Prime numbers : a math question for the pro

[Adrian Reef]

Hello everybody , I'm Adrian , new stupid among apes

This might sound silly or obvious according to a viewer's point of view and knowledge on the matter but,is there any visible undeniable linear order or logical distinguishable pattern in the distribution of primes of which humanity knows of , now, in 2012 ?

I really need to know this as I'm getting mad trying to find this answer everywhere my eyes can put their sight on...
A friend of mine says Riemann is the only one who could grasp the signs of a pattern and that his findings are the only available nowadays. Is that true or something new is on the way ?
(PLEASE, I don't want to start a post about him ! Question is simple and clear,I guess...)

I'm just searching for a "no,there isn't" or the exact opposite(possibly with the article/publication source,in the case that happened in a moment of blindness...) :shy:

Best regards , Adrian

P.s. : I'm asking because I'm trying to find it;if that exists I won't waste other time on prime numbers...Quite logical...

 

[Adrian Reef]

Talking about Ulam won't help either...
Anyway , almost one hundred views and no answers ?
I might be tempted to think I'm not that stupid after all...

 

[Robert1986]

Well, there's the Prime Number Theorem. http://en.wikipedia.org/wiki/Prime_number_theorem

It says that $\pi(x) \simeq \frac{x}{logx}$

That is, the number of prime numbers less than $x$ approaches $x/logx$. But this is just asymtotic and I am not aware (and in fact am quite surethere isn't) of any exact things.

 

[Mandlebra]

A lot of modern analytic number theory advances are being made using hardy's major and minor circle (arc?) Technique, but most advances just seem to be bounds improvements

 

[Adrian Reef]

So...prime number theorem..?

From Wikipedia, the free encyclopedia
Statement of the theorem
Let π(x) be the prime-counting function...

Ok...
Prime-counting function
In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x.[1][2] It is denoted by π (this does not refer to the number π).

Well...We know that...Problem is it doesn't answer my question and it doesn't clarify which is the fastest "counting function" from a computational point of view,the most important part of the whole problem...Because,if there was a pattern,that famous pattern someone's talking about,we would be able to find them even faster by knowing "who's the guy" to keep and "who's not" ,a priori...Am I wrong ?

From wiki :Other prime-counting functions are also used because they are more convenient to work with. One is Riemann's prime-counting function...

Can you understand what I'm trying to say now ?
Say you have a huge number ; how can you say "it's prime" ? How do you check it quickly ?

P.s. : thanks Mandlebra , that helps, kind of ,as it involves "PI"...

 

[micromass]

Say you have a huge number ; how can you say "it's prime" ? How do you check it quickly ?

Check this: http://en.wikipedia.org/wiki/Primality_test

 

[Adrian Reef]

Check this: http://en.wikipedia.org/wiki/Primality_test

mmm...

http://en.wikipedia.org/wiki/AKS_primality_test

It has problems too , imo , and the problems are :

- http://en.wikipedia.org/wiki/Modulo_operation
- Performance issues

check this
http://functionalley.eu/Factory/primalityTests.html

Having said so , what else has this world to offer nowadays ?

P.s. : don't give me square roots,just ginseng ^_^

 

[Number Nine]

I honestly don't have any idea what you're asking. The prime number theorem, as far as I can tell, should have answered your question; the prime number theorem and the Reimann hypothesis (if true) make certain "statistical" statements about the distribution of prime numbers, and that's about it. You're not going to find a theorem or result that tells you exactly why each individual prime number is located where it is.

 

[Adrian Reef]

I honestly don't have any idea what you're asking. The prime number theorem, as far as I can tell, should have answered your question; the prime number theorem and the Reimann hypothesis (if true) make certain "statistical" statements about the distribution of prime numbers, and that's about it. You're not going to find a theorem or result that tells you exactly why each individual prime number is located where it is.

So...Did I win a million dollars or what ?

P.s: you wrote Riemann in the wrong way...
P.p.s. : don't tell your friends an italian corrected you ^_^

 

[Adrian Reef]

Just one moment...Cmon...Seriously...

"I honestly don't have any idea what you're asking."
With a degree in cognitive neuroscience he may have missed something ; that's not his fault but,seriously,is there a mathematician who can proudly say "that's about it" ?
I'm not kidding and I'm really searching informations on new findings as I want to disclose my research to the public.

 

[Number Nine]

Just one moment...Cmon...Seriously...

"I honestly don't have any idea what you're asking."
With a degree in cognitive neuroscience he may have missed something ; that's not his fault but,seriously,is there a mathematician who can proudly say "that's about it" ?
I'm not kidding and I'm really searching informations on new findings as I want to disclose my research to the public.

The distribution of primes is tied to the zeta function, which doesn't tell us anything because we don't understand it well enough. Beyond that, the prime number theorem is about as good as you're going to get. If you want specific information, be more specific. If you want to disclose some sort of research to the public, then disclose it.

P.s: you wrote Riemann in the wrong way..

I sincerely apologize. One day, we will recover from this. Time will heal this wound.

