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A set of data that looks like it is random, but isn't. This is the sort of data you get from the RAND function in BASIC, and most programming languages have an equivilent. Usually the generator is started with a seed value (the BASIC function RANDOMIZE does this) from which it generates a number - this number is then used as the seed to generate the next number.

This is fine for anything that only has to look random - like games - but useless for serious work such as cryptography because the encyrption can be broken by attacking the random number generator. While there are some very advanced random generators out there, it is preferable to use a source of true random data whenever possible - no matter how high the period of a generator is, it will exhibit weaknesses that could potentially be exploited.