Yolaçan, Esra2024-05-042024-05-042024T. Rashid, M. M. M. Jaradat, E. Yolacan, H. Ahmad. On Prime Counting Functions Using Odd $K$-Almost Primes. (2024). European Journal of Pure and Applied Mathematics, 17(2), 1146-1154.1146-1154https://ejpam.com/index.php/ejpam/article/view/4961https://doi.org/10.29020/nybg.ejpam.v17i2.4961https://hdl.handle.net/20.500.12695/2733This work takes an interesting diversion, revealing the extraordinary capacity to determine the precise number of primes in a space tripled over another. Exploring the domain of K-almost prime numbers, this paper provides a clear explanation of the complex idea. In addition to outlining the conditions under which odd K-almost prime numbers must exist, it presents a novel method for figuring out how often odd numbers are as 2-almost prime, 3-almost prime, 4-almost prime, and so on, up to a specified limit n. The work goes one step further and offers useful advice on how to use these approaches to precisely calculate the prime counting function, ?(n). Essentially, it offers a comprehensive exploration of the mathematical fabric, where primes reveal their mysteries in both large and small spaces.eninfo:eu-repo/semantics/openAccessPrime counting functionodd K-almost primesArticle17211461154