 

[micromass]

If you want to disclose some sort of research to the public, then disclose it.

No, please do not disclose it on this forum. This forum is not for original research.

Anyway, you got anymore questions, Adrian??

 

[Robert1986]

Do you want a function that will just give you what the $n^{th}$ prime number is? If so, none exist, and I doubt one ever will.

 

[chiro]

Do you want a function that will just give you what the $n^{th}$ prime number is? If so, none exist, and I doubt one ever will.

There are formulas, but they involve computations that are hard to perform as opposed to say a simple polynomial or series expansion. The below link might help:

http://en.wikipedia.org/wiki/Formula_for_primes#Prime_formulas_and_polynomial_functions

 

[Adrian Reef]

the prime number theorem is about as good as you're going to get.

Apparently,it doesn't help in my case...

No, please do not disclose it on this forum. This forum is not for original research.

As long as I have proven paternity and as long as I wish to give it for free to the world , I GUESS I might disclose it whenever & wherever I want (RSA guys opinion apart...).
But any help or suggestion in this direction is really appreciated as I've just wrote ©+name+dd/mm/yyyy on the pages and inserted my work in an envelope I've sent to myself.

Anyway, you got anymore questions, Adrian??

What's next?

simple polynomial or series expansion

Apparently,I'm running in polynomial time,but one of those 3 guys here(I won't tell you who) -->http://en.wikipedia.org/wiki/Schoof%E2%80%93Elkies%E2%80%93Atkin_algorithm<--
said I'm running in exponential time;honestly, I really don't think he completely understood my technique in that hour we met...That's also the reason why I want to disclose it (to compare it) as well the reason why I'm trying to find a similar work (which is also,among many other things,another proof that "pi" is of the form "3n+-1").

Thanx a lot for all your help , I really appreciate your efforts , even if it doesn't quite seem like so...

Best Regards

P.s. :

I sincerely apologize. One day, we will recover from this. Time will heal this wound.

I hope you don't feel offended for those stupid jokes , I was having fun of the situation , I apologize

 

[Robert1986]

There are formulas, but they involve computations that are hard to perform as opposed to say a simple polynomial or series expansion. The below link might help:

http://en.wikipedia.org/wiki/Formula_for_primes#Prime_formulas_and_polynomial_functions

Yes, correct; I was aware of the formula that used the sieve of Eratosthenes, but not the other ones; the system of Diophantine equations was of particular interest to me. What I meant to say was that there isn't a closed-form expression (though, I should be careful, because there might be one I am unaware of.)

 

[Robert1986]

What's next?


Apparently,I'm running in polynomial time,but one of those 3 guys here
said I'm running in exponential time;honestly, I really don't think he completely understood my technique in that hour we met...That's also the reason why I want to disclose it (to compare it) as well the reason why I'm trying to find a similar work (which is also,among many other things,another proof that "pi" is of the form "3n+-1").

Well, I am a little concerned that you think "evaluating a polynomial" and "running in polynomial time" are the same. I hope you were mistaken.

Well, what makes you think you are running in polynomial time?

 

[Adrian Reef]

you think "evaluating a polynomial" and "running in polynomial time" are the same

Nope.

It all started with a quadratic equation ,so,something which grows proportionally to the input.
I've then improved my results,well beyond the square root of n.

Anyway,you might think I'm a crackpot (same thing did "that famous mathematician" ,whose bad expectations changed in a few minutes) but I don't even need to open up a google page to tell you n = m^2 takes quadratic time while n=m^n takes exponential time...

I know what I'm doing...

 

[Robert1986]

Nope.

It all started with a quadratic equation ,so,something which grows proportionally to the input.
I've then improved my results,well beyond the square root of n.

Anyway,you might think I'm a crackpot (same thing did "that famous mathematician" ,whose bad expectations changed in a few minutes) but I don't even need to open up a google page to tell you n = m^2 takes quadratic time while n=m^n takes exponential time...

I know what I'm doing...

OK, I'm glad to know my fears are not justified.

what do you mean by:

(same thing did "that famous mathematician" ,whose bad expectations changed in a few minutes)

Hey, if you have a good algorithm, publish it in a journal somewhere. Since at that point it will be accepted by computer scientists and mathematicians, I'm sure you can post your results on PF - but I don't know for certain.

 

[Adrian Reef]

if you have a good algorithm, publish it in a journal somewhere.

I would love to do it,problem is the waiting time...
I'd prefer to "secure it" and disclose it everywhere,for free; I hate when someone makes money out of something they didn't even invent as they just discovered part of the realm of assumptions this universe is made of.

Btw,for the sake of the conversation,I would like to share some crackpot analysis I've made out of my assumptions by playing around with some equations taken from my work. Maybe you(all) have seen them somewhere else , who knows...

Flickr set of images

Personally,I'm in love with this one

Thoughts are welcome.

P.s. : that pic seems like Sierpinski is gone wild

 

[micromass]

I know what I'm doing...

Good for you!

Thread closed.