The mass spectrum of elementary particles, in the form of systematically increasing mass values, is obtained from the fractal mechanism of leptosynthesis and baryosynthesis. A theoretical justification for the mass spectrum of elementary particles is provided. The law of baryogenesis serves as the generator of the mass spectrum of elementary particles. The law of baryogenesis implies mass values for both known and yet undiscovered elementary particles. The generated mass spectrum is represented by multiplets of three mass values each. The mass difference within triplets is very small and less than the mass of an electron. The mass values of elementary particles in the mass spectrum adhere to a strict law, forming a systematic increasing sequence. The regularity in the dynamics of mass values growth of elementary particles is close to the law of increasing numbers in the Mersenne sequence. From the mass spectrum of elementary particles, it follows that the predicted number of undiscovered elementary particles far exceeds the number of known particles. In the mass range from the electron to the deuteron, 56 elementary particles remain undiscovered. Expected mass values are provided for new elementary particles that are yet to be discovered in experiments.