20180117, 13:40  #1 
"khvicha matkava"
Jan 2018
georgia
1 Posts 
prime number
ready full justification of prime numbers their exact location distribution concept twin different from classical also new formulas for finding them and much more related to prime numbers need a site to make a presentation I hope for the help of interested persons in this field
I do not know English well with a translator 
20180117, 14:56  #2 
"Luke Richards"
Jan 2018
Birmingham, UK
120_{16} Posts 
Your request does not translate well into English, but I'll give you some basic point. I will use some of the key words in your request as starting points:
I hope this is helpful. 
20180117, 15:08  #3  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:
There's always a prime between n and 2n Theres a polynomial in roughly 25 variables that has all its positive values be the primes. Lucas lehmer implementations can be complex because they use FFT, otherwise the test is fairly easy to program for. 

20180117, 18:04  #4 
Aug 2006
3×19×103 Posts 
I have an unpublished (so far) list of 60+ formulas for primes, including the Jones, Sato, Wada, & Wiens polynomial that sm88 mentioned.
I think what was intended is that there are no *efficient* formulas for primes, it's faster to find them by various algorithms. Last fiddled with by CRGreathouse on 20180117 at 18:05 
20180118, 15:01  #5 
Feb 2017
Nowhere
D10_{16} Posts 
If memory serves, there are "formulas" for primes in Hardy and Wright, some involving trigonometric series. They are, of course, computationally useless. There is also a formula of sorts involving Mills' Constant. The joker here is (at least if I understand correctly) that the value of the constant has to be "reverse engineered" from the sequence of primes it produces!
My alltime favorite is from a Martin Gardner "Mathematical Games" column. It produces a prime for every positive integer n: 4 + (1)^{n} Last fiddled with by Dr Sardonicus on 20180118 at 15:02 Reason: Fixing typos 
20180118, 17:24  #6 
Aug 2006
5871_{10} Posts 
Hardy & Wright has
\[\pi(n) = 1+\sum_{j=3}^n (j2)!  j \left\lfloor\frac{(j2)!}{j}\right\rfloor\] and also references some previously published formulas (Mills', I think). The result doesn't appear until the fifth edition so I think it's properly credited to Wright alone (as Hardy had been dead for 32 years when it came out). 
20180119, 00:29  #7 
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} Posts 
http://primes.utm.edu/glossary/ may be one good read.
http://mathworld.wolfram.com may be another, forsome involved. 
20180123, 13:58  #8  
"Oliver"
Sep 2017
Porta Westfalica, DE
2^{2}·3^{2}·7 Posts 
Quote:
\[\pi(n) =\sum_{i=1}^n \left\lceil\frac{(i1)!^2}{i}\right\rceil  \left\lfloor\frac{(i1)!^2}{i}\right\rfloor\] Maybe this is a well known formula? 

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