August 21st, 2017, 10:19 PM  #51 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  
August 22nd, 2017, 05:40 AM  #52  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,642 Thanks: 960 Math Focus: Elementary mathematics and beyond  Quote:
 
August 22nd, 2017, 06:09 AM  #53  
Senior Member Joined: May 2016 From: USA Posts: 825 Thanks: 335  Quote:
Counting the primes in order of magnitude, is there a procedure or formula for finding the nth prime more efficient than than just testing the odd numbers above the (n1)th prime in succession?  
August 22nd, 2017, 06:51 AM  #54 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,642 Thanks: 960 Math Focus: Elementary mathematics and beyond 
I believe that one can use the Riemann hypothesis for primes up to $10^{13}$. It gives a good approximation with accuracy increasing as numbers get larger. Maybe that's as good as it gets.

August 23rd, 2017, 05:22 AM  #55  
Banned Camp Joined: Dec 2012 Posts: 1,028 Thanks: 24  Quote:
On this topic you can find some more detail: Supersymmetric Complicate Numbers Sorry to be incomplete, but all is under development and was the 3th very hard (unpaid) job for me... Thanks ciao Stefano  
September 11th, 2017, 06:54 AM  #56 
Newbie Joined: Jan 2010 Posts: 9 Thanks: 0 
The formula that generates whole prime numbers : y=(2^(x1)1)/x ( formula1) If y is an integer , then x must be absolutely a prime number . the set of x for any value of integer y ; x = { 3,5,7,11,13,....} and it generates all the prime numbers . The question is that for the set of prime numbers ( x1 , x2) does the formula generates all the even numbers or not ? y1 = (2^(x11) 1 ) /x1 + (2^(x21) 1 ) /x2 for ( x1 , x2) = ( 3,3) then y1 = 2 ; for ( x1 , x2) = ( 3,5) then y2 = 4 ; for ( x1 , x2) = ( 5,5) then y3 = 6 ; for ( x1 , x2) = (5,7) then y4 = 8 ; .................... The result for whole prime sets of ( x1 , x2) then you can generate all the even number's set . P.S.: For the proof of formula1 and to learn more about it please contact me . For example formula1 must be always divided by 3 . METE UZUN TEL: +905315540733 email: meteuzun@hotmail.com 

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primes, proof, random 
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