Abstract
PRNGs may be compared to antibiotics. Every type of generator has its unwanted side-effects. There are no safe generators. Good random number generators are characterized by theoretical support, convincing empirical evidence, and positive pratical aspects. They will produce correct results in many - though not all - simulations. Important open questions in this field concern reliable parallelization, the creation of good generators on demand, and the mathematical foundation of forecasting the empirical performance by theoretical figures of merit. Three safety-measures for numerical practice are recommended: (a) check simulation results with widely different generators before taking them seriously, (b) avoid to combine, vectorize, or parallelize PRNGs without theoretical and empirical support, and (c) get to know the properties of your preferred PRNGs.
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