Crises like COVID-19 or the Japanese earthquake in 2011 exposed the fragility of corporate supply networks. The production of goods and services is a highly interdependent process and can be severely impacted by the default of critical suppliers or customers. While knowing the impact of individual companies on national economies is a prerequisite for efficient risk management, the quantitative assessment of the involved economic systemic risks (ESR) is hitherto practically non-existent, mainly because of a lack of fine-grained data in combination with coherent methods. Based on a unique value added tax dataset we derive the detailed production network of an entire country and present a novel approach for computing the ESR of all individual firms. We demonstrate that a tiny fraction (0.035%) of companies has extraordinarily high systemic risk impacting about 23% of the national economic production should any of them default. Firm size alone cannot explain the ESR of individual companies; their position in the production networks does matter substantially. If companies are ranked according to their economic systemic risk index (ESRI), firms with a rank above a characteristic value have very similar ESRI values, while for the rest the rank distribution of ESRI decays slowly as a power-law; 99.8% of all companies have an impact on less than 1% of the economy. We show that the assessment of ESR is impossible with aggregate data as used in traditional Input-Output Economics. We discuss how simple policies of introducing supply chain redundancies can reduce ESR of some extremely risky companies.