How to Detect if Numbers are Random or Not

In this article, you will learn some modern techniques to detect whether a sequence appears as random or not, whether it satisfies the central limit theorem (CLT) or not -- and what the limiting distribution is if CLT does not apply -- as well as some tricks to detect abnormalities. Detecting lack of randomness is also referred to as signal versus noise detection, or pattern recognition. It leads to the exploration of time series with massive, large-scale (long term) auto-correlation structure, as well as model-free, data-driven statistical testing. No statistical knowledge is required: we will discuss deep results that can be expressed in simple English. Most of the testing involved here uses big data (more than a billion computations) and data science, to the point that we reached the accuracy limits of our machines.