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Surprisingly, the general-purpose random number generators that are in most widespread use are easily predicted. (In contrast RNGs used to construct stream ciphers for secure communication are believed to be infeasible to predict, and are known as cryptographically secure).

Benford's law (also called the first digit law) states that the leading digits in a collection of data sets are probably going to be small. For example, most numbers in a set (about 30%) will have a leading digit of 1, when the expected probability is 11.1% (i.e. one out of nine digits).

Benford's Law holds true for a data set that grows exponentially (e.g., doubles, then doubles again in the same time span), but also appears to hold true for many cases in which an exponential growth pattern is not obvious (e.g., constant growth each month in the number of accounting transactions for a particular cycle

Benford's Law proves that in any set of truly random data, the first digit will be one most prominently, and the likelihood of other digits occurring decreases in chronological order. The only material used was the random number generator inside a TI-83 PLUS graphing calculator.

Benford's Law can recognize the probabilities of highly likely or highly unlikely frequencies of numbers in a data set. The probabilities are based on mathematical logarithms of the occurrence of digits in randomly generated numbers in large data sets.

For instance, Benford's Law will not hold true for data sets of human heights, human weights and intellectual quotient (IQ) scores. Another example would be small insurance claims (e.g., between US $50 and US $100). The theory also does not hold true when a data set covers only one or two orders of magnitude.

One such test is to see how well the data follow Benford's Law. Benford's Law involves the distribution of lead digits in ?naturally occurring numbers,? e.g., vendor payments, customer invoices, and similar financial values that occur in the normal course of business.