"Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method."Since random numbers are important in computer simulations, such as the Monte Carlo method, von Neumann went against his own advice and developed a simple pseudorandom number generator, called the middle-square method, which was useful in the early days of computing. Unknown to von Neumann, but known to the present readers of Wikipedia, this simple method of generating pseudorandom numbers was invented by Brother Edvin, a Franciscan friar, circa 1245. There are two problems with this method, but they're fortunately very apparent when they happen. The first is when the middle digits become all zeros. After that point, the generator output is always zero. The other problem is that the generator can enter a mode in which it outputs the same short sequence, over and over. linear congruential generator, a recurrence relation published by D.H. Lehmer in 1948, as follows:

This generator gives a long list of pseudorandom numbers when proper values are selected forX_{n}= (aX_{n-1}+ c) mod m

a=6364136223846793005, c=1442695040888963407, and m = 2The choice of a power of two for^{64}.

Six dice will generate random numbers from 111,111 to 666,666, which could be scaled to the range, 0 to 555,555. Each die, of course, needs to be assigned to a decimal place. (Illustration by the author.) |

Figure three of the Lavarand patent.[2] (Via Google Patents.) |

Apparatus for one-time pad generation using light scattering.Fig. 2b of ref. 3, (Via arXiv.)[3] |

- This cartoon may have been inspired by the Beatles composition, Revolution 9, which appeared on their white album. This experimental music track has a male voice repeatedly saying, "number nine."
- Landon Curt Noll, Robert G. Mende and Sanjeev Sisodiya, "Method for seeding a pseudo-random number generator with a cryptographic hash of a digitization of a chaotic system," US Patent No. 5,732,138, March 24, 1998.
- Roarke Horstmeyer, Benjamin Judkewitz, Ivo Vellekoop and Changhuei Yang, "Physical key-protected one-time pad," arXiv Preprint Server, May 16, 2013.
- One-Time Pad Reinvented to Make Electronic Copying Impossible, Physics arXiv Blog, Technology Review, May 20, 2013.
- Tony Warnock, "Random-Number Generators," Los Alamos Science (Monte Carlo Special Issue, 1987), pp. 137-141 (PDF file).
- Laszlo Hars, "Random Topics," SummerCon (June 11-13, 2004, Pittsburgh, PA).