Abstract: Our study initiates by introducing the HL (Hyperbolic Lattice Grid) formulated as HL[x,y] = x*y. This grid lays the foundation for our exploration. Subsequently, we unveil the SMT (Square Multiplication Table) as an outcome of integer coordinates within the HL in the initial quadrant. This serves as a pivotal point for our further analysis. From the SMT, we define the SMTSP (Square Multiplication Table Sieve of Primes), delving deeper into the characteristics and patterns emerging from this structure. We proceed by demonstrating the coverage of the SMT through quadratic sequences, expressed as x=y(y±b). This expansion broadens our understanding of the relationships present within the SMT. Expanding beyond the confines of the SMT, we unveil the FMT (Full Multiplication Table), a comprehensive representation that allows us to define all integers in terms of Pairs of Complementary Divisors (x;y). This distinction draws a clear line between factors and divisors, providing a deeper insight into the nature of these numerical entities. Drawing from these foundational properties, we introduce the TMTSP (Triangular Multiplication Table Sieve of Prime Numbers), which stems from the inherent characteristics of the FMT. The identification of Pairs of Complementary Divisors (x;y) for integers aligns precisely with the pairs of integer coordinates (x,y) defining Cartesian points within the TMTSP on the XY-plane. This exploration leads us to assert that all integers can be categorized as either primes or composites, without exception, based on insights garnered from the multiplication table's intricacies and patterns. Notably, we establish an equivalence, or isomorphism, between the Hyperbolic Sieve of Primes and the Parabolic Sieve of Primes, demonstrating their identical outcomes. Please note that this document is a preprint and has not yet been peer-reviewed. It is intended for discussion and feedback within the scientific community to refine the approaches and conclusions presented. Keywords: Sieve of prime numbers, primes and composites, multiplication table, pair of complementary divisors, hyperbolic lattice grid. 2020 Mathematics Subject Classification: 11N32; 11N35; 11N80; 11A05; 35L02.