently has all the necessary prime properties, that it's simply "masquerading" as a prime ?

After all, if 1 could be considered for millenia by mathematicians to be a genuine member of the prime family and only recently stripped of it's "primehood", who's to say that 2 should be GUARANTEED prime status ?

It's a matter of definition. It doesn't matter much what the definitions are. You can't change them anyway. Two is certainly prime, no doubt about it. And it is definitely not special. I don't think you are getting my point that out of all primes, an infinity of them, there is only ONE that has the sublime and unique property of SEVENTEEN-ness (being a multiple of 17).

If we can't agree on that, well, maybe you'll understand later. I started out just like you, covering sheets of papers with numbers and looking for patterns 30 years ago. Intuition is very important in maths, but you have to write things down as a math lemma or theorem, then prove them. That's what doing math is about. It's not about changing definitions when you don't like them.

OK let's start a math politics forum. I don't like negative integers, it's unfair to discriminate against HALF of the integer population. Let's start a protest, and demand the suppression of the minus sign.

BTW the "unique" property of 24, as I said in the other thread, is a consequence of 24 = 4x6. That's why there's 2x4 special "rays". As 6 is 2x3, you are obsessed by the idea that 2 and 3 are somehow special. They aren't.

Originally posted by tauristercus
6 + 5 = 11 PRIME ....... and on to infinity (and beyond !

)

This is more interesting, an unsolved problem :
Golbach's conjecture

[edit on 2009-9-30 by nablator]

Originally posted by ipsedixit
Edit: I'm reading tauristercus's thread on the primes and am informed that one is not considered to be a prime because mathematicians decided that primes must be evenly divisible, uniquely, by both themselves and one. One, surely the cleverest number in the whole number system, flouts that rule by leaving out one step. On that ground, and that ground alone (until I am informed otherwise), it is not considered to be a prime.

Number 1 used to be considered prime, until the Fundamental Theorem of Arithmetic came into very, very rigorous scrutiny. Then, an adjustment in definition was made regarding the primes: If you give a mathematician numbers from 1 to 100 and ask him to pick up only those numbers which have only two factors p and q, where p is a smaller number then q, then the number cruncher picks all primes from 1 to 100 including 2 but excluding 1.

tauristercus, why don't you include numbers 2 and 3 as primes in your first diagram? I read that far and came to a screeching halt.

LOL. Not all odd numbers are primes, as not all folks who talk about primes are mathematicians.


[edit on 9/30/2009 by stander]

4, 6, 8, 10, ... are multiples of 2 and sometimes 3
6, 9, 12, 15,... are multiples of 3 and sometimes 2 and 5

Noting special about 2. Even and odd are just definitions.

If you include 1 as a prime number, it screws up the Fundamental Theorem of Arithmetic.

Why? 2 = 1 x 2 = 1 ^ 2 x 2 = 1 ^ 3 x 2 and so on.

1 is an identity.

reply to post by ipsedixit

But here's the kicker. The only way they can do that is if one prime, two, does fifty percent of the work.

Here's a kicker: there is no "percentages" of the numbers of multiplies of some integers. All are countable, i.e. they are of equal number of numbers in sets. Infinities are weird.

Originally posted by Deaf Alien
Here's a kicker: there is no "percentages" of the numbers of multiplies of some integers. All are countable, i.e. they are of equal number of numbers in sets. Infinities are weird.

Are you saying because you can take each of those, put them in a set (say of multiples of primes, 3, 2, etc.) and number them in correspondence with the natural integers, 1, 2, 3, etc. That is a particular type of infinity called "countably infinite". Those sets have cardinality Aleph-0.

ps: 1-2, 2-3, 3-5, 4-7, 5-11...
x3: 1-3, 2-6, 3-9, 4-12, 5-15...
x2: 1-2, 2-4, 3-6, 4-8, 5-10...
etc, etc, etc...

