Before revision:  Knowledge of random testing outcomes will therefore (i) significantly improve the predictability of the course of the pandemic, (ii) allow informed and optimized decisions on how to modify restrictive measures, with much shorter delay times than the present ones, and (iii) enable the real-time assessment of the efficiency of new means to reduce transmission rates (such as new tracing strategies based on the mobile telephone network, wearing face masks, etc. ). Frequent random testing for COVID-19 infections has the essential benefit of providing more reliable and refined data than currently available, in both time and space. This is crucial to accompany and monitor the safe release of restrictive measures. Here we show that independent of the total size of population with frequent interactions among its members, about 15000 tests with randomly selected people per day  suffice to obtain valuable data about the current number of infections and their evolution in time .
After revision:  Knowledge of random testing outcomes will therefore (i) significantly improve the predictability of the course of the pandemic, (ii) allow informed and optimized decisions on how to modify restrictive measures, with much shorter delay times than the present ones, and (iii) enable the real-time assessment of the efficiency of new means to reduce transmission rates . Here we suggest, irrespective of the size of a suitably homogeneous population, a conservative estimate of 15000 tests with randomly selected people per day suffice to obtain valuable data about the current number of infections and their evolution in time .