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 2011-06-02, 07:05 #1 columbus   Jun 2011 23 Posts Chance of finding new prime number formulas? What is the chance to find the new formulas for primes? Is it worth trying?
2011-06-02, 07:33   #2
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

101001101110102 Posts

Quote:
 Originally Posted by columbus 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

 2011-06-02, 09:35 #3 davieddy     "Lucan" Dec 2006 England 2·3·13·83 Posts 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
2011-06-02, 13:11   #4
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by columbus 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"

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.

2011-06-02, 13:17   #5
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by xilman 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.

2011-06-02, 13:20   #6
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by davieddy 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.

2011-06-02, 14:03   #7
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

101001101110102 Posts

Quote:
 Originally Posted by R.D. Silverman 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

2011-06-02, 14:54   #8
columbus

Jun 2011

816 Posts

Quote:
 Originally Posted by R.D. Silverman 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

2011-06-02, 16:13   #9
davieddy

"Lucan"
Dec 2006
England

2·3·13·83 Posts

Quote:
 Originally Posted by R.D. Silverman 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

2011-06-02, 18:37   #10
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by columbus I mean extending this list. http://en.wikipedia.org/wiki/Formula_for_primes
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.

2011-06-02, 18:39   #11
R.D. Silverman

Nov 2003

1D2416 Posts

Quote:
 Originally Posted by davieddy 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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