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October 12th, 2016, 08:26 AM  #1 
Newbie Joined: Oct 2016 From: United States Posts: 2 Thanks: 0 
Hi everyone! I am new to the forum. In my spare time, I've been trying to find a way to count twin primes under any given x. I know there is a method that exists that utilizes the Twin Prime Constant. Anyways, I found the distribution of twin primes to be related to the EulerMascheroni constant and it took me by surprise. To estimate how many twin primes there are between consecutive squares of primes [P(n+1)^2  P(n)^2] I did the following: [Prime(n+1)^2  Prime(n)^2] / [(Product of all primes up to n)/(Product of all Prime2 up to n, starting with P=5)] Take that result and multiply it by (1/4) * e^(2*(EulerMascheroni Constant)) = 0.79305474 So for example, to estimate the amount of twin primes between 13^2 and 17^2 = [17^2  13^2] / [(2*3*5*7*11*13)/(3*5*9*11)] = 120 / 20.222 = 5.934 = Take that result and multiply it by 0.7905474 = 4.71 Twin Primes between 13^2 and 17^2 I tried to insert a table to show you how close my estimate is to the actual number of twin primes, but could not figure it out. Anyways, here is a link to the table: Math: Twin Primes  Album on Imgur What are your thoughts on this? Is it directly related to the Twin Prime counting function that already exists? Last edited by skipjack; October 12th, 2016 at 10:38 AM. 

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constant, counting, euler, function, prime, twin 
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