The Middle-Square PRNG Family

History

The Middle-Square Method may be one of the oldest recorded methods of producing pseudo-random numbers. It was allegedly created by a Francisian Friar known as Br. Edwin in 1250 AD. According to the surviving texts, Br. Edwin wanted to create a means of rolling dice that could not be manipulated by cleverness or slight of hand. His eventual solution was to have both parties devise a number that would then be passed through some simple calculations, resulting in a new number that would represent the die roll. He reasoned that the new number would likely be unpredictable, and thus appear random.

During a conference in 1949, John von Neumann referenced this method of creating seemingly random numbers as an example of why true randomness cannot be created using math. As this popularized the Middle-Square method, John von Neumann has, for better or worse, become known as its "inventor".

Tested Variants

The Middle-Square Method
The original version of the Middle-Square Method, as proposed by Br. Edwin in the mid-1200s.

The Middle-Square Weyl Sequence RNG
A recent adaptation of the Middle-Square Method by Bernard Widynski, which improves the design by incorporating a Weyl sequence into the generator.