Prime Numbers Through the Ages: Implementing the Sieve of Eratosthenes in Java
Session
Computer Science and Communication Engineering
Description
The Sieve of Eratosthenes is one of the oldest yet most efficient algorithms for finding prime numbers up to a given limit. This paper presents an analytical and practical implementation of the sieve, focusing on its mathematical foundations and optimized algorithmic behavior using the Java programming language. The aim is to demonstrate how ancient mathematical logic continues to be applicable in modern computational practices. The study outlines the basic sieve method, explores three critical optimizations that reduce time complexity, and evaluates the algorithm's performance in different scenarios. Moreover, this work contrasts the classical approach with similar prime-finding algorithms and emphasizes its didactic value in both education and practical programming. By translating historical mathematical insight into executable code, the paper illustrates the enduring relevance of classical thought in contemporary problem-solving contexts.
Keywords:
Sieve of Eratosthenes, prime numbers, algorithm optimization, time complexity, Java implementation etc
Proceedings Editor
Edmond Hajrizi
ISBN
978-9951-982-41-2
Location
UBT Lipjan, Kosovo
Start Date
25-10-2025 9:00 AM
End Date
26-10-2025 6:00 PM
DOI
10.33107/ubt-ic.2025.113
Recommended Citation
Vrellaku, Vesë; Leka, Hizer; and Novoberdaliu, Alma, "Prime Numbers Through the Ages: Implementing the Sieve of Eratosthenes in Java" (2025). UBT International Conference. 45.
https://knowledgecenter.ubt-uni.net/conference/2025UBTIC/CS/45
Prime Numbers Through the Ages: Implementing the Sieve of Eratosthenes in Java
UBT Lipjan, Kosovo
The Sieve of Eratosthenes is one of the oldest yet most efficient algorithms for finding prime numbers up to a given limit. This paper presents an analytical and practical implementation of the sieve, focusing on its mathematical foundations and optimized algorithmic behavior using the Java programming language. The aim is to demonstrate how ancient mathematical logic continues to be applicable in modern computational practices. The study outlines the basic sieve method, explores three critical optimizations that reduce time complexity, and evaluates the algorithm's performance in different scenarios. Moreover, this work contrasts the classical approach with similar prime-finding algorithms and emphasizes its didactic value in both education and practical programming. By translating historical mathematical insight into executable code, the paper illustrates the enduring relevance of classical thought in contemporary problem-solving contexts.