Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2286 2022 2022 Thi-Qar Oil Company, Iraqi Ministry of Oil, Iraq Tareq M. .. Department of Computer Science, College of Computer Science & Mathematics, University of Thi-Qar , Iraq Rasha B. Yousif This research paper focuses on a captivating mathematical phenomenon that arises when examining the total summation of prime and composite numbers. It brings to light two specific cases where the sum of numbers from a certain range is equal for both prime and composite numbers. The paper offers a deep exploration into the theoretical foundations and intricate mathematics that underlie this phenomenon. The research paper conducts a comprehensive analysis of the phenomenon, examining the specific ranges and conditions in which the total summation equality occurs. It delves into the mathematical principles involved, investigating the relationships between prime and composite numbers and their summations. The implications of these findings are explored, shedding light on the underlying patterns and structures in number theory. 2023 2023 38 44 10.54216/GJMSA.090104 https://www.americaspg.com/articleinfo/33/show/2286