Mersenne twister

The Mersenne Twister is a pseudorandom number generator (PRNG). It is by far the most widely used general-purpose PRNG. Its name derives from the fact that its period length is chosen to be a Mersenne prime.The Mersenne Twister is the default PRNG for the following software systems: Microsoft Excel, GAUSS, GLib, GNU Multiple Precision Arithmetic Library, GNU Octave, GNU Scientific Library, gretl, IDL, Julia, CMU Common Lisp, Embeddable Common Lisp, Steel Bank Common Lisp, Maple, MATLAB, Free Pascal, PHP, Python, R, Ruby, SageMath, Scilab, Stata.An alternative generator, WELL ('Well Equidistributed Long-period Linear'), offers quicker recovery, and equal randomness, and nearly equal speed. Marsaglia's xorshift generators and variants are the fastest in this class.A pseudorandom sequence xi of w-bit integers of period P is said to be k-distributed to v-bit accuracy if the following holds.For a w-bit word length, the Mersenne Twister generates integers in the range .CryptMT is a stream cipher and cryptographically secure pseudorandom number generator which uses Mersenne Twister internally. It was developed by Matsumoto and Nishimura alongside Mariko Hagita and Mutsuo Saito. It has been submitted to the eSTREAM project of the eCRYPT network. Unlike Mersenne Twister or its other derivatives, CryptMT is patented.