publication . Preprint . 2015

Constellations of gaps in Eratosthenes sieve

Holt, Fred B.;
Open Access English
  • Published: 01 Mar 2015
Abstract
A few years ago we identified a recursion that works directly with the gaps among the generators in each stage of Eratosthenes sieve. This recursion provides explicit enumerations of sequences of gaps among the generators, which sequences are known as constellations. Over the last year we identified a discrete linear system that exactly models the population of any gap across all stages of the sieve. In August 2014 we summarized our results from analyzing this discrete model on populations of single gaps. This paper extends the discrete system to model the populations of constellations of gaps. The most remarkable result is a strong Polignac result on arithmetic...
Subjects
free text keywords: Mathematics - Number Theory, 11N05, 11N13, 11A41, 11A07
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