(I'll just go back to hocking metaphysical loogies )

reply to post by Deaf Alien

Mathematics might be a pseudo science or maybe an art form.

People change the rules and add new mathematical conceptions to enable them to reach satisfactory solutions to different sorts of problems. Even whimsical names for mathematical conceptions start appearing a la the "charming" and "cute" quarks of physics, "imaginary" numbers for example.

People define new kinds of space and new kinds of logic and then see where the new rules take them.

Infinities are wierd.



[edit on 30-9-2009 by ipsedixit]

reply to post by Phage


Good point Phage, but tristate quantum primes do need + or -

Primes are essential to;
Vedic Maths
Ternary
Fibonucci;
Pi, phi, fi*

No primes - No harmonics

Crack the recursive primes and you have fi*

HADES

reply to post by ipsedixit


The number 2 can also be considered as an inverse variable which explains why it "adds up" to the missing 50% if multiplying primes alone are equal to an odd number.

James Clarke Maxwell would have loved this, Einstein hated it, Tesla understood.

HADES

reply to post by zerotensor


Nice work Zerotensor (ZPE nicknme??),

S&F

Is it just me or does that binary representation look like a fractal? Can you post a 3d version, I suspect that it might surprise a few people because to draw a 3d version (visualising as I go) when using 1, 2, and 3 (the first 3 primes)

And just for a laugh through throw fi* into the picture, I think it may twist a few heads if not produce and illusion.

"I ride my horse, that horse is my mind"

HADES

Originally posted by Deaf Alien

If you include 1 as a prime number, it screws up the Fundamental Theorem of Arithmetic.

Why? 2 = 1 x 2 = 1 ^ 2 x 2 = 1 ^ 3 x 2 and so on.

1 is an identity.

LOL. You can take a shot at some of 18th century math, coz it's not that abstract issue.

So we have this Fundamental Theorem of Arithmetic.

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of one or more primes

Pay attention to the word "product." LOL

And so we do some numerical testing to see if that theorem isn't some BS:

Number 6 has two prime factors: 2 and 3
How come?
That's because 6 = 2 x 3.

Number 15 has two prime factors: 3 and 5
How come?
That's because 15 = 3 x 5.

Number 30 has three prime factors: 2, 3 and 5.
How come?
That's because 30 = 2 x 3 x 5.

Number 17 has one prime factor: 17.
How come?
That's because 17 =

Is it because 17 = 1 x 17?

See, the word "product" is a synonym to "result of a multiplication." Since the minimum AND the necessary requirement to do a multiplication are two numbers called "factors." then number 17 and all primes must have two factors, one of which is always number 1. But that number is not considered a prime number!

The bug is out . . . LOL.

As you pointed it out, the question how many factors any prime number have cannot be answered if number 1 is considered a prime, coz in the case of prime number 17, there is no unique answer:

17 = 1 x 17
17 = 1 x 1 x 17
17 = 1 x 1 x 1 x 17
and so on.

So in order to kick out number 1 from the population of primes, some adjustments needed to be made to what is product and what isn't product. That's why the wording of the Fundamental Theorem of Arithmetic sounds so funny. See, the mathematicians have not become "rigorously liberal" yet to properly deal with primes and solve the most famous problem in the whole of mathematics called the "Goldbach Conjecture" -- an eighteen century insight into the behavior of prime numbers by a mathematician-amateur.




[edit on 10/1/2009 by stander]

reply to post by tauristercus

tauristercus, your linked thread is very interesting. I'm just starting to get into it. It will take some time for me to read it carefully and think about it, but I wanted to ask you, "How sure are you that every number on the list of known primes falls on one of your special rays?"

The list of primes has some strange skips and gaps and has fooled many mathematicians who made educated and even tested assumptions about it.

In the thread one poster suggested that you try circles of 8 rays and said that 3 occurs on a ray with other primes if that is done. How much comparison work have you done with circles of different numbers of rays?

