English

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.

Keywords

Cite

@article{arxiv.2210.08614,
  title  = {Prime Counting Function Identity},
  author = {Suyash Garg},
  journal= {arXiv preprint arXiv:2210.08614},
  year   = {2022}
}

Comments

3 pages

R2 v1 2026-06-28T03:45:29.490Z