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Old 2011-06-02, 07:05   #1
columbus
 
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Default Chance of finding new prime number formulas?

What is the chance to find the new formulas for primes? Is it worth trying?
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Old 2011-06-02, 07:33   #2
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Quote:
Originally Posted by columbus View Post
What is the chance to find the new formulas for primes? Is it worth trying?
Who knows?

Worth trying, perhaps, but don't set your hopes too high.

Paul
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Old 2011-06-02, 09:35   #3
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I got the impression from Marcus du Sautoy(?)'s popular book
that Riemann had a way (in principle) of finding the number of primes < N
precisely.
How does such a thing tally with the "random" occurence of primes?

David

Last fiddled with by davieddy on 2011-06-02 at 09:36
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Old 2011-06-02, 13:11   #4
R.D. Silverman
 
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Quote:
Originally Posted by columbus View Post
What is the chance to find the new formulas for primes? Is it worth trying?
When you say "the new formulas" one must ask:

Which ones did you have in mind? What do you mean when you
ask for new formulas? What is a "formula for primes"??

We have accurate approximations for pi(x). We even have exact
formulations for pi(x) [although they are extremely difficult to compute].

We have exact formulae for the n'th prime. [although difficult to compute].

What is it that you think that we don't have? If you imagine that easy
to compute formulae giving the n'th prime exactly would be nice, I agree.
It is extremely unlikely that such formulae exist.

Read Ribenboim's book "The Book of Prime Number Records".

Read Hardy & Wright's "Introduction to the Theory of Numbers"

After you learn something about this subject we can discuss some
actual mathematics if you like. Whether finding new formulae is worth
trying depends on one's level of knowledge of number theory. If you
don't have a degree in math and a solid background in number theory,
then the answer is no; it is not worth trying.
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Old 2011-06-02, 13:17   #5
R.D. Silverman
 
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Quote:
Originally Posted by xilman View Post
Who knows?

Worth trying, perhaps, but don't set your hopes too high.

Paul
Worth trying by whom? By me? perhaps, but I doubt it.
By the OP? Forget it.

OTOH, if the objective is to learn some number theory [rather than
actually achieve some new formula], then it is worth trying. But one
needs SOME knowledge of what already exists, what has been tried,
and what is known NOT to work.

I mean no insult to the O.P. However, the way she/he phrased the question
carries strong implications that she/he has insufficient "mathematical
maturity". It was poorly and vaguely phrased.
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Old 2011-06-02, 13:20   #6
R.D. Silverman
 
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Quote:
Originally Posted by davieddy View Post
I got the impression from Marcus du Sautoy(?)'s popular book
that Riemann had a way (in principle) of finding the number of primes < N
precisely.
How does such a thing tally with the "random" occurence of primes?

David
Such formulae exist. They are well known to number theorists.

Stop reading "popular" books. Start reading some books with real
content. I already suggested two in this thread.
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Old 2011-06-02, 14:03   #7
xilman
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Quote:
Originally Posted by R.D. Silverman View Post
Worth trying by whom? By me? perhaps, but I doubt it.
By the OP? Forget it.

OTOH, if the objective is to learn some number theory [rather than
actually achieve some new formula], then it is worth trying. But one
needs SOME knowledge of what already exists, what has been tried,
and what is known NOT to work.

I mean no insult to the O.P. However, the way she/he phrased the question
carries strong implications that she/he has insufficient "mathematical
maturity". It was poorly and vaguely phrased.
Worth trying by anyone. That statement, of course, presumes that the necessary background has been acquired through appropriate study.

Even if no new formulae are forthcoming, it's still worth trying (IMO) purely for the gains to be made elsewhere.

Paul

Last fiddled with by xilman on 2011-06-02 at 14:04
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Old 2011-06-02, 14:54   #8
columbus
 
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Quote:
Originally Posted by R.D. Silverman View Post

Which ones did you have in mind? What do you mean when you
ask for new formulas? What is a "formula for primes"??

What is it that you think that we don't have?
I mean extending this list.
http://en.wikipedia.org/wiki/Formula_for_primes
I am interested in studies measuring computational complexity of different approaches. Especially based on Wilson theorem. Do you know this type of studies?

Last fiddled with by columbus on 2011-06-02 at 14:58
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Old 2011-06-02, 16:13   #9
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Quote:
Originally Posted by R.D. Silverman View Post
Such formulae exist. They are well known to number theorists.

Stop reading "popular" books. Start reading some books with real
content. I already suggested two in this thread.
Try "How to win friends and influence people"
Forgotten who wrote that one ATM.

David

Last fiddled with by davieddy on 2011-06-02 at 16:13
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Old 2011-06-02, 18:37   #10
R.D. Silverman
 
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Quote:
Originally Posted by columbus View Post
Did you imagine that the list from above is exhaustive??

Many more formulae are known. Read the references that I provided.

Quote:
I am interested in studies measuring computational complexity of different approaches. Especially based on Wilson theorem. Do you know this type of studies?
Yes, I know of such studies. A variety of people have studied the efficiency
of different approaches. Approaches that use Wilson's theorem are all exponential.
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Old 2011-06-02, 18:39   #11
R.D. Silverman
 
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Quote:
Originally Posted by davieddy View Post
Try "How to win friends and influence people"
Forgotten who wrote that one ATM.

David
Suggestions that one study real math rather than 'popular' math are unfriendly?????
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