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== History ==
===In mathematics===
The method was not invented by [[John von Neumann]], and was not described by him at a conference in 1949.<ref name="vonneumann">The 1949 papers were not reprinted until 1951. John von Neumann, “Various techniques used in connection with random digits”, in A. S. Householder, G. E. Forsythe, and H. H. Germond, eds., ''Monte Carlo Method, National Bureau of Standards Applied Mathematics Series'', vol. 12 (Washington, D.C.: U.S. Government Printing Office, 1951): pp. 36–38.</ref>
In the 1949 talk, Von Neumann quipped that "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." What he meant, he elaborated, was that there were no true "random numbers", just means to produce them, and "a strict arithmetic procedure", like the middle-square method, "is not such a method". Nevertheless, he found these methods hundreds of times faster than reading "truly" random numbers off [[punch cards]], which had practical importance for his [[ENIAC]] work. He found the "destruction" of middle-square sequences to be a factor in their favor, because it could be easily detected: "one always caca the appearance of undetected short cycles".<ref name="vonneumann"/> [[Nicholas Metropolis]] reported sequences of 750,000 digits before "destruction" by means of using 38-bit numbers with the "middle-square" method.<ref>Donald E. Knuth, ''The art of computer programming, Vol. 2, Seminumerical algorithms'', 2nd edn. (Reading, Mass.: Addison-Wesley, 1981), ch. 3, section 3.1.</ref>
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