20200912, 19:39  #1 
Dec 2018
Miami
29 Posts 
The prime counting function conjecture
Don't swallow me alive for this, but I was wondering if somebody can be kind enough to test this conjecture with a large enough say using a powerful computer:
If you can let me know, and am willing to provide you with the typed out formula to be used in your math software. Notice this formula assumes 1 is not a prime (as it should.) The reasoning behind it can be found here. Last fiddled with by jrsousa2 on 20200912 at 19:42 
20200912, 19:55  #2  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}·7·163 Posts 
The reasoning behind posting here on this forum can be found here:
Quote:


20200912, 21:33  #3 
Feb 2017
Nowhere
3,583 Posts 
I question the use of the term "conjecture," which, as explained here, implies the statement is important and worthy of study. The term "claim" appears to be more appropriate. Offhand, I see no reason to consider it, even if correct, as anything other than a curiosity.
The claim is also poorly stated. The phrase "if x is sufficiently large" is entirely superfluous. The definition of asymptotic equality involves the limit as x increases without bound, or tends to plus infinity. Your request indicates to me that your series is difficult to evaluate. There are already expressions proven to be asymptotically equal to the primecounting function, such as li(x) and x/log(x), which are easy to evaluate. 
20200913, 04:04  #4 
Aug 2006
17·349 Posts 

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