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Widely used in many programs, e.g. it is used in Excel 2003 and later versions for the Excel function RAND and it was the default generator in the language Python up to version 2.2. Rule 30: 1983 S. Wolfram Based on cellular automata. Inversive congruential generator (ICG) 1986 J. Eichenauer and J. Lehn Blum Blum Shub: 1986
A simple formula is. for positive integer , where is the floor function, which rounds down to the nearest integer. By Wilson's theorem, is prime if and only if . Thus, when is prime, the first factor in the product becomes one, and the formula produces the prime number . But when is not prime, the first factor becomes zero and the formula ...
Random number generation is a process by which, often by means of a random number generator ( RNG ), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but impossible to foresee.
The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation.
A pseudorandom number generator ( PRNG ), also known as a deterministic random bit generator ( DRBG ), [1] is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value ...
Rule 30 has also been used as a random number generator in Mathematica, and has also been proposed as a possible stream cipher for use in cryptography. Rule 30 is so named because 30 is the smallest Wolfram code which describes its rule set (as described below). The mirror image, complement, and mirror complement of Rule 30 have Wolfram codes ...
The Lehmer random number generator [1] (named after D. H. Lehmer ), sometimes also referred to as the Park–Miller random number generator (after Stephen K. Park and Keith W. Miller), is a type of linear congruential generator (LCG) that operates in multiplicative group of integers modulo n. The general formula is.
Blum Blum Shub ( B.B.S.) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub [1] that is derived from Michael O. Rabin 's one-way function. Blum Blum Shub takes the form. , where M = pq is the product of two large primes p and q. At each step of the algorithm, some output is derived from xn+1; the ...