April 3rd, 2019, 01:13 PM  #1 
Senior Member Joined: Mar 2019 From: iran Posts: 318 Thanks: 14  prime counting function
pi(n) = n/ln(n) + n/ln^2(n) + n/ln^3(n) + ... I think this is stronger than prime number theorem and closer to the true value of pi(n). Last edited by skipjack; April 3rd, 2019 at 03:53 PM. 
April 3rd, 2019, 02:17 PM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 742 Thanks: 98 
It is similiar to $\displaystyle \pi(x) $~$\displaystyle Li(x)$.

April 4th, 2019, 03:01 AM  #3 
Senior Member Joined: Dec 2015 From: somewhere Posts: 742 Thanks: 98 
Here is the similiar formula : Prime Number Theorem  from Wolfram MathWorld 

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counting, function, prime 
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