Distribution of Primes and of Interval Prime Pairs Based on $Θ$ Function

Details Distribution of Primes and of Interval Prime Pairs Based on $Θ$ Function Distribution of Primes and of Interval Prime Pairs Based on $Θ$ Function

2010-04-19

arxiv.org/abs/1004.3080v1

Physics

Mathematical Physics

21 pages, 4 figures

Scientific paper

$\Theta$ function is defined based upon Kronecher symbol. In light of the principle of inclusion-exclusion, $\Theta$ function of sine function is used to denote the distribution of composites and primes. The structure of Goldbach Conjecture has been analyzed, and $\Xi$ function is brought forward by the linear diophantine equation; by relating to $\Theta$ function, the interval distribution of composite pairs and prime pairs (i.e. the Goldbach Conjecture) is thus obtained. In the end, Abel's Theorem (Multiplication of Series) is used to discuss the lower limit of the distribution of the interval prime pairs.

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