On The Elementary and Numerical Approach to k-tuple Conjecture

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Published: 2023-07-27

Page: 298-320


Salman Mahmud *

Department of Physics, University of Dhaka, Bangladesh.

*Author to whom correspondence should be addressed.


Abstract

In 1922 Hardy and Littlewood proposed a conjecture on the asymptotic density of admissible prime k-tuples. Here we have used a sieve method and shown an elementary process to calculate the approximate number of admissible prime k-tuples and compared with Hardy-Littlewood conjecture and real values. Then we have combined our elementary formula with the results obtained from numerical data of real values and generated a new formula which gives almost same results as Hardy-Littlewood conjecture. We have also proposed an easy form of this conjecture which gives us a new perspective to think about it.

Keywords: Prime k-tuples, asymptotic density, Hardy-Littlewood conjecture, elementary approach, prime constellations, admissible k-tuples, twin prime


How to Cite

Mahmud , S. (2023). On The Elementary and Numerical Approach to k-tuple Conjecture. Asian Journal of Pure and Applied Mathematics, 5(1), 298–320. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1841

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References

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