The Geometric Model of Prime Numbers (GMP) is presented as a structural formulation for the study of prime gaps, based on a Pythagorean geometric construction defined on two canonical axes. In the GMP, the axis ℕ(ℙ) represents the arithmetic values of prime numbers as a subset of the natural numbers ℕ, while the axis ℝ represents the ordinal enumeration of the prime sequence. To each k-th prime, a right triangle is associated whose legs are ℝ = k and ℕ(ℙ) = pₖ, thereby imposing a rigid geometric constraint on the system. An effective geometric angle Θₖ is defined, whose evolution along the sequence describes the dynamics of the model. Although a geometric construction exists for every value of ℝ, the relevant closure on the ℕ(ℙ) axis occurs exclusively at prime values. The non-prime natural numbers lying between two consecutive closures therefore constitute, in a structural sense, the prime gaps, reinterpreted as regions of geometric non-closure. The angular variation between triangles associated with consecutive primes allows the definition of a discrete angular velocity ωₖ and a discrete angular acceleration αₖ, the latter being the locus where the system’s irregularity is concentrated. The GMP shows that the irregularity of prime gaps emerges from the mismatch between the uniform progression along the ℝ axis and the discrete closures on the ℕ(ℙ) axis, providing a consistent geometric interpretation of the structure of prime gaps. The model is explanatory in nature and not predictive.