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(number theory) How tommy1729 does it. - Printable Version

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(number theory) How tommy1729 does it. - tommy1729 - 08/12/2013

Let pi(n,2^d) be the counting function for numbers of the form (p,p+2^d) with p,p+2^d prime below n.

My estimate - in contrast to Hardy and Littlewood - is

For slog(n)+6<2^d :

pi(n,2^d) = C [ ( n - 2^d ) / ( ln(n)ln(n-2^d) ) ] + O(d ln(n)^2 sqrt(n))

I believe my estimate is valid on average and is a better estimate.

Im even more skeptical about prime constellations of longer length, such as (p,p+2^a,p+2^(a+b)) and one of the reasons is the mystery of fermat primes and mersenne primes.

An estimate for triplets is beyond my courage and confidence to even conjecture.

Since critisism of ideas like AC or H-L are not very popular and controversial , I post them here.