- --- "Werner D. Sand" <Theo.3.1415@...> wrote:

> Demonstration of the statement "the prime numbers

It is in fact a tautology to define primes by the way

> are distributed as

> regularly as possible":

>

> Regula 1: All numbers > 1 are prime.

> Try: 2,3,4 oops, 4 is not prime. 4 is equal, hence

>

> Regula 2: All numbers >1 which are not multiple of 2

> are prime.

> Try: 2,3,5,7,9 oops, 9 is not prime. 9 is multiple

> of 3, hence

>

> Regula 3: All numbers >1 which are not multiple of 2

> or 3 are prime.

> Try: 2,3,5,7,11,13,17,19,23,25 oops, 25 is not

> prime. 25 is multiple

> of 5, hence

>

> Regula 4: All numbers >1 which are not multiple of 2

> or 3 or 5 are

> prime.

> Try: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,49

> oops

>

> and so on. The regulas become more and more exact.

> The prime numbers

> are distributed "as regularly as possible".

> It's simply the Sieve of Eratosthenes.

>

> Werner

>

you find them. Whatever you find by the Sieve is

prime. If the Sieve way is regular, then prime is of

course regular. but it is a tautology. The fact that

the Sieve is regular cannot prove itself to be

regular. If regularity is already defined in to

primes, that same regularity cannot be used to prove

that prime is regular. the same kind of regularitys

cannot prove the same regularity. If prime is defined

by regularity or the regular way of finding primes,

those way of finding primes cannot be used to prove

that primes are regular. What needs to be done is to

define primes by a kind of regularity that can then be

used to prove another kind of prime regularity.

Regularity A proves regularity B (B could be the sieve

or the non-divisibility). But regularity B cannot

prove itself. If prime is defined by regularity B,

then B cannot be used to prove prime regularity. It

is to use B to prove B, a tautology. You have to use

A to prove B. To prove prime is regular is to prove

that the essence of prime is regular. From that

regular essence, we deduce other manifest regularities

such as the Sieve or the non-divisibility. But the

regularity manifestation of a prime does not

necessarily mean or prove that the essence of prime is

regular. The essence could be random but still

produce a manifestation of regularity. The manifest

regularity of nature does not prove that the essence

of the universe, the quanta, are regular. In fact,

many believe that the regularity nature is caused by a

random essence. Thus, the regularity of primes (the

sieve or non-divisibility) could be caused by a random

essence and does not prove that prime has the true

property of being as regular as possible.

To prove or explain the hardness and rareness

properties of diamonds, one must start from its

essence carbon and its way of creation. To explain

matter, one must start with its essence quantum

particles and its way of creation. To prove or

explain the regularity of a non-prime number, one must

start from its essence which is the prime number and

its way of creation.

To prove or explain the regularity of primes, one also

must or may have to start from its essence and its way

of creation. What is the essence is unknown at

present, which is most likely the reason why the RH

cannot be proven. Non-divisibility is not the essence

of primes, just like divisibility is not the essence

of non-primes (the essence of non-prime is the prime).

Essence here simply means the building block. If the

essence of non-prime is the prime, it is only fair and

logical to go down the hierarchy to ask what is the

essence of prime. That essence logically cannot be a

number since prime number is the lowest level a number

can be.

Assuming we know the essence of prime, we can imagine

two ways to create a prime. A random way of

manipulating the essence or a non-random and highly

regular way. It is of course possible with near zero

probability for the random way to create a population

of primes that would show regular pattern. But it is

far more likely that the random way will not produce

any regular pattern of primes. On the other hand, the

non-random and regular way of creating primes would

exclude any irregularity as a viable outcome. It

would demand or predict that primes are distributed as

regular as possible. In this case, the RH would be a

logical deduction of the prime essence and its lawful

way of creation, just like hardness and rareness of a

diamond is a logical deduction of the carbon essence

and its way of creation. What canbe logically

deducted from an essence or axiom must be true. To

prove something is to deduce it from some basic truth,

essence, or axioms. To prove that human is made by

God using quantum particles is to deduce humans from

the particles essence and God in a step by step and

lawful way. Without knowing the law of God or the way

of creation using particles, we can never prove or

disprove the hypothesis that God created humans.

