Economic development requires a constant supply of energy. The utilization of fossil fuels causes environmental pollution and greenhouse gas emissions. The effects of fossil fuel use have impacted global warming, which may affect the world. The problem of environmental degradation can be decreased by using renewable energy sources and nuclear energy. The role of nuclear energy is increasing. More than 10% of electric energy is now produced from nuclear energy worldwide. However, the share varies by country. For example, in France, it is 70%, in Slovakia, it is 55%, and in Ukraine, it is 53%. Many countries do not have nuclear energy at all. This study aims to investigate the development of gross nuclear electricity production both in the world and in the European Union (EU) in terms of stationarity and prognosis. To achieve the goal of this study, the authors utilized descriptive statistics. The time range included the period 1990–2022. This long time period enabled us to conduct the ADF (Augmented Dickey Fuller) test. According to our analysis, gross nuclear electricity production in the European Union (EU) was stationary. We also evaluated future prognosis using the ARIMA (Autoregressive Moving Average) model. We also used the Vector Autoregressive (VAR) model to evaluate changes within nuclear electricity production. Based on our research, we can conclude that the data were stationary. Finally, we concluded that gross nuclear electricity production in the European Union (EU) will increase in eight countries. In 2022, countries such as Belgium, Bulgaria, Czechia, Spain, France, Hungary, the Netherlands, Romania, Slovenia, Slovakia, and Finland increased their gross nuclear electricity production compared to 1990. Based on the ARIMA model prognosis, the following countries will increase their gross nuclear electricity production in the period 2023–2032: Belgium, Bulgaria, Czechia, Finland, Hungary, the Netherlands, Romania, Slovakia, and Slovenia. Based on the VAR model, we elaborated the prognosis, according to which countries such as France, Romania, Spain, and Sweden will increase their gross nuclear electricity production in the period 2023–2032.