A pseudo-random number generator (PRNG) is a program written for, and used in, probability and statistics applications when large quantities of random digits are needed. Most of these programs produce endless strings of single-digit numbers, usually in base 10, known as the decimal system. When large samples of pseudo-random numbers are taken, each of the 10 digits in the set {0,1,2,3,4,5,6,7,8,9} occurs with equal frequency, even though they are not evenly distributed in the sequence.

Many algorithm s have been developed in an attempt to produce truly random sequences of numbers, endless strings of digits in which it is theoretically impossible to predict the next digit in the sequence based on the digits up to a given point. But the very existence of the algorithm, no matter how sophisticated, means that the next digit can be predicted! This has given rise to the term pseudo-random for such machine-generated strings of digits. They are equivalent to random-number sequences for most applications, but they are not truly random according to the rigorous definition.

The digits in the decimal expansions of irrational number s such as pi (the ratio of a circle's circumference to its diameter in a Euclidean plane), *e* (the natural- logarithm base), or the square roots of numbers that are not perfect squares (such as 2 ^{1/2} or 10 ^{1/2} ) are believed by some mathematicians to be truly random. But computers can be programmed to expand such numbers to thousands, millions, billions, or trillions of decimal places; sequences can be selected that begin with digits far to the right of the decimal (radix) point, or that use every second, third, fourth, or *n* th digit. However, again, the existence of an algorithm to determine the digits in such numbers is used by some theoreticians to argue that even these single-digit number sequences are pseudo-random, and not truly random. The question then becomes, Is the algorithm accurate (that is, random) to infinity, or not? -- and because no one can answer such a question definitively because it is impossible to travel to infinity and find out, the matter becomes philosophical.

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