Prime Counting Function Identity
Number Theory
2022-10-18 v1
Abstract
In this paper, a new formula for {\pi}^(2)(N) is formulated, it is a function that counts the number of semi-primes not exceeding a given number N. A semi-prime is a natural number that is the product of precisely two prime numbers, the two primes in the product may equal each other. Semi-prime numbers are also a case of almost primes. Since a formula for this is already known, a new identity that uses the prime counting function is created by equating the two functions.
Cite
@article{arxiv.2210.08614,
title = {Prime Counting Function Identity},
author = {Suyash Garg},
journal= {arXiv preprint arXiv:2210.08614},
year = {2022}
}
Comments
3 pages