Analagously, without knowing the way of creating

primes from its essence, we can never prove or

disprove the hypothesis that prime is created in a way

that is as regular as possible, which automatically

predicts the RH.

The regularity of primes is what we observe. The

regularity includes many forms, such as

non-divisibility, prime number theorem, and the RH.

But it leaves open the question of what causes the

regularity, is it randomly caused or not. To prove

the RH means we can exclude any randomness in primes

including their causes. If the RH is true, the cause

for the regularity of prime cannot be random. The

phyical universe provides a good analagy. The

regularity and lawfulness of matter above the quantum

level is what scientists observe and is why scientists

have a job. The regularity includes many forms, such

as the various physics laws and the fact that life is

built by DNA. But it leaves open the question of what

causes the regularity, is it randomly caused or not.

Scientists believe, without any proof, that it is

randomly caused because of lucky accidents. Religions

say it is caused by God. The position of science can

never be proven since randomness can cause many

outcomes, including randomness itself and the near

zero probability event of regularity. Since both

randomness and regularity can be logically deduced

from a random cause, neither is a certainty and

neither can be proven by invoking a random cause. But

the God position has a chance to be proven true. If

we give God a creation law and that law predicts only

one outcome which is regularity, then we would have

proven that the regularity of nature is caused in a

non-random way which is a way of law that predicts

only one specific outcome of regularity. To prove

that an outcome is caused by the essence is to show

that all other outcomes are non-viable. The random

position cannot exclude randomness as a viable outcome

and cannot therefore prove that the regularity outcome

is caused by the random essence.

So to prove the RH, we need a creation law for the

primes that predicts only one outcome regularity.

Irregularity is not allowed by that law and is not a

viable outcome. By finding that law, we prove that

the cause for the regularity of primes is not random.

If the cause is not random, then there is no chance

for the primes to display any aspects of randomness,

which is the same as saying that primes are as regular

as possible, which thus proves the RH.

So it is my assertion that the only way to prove the

RH is to find the essence of primes and the law of

creation. It is comparable to prove the hypothessis

that the regularity of nature is caused by God and his

law rather than randomness. But the only way to prove

God is to find his law of creation using particles.

Until one finds a creation law that uses

essence/particles to create primes/nature, one can

always say that the regularity of primes/nature is

caused by chance, no matter how small a chance. One

can never say that primes/nature are as regular as

possible or as non-random as possible. If a thing is

caused randomly, it surely cannot qualify as the most

regular possible or as regular as possible, because

another equivalent thing that is caused non-randomly

would have more regular properties and would better

qualify as the most regular possible.

To say primes are as regular as possible means

everything about primes, including its way of

creation, are non-random. The RH makes a big claim

that is inherently or in principle unprovable by

anything that deals only with behaviors of primes.

The RH does not deal with how prime is created from

its essence. Thus, even if proven true, it cannot

support its claim that primes are as regular as

possible. The RH is logically in capable of proving

its own claim. This is perhaps the reason why it

remains unprovable. Its claim is bigger than it can

possbily deliever. It simply cannot deliver its

claim. Proving the RH will not prove its big claim,

which is the same as saying proving the RH will not

prove the RH. The claim of RH is logically in capable

of being proven by proving the RH. The RH is simply

unprovable from its own perspective. Its claim has to

be proven from another perspective.

To use an analagy. The laws of physics above the

quantum level says that nature is as regular as it can

be, limited only by the random noise of atoms. But

such a claim imply that the cause of nature is also

regular, since a nature that is regularly caused would

be more regular than a nature that is randomly caused.

Proving the laws of nature that describe behaviors of

nature cannot prove that nature is caused/created

non-randomly. So they can never justify the claim

that nature is as regular as possible. The claim can

only be proven or justified from finding the

non-random law that is used to create nature.

