Making an approximations for nth index using Prime number Theorem

Aziz Lokhandwala

doi:https://doi.org/10.14445/22315373/IJMTT-V65I5P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 5 | Year 2019 | Article Id. IJMTT-V65I5P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I5P515

Making an approximations for nth index using Prime number Theorem

Aziz Lokhandwala

Citation :

Aziz Lokhandwala, "Making an approximations for nth index using Prime number Theorem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 5, pp. 106-109, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I5P515

Abstract

Using of Gauss’s Prime number theorem for finding number of primes can also tell us which primes are located for a desired index. But it will give a rough approximation because prime number theorem by Gauss is a rough approximation for number of primes.

Keywords

Prime number theorem

References

[1] Prime number theorem(https://faculty.math.illinois.edu/~r-ash/CV/CV7.pdf)
[2] Newman’s short proof(https://people.mpim- bonn.mpg.de/zagier/files/doi/10.2307/2975232/fulltext.pdf)