20110602, 07:05  #1 
Jun 2011
2^{3} Posts 
Chance of finding new prime number formulas?
What is the chance to find the new formulas for primes? Is it worth trying?

20110602, 07:33  #2 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10100110111010_{2} Posts 

20110602, 09:35  #3 
"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 20110602 at 09:36 
20110602, 13:11  #4  
Nov 2003
2^{2}·5·373 Posts 
Quote:
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. 

20110602, 13:17  #5  
Nov 2003
7460_{10} Posts 
Quote:
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. 

20110602, 13:20  #6  
Nov 2003
2^{2}×5×373 Posts 
Quote:
Stop reading "popular" books. Start reading some books with real content. I already suggested two in this thread. 

20110602, 14:03  #7  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10100110111010_{2} Posts 
Quote:
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 20110602 at 14:04 

20110602, 14:54  #8  
Jun 2011
8_{16} Posts 
Quote:
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 20110602 at 14:58 

20110602, 16:13  #9  
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
Quote:
Forgotten who wrote that one ATM. David Last fiddled with by davieddy on 20110602 at 16:13 

20110602, 18:37  #10  
Nov 2003
2^{2}×5×373 Posts 
Quote:
Many more formulae are known. Read the references that I provided. Quote:
of different approaches. Approaches that use Wilson's theorem are all exponential. 

20110602, 18:39  #11 
Nov 2003
1D24_{16} Posts 

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