So, if the RH really claims, in layman terms as the

Wikepedia says, that primes are as regular as

possible, proving RH will not justify the claim. This

simply means that the RH is inherently unprovable from

the same level of thinking that leads to the RH. It

means that the RH cannot be proved by any number

theory. It can only be proven by finding the essence

of primes and by finding the non-random law of prime

creation. To prove the RH is the same as to prove

that the regularity of nature is caused by a

non-random creation law and a law giver. In this

sense, it is the same as to prove God. This is the

reason for the RH to be regarded as the most

fundamental problem of mankind. It is interesting

that another equally fundamental problem with

relevance to God, the Darwinian theory of evolution,

came out the same year as the RH in 1859. Darwinists

are people who look at the primes and say that they

are caused randomly. The RH implies that everything

about primes, including its essence and its way of

creation, is not random. To prove the RH is to

disprove Darwinism and is to prove God. The two

opposite theories have the same birthday and most

likely will have the same judgement day, which

hopefully will be very soon.

Shi

____________________________________________________________________________________

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Everyone is raving about the all-new Yahoo! Mail beta.

http://new.mail.yahoo.com - --- "Werner D. Sand" <Theo.3.1415@...> wrote:

> Hello Shi,

Werner,

>

> I do not define the primes by the E-Sieve, they are

> defined as they

> are. The Sieve is only a method to develop them. I

> don't prove a

> regularity of the primes by a regularity of the

> Sieve, but I show

> that the Sieve IS a regularity and thus the primes

> follow this

> regularity. A regularity is not necessarily a

> formula like f(n) but

> may also be a calculation instruction like Euclid's

> algorithm or the

> Fibonacci numbers or the prime numbers. The prime

> numbers are a

> natural constant just as pi or e or sqrt(2). You

> cannot predict the

> 678th digit of pi, but pi/4 = 1 - 1/3 + 1/5 - 1/7 +

> Random or not?

> Do you call sqrt(2) random because you cannot

> predict the 101th

> digit? Probably you say "sqrt(2) is as it is". And

> such are the

> primes.

>

> Tell me something about the "essence" of

> mathematical constants: are

> they "God"? Are they "Tao"? Are they "Nothing"?

>

> Werner

>

You certainly have no jusitification or proof to call

primes mathematical constants. If everyone agrees

that the essence of numbers or non-prime numbers is

the prime, then tell me what is the essence of prime?

Dont tell me that prime has no essence. That simply

shows that you dont know the answer.

Just like from the essence of non-primes, we can prove

or deduce that non-primes are always regular and

predictable, we should be able to deduce or prove from

the essence of primes whether primes are always

regular but unpredictable. Whthout knowing the

essence of primes, certain things can never be proven,

such as the predictability or the RH. Without knowing

the essence of diamond to be carbon, how can you be

sure or prove that diamond cannot be rock made of

silicon?

Primes are touted as the building blocks or atoms of

numbers. Well, you should ask what is the building

block of primes, is it quantum particles? Isnt is odd

that no one has a clue about such fundamental

questions?

Shi

____________________________________________________________________________________

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http://searchmarketing.yahoo.com/arp/sponsoredsearch_v2.php - Shi,

first of all: what do you mean by "essence"? I love doing philosophy

instead of mathematics, but I must know about what we are speaking.

Maybe I tell you that the "essence" of the primes are the primes. You

didn't answer my question about pi or e or sqrt(2). What do you

consider to be the essence of sqrt(2)? Sqrt(2) has a definition, but

no essence. What difference is there between the prime numbers and

pi or e? pi=3.1415926 , e=2.718281828 , p=2.35711131719 That's my

justification to call the primes a natural or mathematical

constant.You may as well call the set of the prime numbers

P={2,3,5,7 } or each single prime number a constant.

