Demography is one of the important factors of the Great Convergence. We estimate the contribution of the demographic factor to the prospective GDP dynamics for all countries of the world up to 2100. We use a long-term economic growth model that is based on estimates of labor productivity growth rates and incorporates the demographic forecast for both population and life expectancy. Globally, our model estimates long-term economic growth of world GDP at an average annual rate of 1.7 per cent, of which the demographic factor accounts for 0.54 percentage points, or about one-third (31.8 per cent) of the projected world economic growth in the twenty-first century. In our forecasts, we have relied on the logic of the previous research on convergence, which considered a sufficiently high level of the human capital development and a sufficient degree of economic openness as necessary conditions for convergence, which have now largely been achieved throughout the world precisely through the globalization processes (especially in the core and the semi-periphery of the World System). However, the inclusion of the demographic projections in our forecasts allows us to emphasize an important feature of the perspective convergence – it is not the semi-periphery, but rather the periphery of the World System, or the ‘bottom billion’ according to Collier, that is likely to converge particularly rapidly with both the core and the semi-periphery (such as the BRICS countries) thanks to favorable demographic structure. The paper has been prepared within the framework of RANEPA state assignment in 2023.