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The Mersenne-Twister is one of the most popular generators of uniform pseudo-random numbers. It is used in many numerical libraries and software. In this paper, we look at the Komolgorov entropy of the original Mersenne-Twister, as well as of more modern variations such as the 64-bit Mersenne-Twisters, the Well generators, and the Melg generators.
When the Mersenne Twister made his first appearance in 1997 it was a powerful example of how linear maps on $mathbf F_2$ could be used to generate pseudorandom numbers. In particular, the easiness with which generators with long periods could be defi
In this research paper, relationship between every Mersenne prime and certain Natural numbers is explored. We begin by proving that every Mersenne prime is of the form {4n + 3,for some integer n} and generalize the result to all powers of 2. We also
We investigate various questions concerning the reciprocal sum of divisors, or prime divisors, of the Mersenne numbers $2^n-1$. Conditional on the Elliott-Halberstam Conjecture and the Generalized Riemann Hypothesis, we determine $max_{nle x} sum_{p
Compressed Counting (CC)} was recently proposed for approximating the $alpha$th frequency moments of data streams, for $0<alpha leq 2$. Under the relaxed strict-Turnstile model, CC dramatically improves the standard algorithm based on symmetric stabl
The property of Tsallis entropy is examined when considering tow systems with different temperatures to be in contact with each other and to reach the thermal equilibrium. It is verified that the total Tsallis entropy of the two systems cannot decrea