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http://dx.doi.org/10.20465/KIOTS.2020.6.4.049

A study on the approximation function for pairs of primes with difference 10 between consecutive primes  

Lee, Heon-Soo (Department of Mathematics Education, Mokpo National University)
Publication Information
Journal of Internet of Things and Convergence / v.6, no.4, 2020 , pp. 49-57 More about this Journal
Abstract
In this paper, I provided an approximation function Li*2,10(x) using logarithm integral for the counting function π*2,10(x) of consecutive deca primes. Several personal computers and Mathematica were used to validate the approximation function Li*2,10(x). I found the real value of π*2,10(x) and approximate value of Li*2,10(x) for various x ≤ 1011. By the result of theses calculations, most of the error rates are margins of error of 0.005%. Also, I proved that the sum C2,10(∞) of reciprocals of all primes with difference 10 between primes is finite. To find C2,10(∞), I computed the sum C2,10(x) of reciprocals of all consecutive deca primes for various x ≤ 1011 and I estimate that C2,10(∞) probably lies in the range C2,10(∞)=0.4176±2.1×10-3.
Keywords
approximation function; pair of primes; distribution of pair of primes; sum of reciprocals of primes; Mathematica;
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Times Cited By KSCI : 2  (Citation Analysis)
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