On the distribution of prime numbers (II)

Doron Gepner

On the distribution of prime numbers (II)

Number Theory 2007-05-23 v1 High Energy Physics - Theory

Authors: Doron Gepner

Abstract

Recently, I have defined the so called PDF's (prime distribution factors) which govern the distribution of prime numbers of the type $p,p+a_i$ being all primes up to some number $n$ . It was shown that the PDF's are expressible in terms of the basic PDF's which are defined as $a_i-a_j$ or $a_i$ being composed of primes which are less or equal to the number of primes. For example, $p,p+2$ (twin primes), or $p,p+2,p+6$ being all primes (basic triplets). We give here a conjecture for the number of basic prime PDF's in terms of Hardy-Littlewood numbers, thus completing the determination of PDF's. These conjectures are supported by extensive calculations.

Keywords

prime distribution factors hardy-littlewood numbers twin primes basic triplets prime number distribution

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@article{arxiv.math/0502376,
  title  = {On the distribution of prime numbers (II)},
  author = {Doron Gepner},
  journal= {arXiv preprint arXiv:math/0502376},
  year   = {2007}
}

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6 pages

On the distribution of prime numbers (II)

Abstract

Keywords

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