In a sense you can say the primes are the atoms of the numbers. Then

you mean multiplication. In another sense you can call One the atom

of the numbers. Then you mean addition. What do you think about

the "essence" of One? Perhaps the "essence" of the prime numbers is

the combination of addition and multiplication. If there is only

either addition or multiplication, there are no prime numbers. If you

have the number 2 and only multiplication, you get only numbers 2^k.

If you have the number 1 and only addition, you don't know what

division is. It is somewhat like Yin and Yang: each of them alone is

nothing, both of them together are the reality. Is that a bit nearer

to what you call "essence"?

Werner - snip>

> Primes are touted as the building blocks or atoms of

I have heard and read that the primes are the building blocks of

> numbers. Well, you should ask what is the building

> block of primes, is it quantum particles? Isnt is odd

> that no one has a clue about such fundamental

> questions?

>

> Shi

numbers and I don't appreciate that at all. I was going to say "get

that" but that isn't true, I do get it, I just don't appreciate it

well. "1" is the building block of numbers. If you build numbers

from 1, you get a finitely generated abelian group with group

operation addition. If you build the numbers multiliplicatively,

then you get an infinitely generated monoid with no zero divisors

("cancellative monoid"?). I vote for the abelain group over the

monoid. It is a stretch to even understand the monoid without

addition-I have got this big multiplication table and I "happen" to

observe certain entries that are minimums in the POSet ordered by

divisibility. That is really stretching the layman's understanding

of "number". I think it is even stretching the mathematician usual

view of "number".

Adam - --- Shi Huang <shuangtheman@...> wrote:
> --- "Werner D. Sand" <Theo.3.1415@...> wrote:

Has this thread not suffocated from the morass of ill- or un-defined terms yet?

> > Demonstration of the statement "the prime numbers

> > are distributed as

> > regularly as possible":

> >

> > Regula 1: All numbers > 1 are prime.

> > Try: 2,3,4 oops, 4 is not prime. 4 is equal, hence

> >

> > Regula 2: All numbers >1 which are not multiple of 2

> > are prime.

> > Try: 2,3,5,7,9 oops, 9 is not prime. 9 is multiple

> > of 3, hence

> >

> > Regula 3: All numbers >1 which are not multiple of 2

> > or 3 are prime.

> > Try: 2,3,5,7,11,13,17,19,23,25 oops, 25 is not

> > prime. 25 is multiple

> > of 5, hence

> >

> > Regula 4: All numbers >1 which are not multiple of 2

> > or 3 or 5 are

> > prime.

> > Try: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,49

> > oops

> >

> > and so on. The regulas become more and more exact.

> > The prime numbers

> > are distributed "as regularly as possible".

> > It's simply the Sieve of Eratosthenes.

> >

> > Werner

It certainly looks moribund.

> It is in fact a tautology to define primes by the way

What do you mean by 'tautology' here?

> you find them.

> Whatever you find by the Sieve is

What do you mean by 'regular' here?

> prime. If the Sieve way is regular,

> then prime is of

What do you mean by 'regular' here?

> course regular.

> but it is a tautology.

grrrr.

> The fact that

grrrr.

> the Sieve is regular

> cannot prove itself to be

What do you mean by a sieve 'proving itself to be [something]'?

> regular.

> If regularity is already defined in to

grrrr.

> primes,

> that same regularity

grrrr.

> cannot be used to prove

grrrr.

> that prime is regular.

grrrr.

> the same kind of regularitys

grrrr.

> cannot prove

grrrr.

> the same regularity.

grrrr.

> If prime is defined

grrrr.

> by regularity

> or the regular

grrrr.

> way of finding primes,

grrrr.

> those way of finding primes cannot be used to prove

> that primes are regular.

> What needs to be done is to

grrrr.

> define primes by a kind of regularity

> that can then be

grrrr.

> used to prove another kind of prime regularity.

> Regularity A proves regularity B (B could be the sieve

I give up.

> or the non-divisibility). But regularity B cannot

> prove itself. [...]

Make it stop, please!

Phil

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