TL;DR
This paper introduces a new identity involving the prime counting function to accurately count semi-primes up to a given number, enhancing understanding of almost primes.
Contribution
It presents a novel formula for the semi-prime counting function using the prime counting function, offering a new perspective on almost prime enumeration.
Findings
Derived a new identity linking semi-primes and prime counting functions
Provided a formula for counting semi-primes up to N
Enhanced methods for analyzing almost primes
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.
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Taxonomy
TopicsComputability, Logic, AI Algorithms