digits after the decimal point.” With this three-digit pseudorandom number in hand, the subsequent pseudorandom number can be calculated, and so on. Of course, since this example involves only three digits, no more than 1,000 different pseudorandom numbers can be generated. And whenever the computer encounters a three-digit number that has been used before, the program will proceed from there with an identical string of numbers. Hence cycles are invariably produced. Their onset can be delayed by making the pseudorandom numbers 15, 20, or more digits long, but in the end even the longest pseudorandom number sequence will end up in a cycle.

Whatever the size of the pseudorandom number, it is imperative that the signal which starts the process come from outside the computer. Otherwise the procedure would always start off with the same seed and all sequences generated by this program would be identical. Many things may serve as a starting signal: the time when the computer operator hits the “Enter” button on the keyboard; the operator’s imperceptible, hence random, hand movement when he or she moves the computer mouse; and so forth.

But however carefully thought out the process might be, in the end all computer-generated random number sequences are of the “pseudo” kind. Scientists nevertheless thought that they could obtain satisfactory results and used their random number generators without many questions. In 1992, however, three physicists found to their horror that their simulations produced incorrect predictions, and hence the conclusions derived from their work were erroneous. Things got even worse. In 2003, two German physicists, Heiko Bauke and Stephan Mertens, proved that generators of random binary numbers produced too many zeros and not enough ones, due to the special role played by zero in algebra.

Organizations specializing in random numbers saw an opportunity. They decided to generate not only the starting value but all numbers outside the computer. The resulting strings of random numbers are put at the disposal of interested parties via the World Wide Web. The sources