One of the difficulties of working with primes is the number crunching. Even if you were to divine a formula that yielded all the primes, it would still have to be verified with a supercomputer, at least to some point this side of infinity, to really convince people that your formula was correct.

What you are working on does fascinate though, even if I feel out of my depth.

Going back to the original point of the thread, do you think that it's possible that there are more than one class of primes? Possibly the numbers two or three initiate a new dispersion of primes somewhere down the list.

That would explain all of the formulas that yield only part of the list of primes. Maybe each of the first 9 digits has its own family of primes with its own dispersion pattern and maybe some of these dispersion patterns are subsets of some and not of others.

All we need is the "one ring to bind them."


[edit on 1-10-2009 by ipsedixit]

Originally posted by FTL_Navigator
Is it just me or does that binary representation look like a fractal? Can you post a 3d version, I suspect that it might surprise a few people because to draw a 3d version (visualising as I go) when using 1, 2, and 3 (the first 3 primes)

A 3-D version? Hmm.. let's see here... (dusting-off my slightly rusty copy of POV-Ray)... Yeah, I guess I could do that:



Not exactly mind-blowing, but maybe if you squint and go into "grok mode", your brain will decypher the pattern

And just for a laugh through throw fi* into the picture, I think it may twist a few heads if not produce and illusion.

I couldn't figure out what you were referring-to at first, but I guess you are referring to "Phi", aka the "Golden Ratio"... Perhaps some possibilities there. An interesting challenge, anyway. We'll see.

Just for kicks, here are 500 more primes in base 2 starting with the millionth. The 1,000,500th prime number is 15,494,071, fyi.

[atsimg]http://files.abovetopsecret.com/images/member/51749f1799bf.jpg[/atsimg]

No more pictures?

The imagination is not kind to the primes, I guess.

So the OP objected to the fact that even number 2 would be included in the series of primes, which are all odd. In this view, shouldn't 1, 3, 5, 7 . . . be called even numbers and 2, 4, 6, 8 . . . be called odd numbers? Like having number 2 included in primes is odd, ain't it?

The issue of having just one even number among the infinitude of odd primes was raised once upon a time by a professor who asked his students to take one number out from this short series: 2, 3, 5, 7, 11.

He made an assumption that one even number among all odd numbers would be the criterion of choice -- number 2 really doesn't belong there. But all students except one highlighted number 7.

The professor was obviously bummed by the choice. How could his students forfeit the type of logic science runs on to numerology and pick number 7, coz it's widely considered a lucky number?

So the next day he had a short speech laced with a disappointment before the students. But the students denied using that "lucky number" attribute to 7 to pick this number. The professor went , asked the students for a moment, but then he shook his head.

So one of the students explained the criterion of choice to him: The students added those five prime numbers to get a clue what to chose: 2 + 3 + 5 + 7 + 11 = 28.

Then they divided 28 with each of the five numbers:

a) 28/2 = 14
b) 28/3 = 9 and 1/3
c) 28/5 = 5 and 3/5
d) 28/7 = 4
e) 28/11 = 2 and 6/11

The only option that made sense was (d) due to 28/[7 = 4]., coz 7 = 4 heavily implies [7 is the 4th prime number.]

And so the professor, whose name was Benjamin Franklin, used this story to settle the dispute about the birthday of the USA when the issue arose back in 1776. The other Founding Fathers rejoiced at the wisdom of the young Americans and all agreed on 7/4 -- July the 4th.


[edit on 10/3/2009 by stander]

reply to post by tauristercus


Hi, thanks for backing me up on the primes, Phage wasn't happy but there is an alternative to current logic thinking with Primes.

HADES

reply to post by zerotensor


Hi ZeroTensor,

Thanks for the uTube link ut I am unable to view (blocked), any chance you could do a screen shot?

When I refer to fi* I am referring to fibonucci fractals, the scientists are only just coming to grips with fractal light as an alternative string theory.

This ties in with Maxwell's Demon.

regards

HADES