In this paper, we will introduce a new definition of k-Mersenne–Lucas numbers and investigate some properties. Then, obtain identities established connection formulas between k-Mersenne through the use Binet’s formula.

Mersenne Twister uniform random number generators are key cores for hardware acceleration of Monte Carlo simulations. In this work, two different architectures are studied: besides the classical tablebased architecture, a new architecture based on a circular buffer and especially targeting FPGAs is proposed. A 30% performance improvement has been obtained when compared to the fastest previous w...

In this paper, we develop new fast algorithms for 2-D integer circular convolutions and 2-D number theoretic transforms (NTT). These new algorithms, which offer improved computational complexity, are constructed based on polynomial transforms over 2, ; these transforms are Fourier-like transforms over Z1,[.r], which is the integral domain of polynomial forms over Z,. Having defined such polynom...

We say a number is flat if it can be written as a non-trivial power of 2 times an odd squarefree number. The power is the “exponent” and the number of odd primes the “length”. Let N be flat and 4-perfect with exponent a and length m. If a 6≡ 1 mod 12, then a is even. If a is even and 3 ∤ N then m is also even. If a ≡ 1 mod 12 then 3 | N and m is even. If N is flat and 3-perfect and 3 ∤ N , then...

In this paper, we first show that the exponential Diophantine equation 2x + 1 = z2has unique solution (x, z) (3, 3). We then for n > 1, exponential. M 2y z2 where Mn := 2n − is nth Mersenne number, has exactly two solutions in non-negative integers viz., 0, 3) and (n 2, 1). Also, prove w4 y, w, n) (5, 3, . Finally, w2m, m 2 no integral solutions. conclude with some examples to illustrate our...

(1) SIMD-oriented Mersenne Twister (SFMT) is a new pseudorandom number generator (PRNG) which uses 128-bit Single Instruction Multiple Data (SIMD) operations. SFMT is designed and implemented on C language with SIMD extensions and also implemented on standard C without SIMD. (2) Properties of SFMT are studied by using finite field theories, and they are shown to be equal or better than Mersenne...

where p is prime. In our paper we use the latter name. In this form numbers Mp at the first time were studied by Marin Mersenne (1588-1648) at least in 1644 (see in [1, p.9] and a large bibliography there). In our paper we show that all composite Mersenne numbers belong to a class S of pseudoprimes of base 2 which is a subclass of super-Poulet pseudoprimes. Analysis of properties of pseudoprime...

We add to the heuristic and empirical evidence for a conjecture of Gillies about the distribution of the prime divisors of Mersenne numbers. We list some large prime divisors of Mersenne numbers Mp in the range 17000 < p < 105.

In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions Binet formulas for these quaternions investigating some properties among them.

It is pointed out that the Mersenne primes Mp = (2 p − 1) and associated perfect numbers Mp = 2 p−1 Mp play a significant role in string theory; this observation may suggest a classification of consistent string theories. Typeset using REVTEX 1 Anomalies and their avoidance have provided a guidepost in constraining viable particle physics theories. From the standard model to superstrings, the i...