Algorithmic and Computational Exploration of Perfect Numbers

Abstract

This paper investigates perfect numbers by tracing their historical significance and computational evolution from ancient mathematics to the modern era. It discusses the formal mathematical definition of perfect numbers, their role in number theory, and key milestones in their discovery. The study further examines how advances in computational techniques and programming expertise have enabled researchers to identify new perfect numbers, significantly expanding the known set. By presenting a comprehensive overview, this paper highlights the essential contributions of both classical mathematical reasoning and contemporary computational methods, emphasizing the enduring relevance of perfect numbers in theoretical and applied mathematics.