Editing Pseudorandom number generator (section)

==Early approaches==
An early computer-based PRNG, suggested by [[John von Neumann]] in 1946, is known as the [[middle-square method]]. The algorithm is as follows: take any number, square it, remove the middle digits of the resulting number as the "random number", then use that number as the seed for the next iteration. For example, squaring the number "1111" yields "1234321", which can be written as "01234321", an 8-digit number being the square of a 4-digit number. This gives "2343" as the "random" number. Repeating this procedure gives "4896" as the next result, and so on. Von Neumann used 10 digit numbers, but the process was the same.

A problem with the "middle square" method is that all sequences eventually repeat themselves, some very quickly, such as "0000". Von Neumann was aware of this, but he found the approach sufficient for his purposes and was worried that mathematical "fixes" would simply hide errors rather than remove them.

Von Neumann judged hardware random number generators unsuitable, for, if they did not record the output generated, they could not later be tested for errors. If they did record their output, they would exhaust the limited computer memories then available, and so the computer's ability to read and write numbers. If the numbers were written to cards, they would take very much longer to write and read. On the [[ENIAC]] computer he was using, the "middle square" method generated numbers at a rate some hundred times faster than reading numbers in from [[punched card]]s.

The middle-square method has since been supplanted by more elaborate generators.

A recent innovation is to combine the middle square with a [[Weyl sequence]]. This method produces high-quality output through a long period (see [[middle-square method]]<!-- [[middle-square method#Middle Square Weyl Sequence PRNG|Middle-Square Weyl Sequence PRNG]] -->).