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arxiv: math/0502376 · v1 · submitted 2005-02-17 · 🧮 math.NT · hep-th

On the distribution of prime numbers (II)

classification 🧮 math.NT hep-th
keywords primesprimebasicdistributionnumbernumbersdefinedterms
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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.

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