October 13th, 2012, 03:46 PM  #1 
Newbie Joined: Oct 2012 Posts: 22 Thanks: 0  My new formula for pi(x)
pi(x) is the count of primers less that x Here is my new formula. It gives very precise results I proved it by evidance in algebrial way. ex. pi(1000) 
October 13th, 2012, 06:12 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: My new formula for pi(x)
You seem to mean which has an atrocious amount of cancellation and a consequently huge error term. Can you even prove that the ratio of this to pi(n) is 1? (It seems to be true...) 
October 13th, 2012, 06:30 PM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: My new formula for pi(x)
The pi(sqrt(n)) part doesn't seem to help, either. Look at 500,000: your formula is too high by 1136.8..., but it would 'only' be off by 1010.8... if you dropped that term. Similarly at 10^9 it worsens the error from 3,319,288.3... to 3,322,689.3.... 
October 14th, 2012, 12:13 AM  #4 
Newbie Joined: Oct 2012 Posts: 22 Thanks: 0  Re: My new formula for pi(x)
thank you for your helpful feedback. I will applead a word file which contains the proof so wiat for me your feedback is very important to me. 
October 14th, 2012, 10:03 AM  #5 
Newbie Joined: Oct 2012 Posts: 22 Thanks: 0  Re: My new formula for pi(x)
this is a pdf file contains the proof I change it from word pdf is better than word in reading, I think so. download the file from this link http://depositfiles.com/files/awg3hvlri size 284 kb it is a bit more than attachment maximum allowed size which is 250 Kb zip file does not help still more than 250 kb 
October 14th, 2012, 01:27 PM  #6 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: My new formula for pi(x)
Your result is incorrect, as shown in your first post: equality does not hold. It may be that the two are approximately equal, but you have not proved this.

October 15th, 2012, 01:21 AM  #7  
Newbie Joined: Oct 2012 Posts: 22 Thanks: 0  Re: My new formula for pi(x) Quote:
my proof does not mean that the result will be exact because (for example) when I remove multiples of 5 as 1/5 from the remain it does not exactly 1/5 from it. the primers will become more and more in the remains while removing the multiples of primers less than sequare root of (n) and this is what makes the approximation become far from pi(n). It seems to me I have to consider the method again.. thank you CRGreathouse you gave me very important notes.  
October 15th, 2012, 06:36 AM  #8  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: My new formula for pi(x) Quote:
It may be an approximate equality, but your 'proof' does not show that. Quote:
I see an error of 2,666,913,530,087 at 10^15; that's much further than the error of the logarithmic integral at the same point (1,052,61.  

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