We present a model that links the fine structure constant α to 1/137, based on the quantization of Minkowski spacetime, gauge invariance and special relativity. We derive a set of integer equations that demand 137 be a Pythagorean prime in triple and quintuple. We derive a Dirac-type equation but in lattice spacetime with quantized internal energy, momentum, and the overall relativistic mass energy. We estimate an electron’s radius to be R_e=1.43957×10^(-15) m. We also found the simple empirical formula for the ratio between two electrons’ Coulomb and gravitational forces at the same distance as F_C/F_G=2√2×(432)^16×1.0008, the Planck length to R_e ratio as L_Planck/R_e= (432)^(-8)×(10^2/3√6)×1.0008, also the ratiom_proton/m_e=3√2×432×1.0018 between a proton and an electron, where 432 (~137π) is the volume of the 4D unit hyper-cell. . Our conjecture could provide a guideline for the theoretical development of quantum gravity. This work not only elucidates the mysterious relation of prime 137 and the fine structure constant in electromagnetism, but it also sheds some light on intricate but presently unknown links to gravity and other types of forces in nature.