Results 21 to 30 of about 1,246,845 (203)
On some new families of $k$-Mersenne and generalized $k$-Gaussian Mersenne numbers and their polynomials [PDF]
, 2023 In this paper, we define the generalized k-Mersenne numbers and give a formula of generalized Mersenne polynomials and further, we study their properties.
Jagmohan Tanti +2 more
core +2 more sources
Generalised Mersenne numbers revisited [PDF]
Mathematics of Computation, 2013 32 pages.
Robert Granger, Andrew Moss
openaire +7 more sources
Primality-testing Mersenne Numbers (II) [PDF]
, 1986 Reports the factor-filtering and primality-testing of Mersenne Numbers Mp for p < 100000, the latter using the ICL 'DAP' Distributed Array ...
Haworth, Guy McCrossan
core +5 more sources
On generalized bihyperbolic Mersenne numbers [PDF]
, 2020 summary:In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained ...
Bród, Dorota +4 more
core +1 more source
Leading Digits of Mersenne Numbers [PDF]
Experimental Mathematics, 2019 It has long been known that sequences such as the powers of $2$ and the factorials satisfy Benford's Law; that is, leading digits in these sequences occur with frequencies given by $P(d)=\log_{10}(1+1/d)$, $d=1,2,\dots,9$. In this paper, we consider the leading digits of the Mersenne numbers $M_n=2^{p_n}-1$, where $p_n$ is the $n$-th prime. In light of
Zhaodong Cai +4 more
openaire +3 more sources
Mathematics of Computation, 1958 Im Jahre 1957 prüfte der Verf. mit Hilfe der Maschine BESK die Mersenneschen Zahlen \(M_p = 2^p-1\) für \(p < 10,000\). Und zwar zunächst alle diese auf etwaige Teiler \(< 10\cdot 2^{20}\) und hierauf diejenigen für \(2300 < p < 3300\), bei denen sich kein solcher Teiler ergab, nach dem Lucas-Test auf ihre Primheit. Dabei ergab sich nur \(2^{3217}- 1\)
openaire +2 more sources
On generalized Mersenne hybrid numbers [PDF]
, 2020 The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper we consider a special kind of hybrid numbers, namely the Mersenne hybrid numbers and we give some of their ...
Szynal-Liana, Anetta +3 more
core +2 more sources
Nature, 1911 I DESIRE to announce the discovery which I have made that (2181 —;1) is divisible by 43441. This leaves only 16 of the numbers (2q — 1) originally reported composite by Mersenne, still unverified. I have submitted my determination to Lt.—Col. Allan Cunningham, R.E., who has kindly verified it.
openaire +1 more source
Fermat numbers and Mersenne numbers [PDF]
Mathematics of Computation, 1964 This paper gives details of the computations made on an IBM 7090 computer to show that the Fermat number \(F_m = 2^{2^m} +1\) is composite for \(m=14\), and that all the Mersenne numbers \(M_p=2^p-1\) \((5000 < p < 6000)\) are composite. The method used to show that the Fermat number is composite was to compute \(3^{2^n}\) modulo \(F_m\).
Selfridge, J. L., Hurwitz, Alexander
openaire +2 more sources
Nature, 1895 IN 1644 the mathematician Mersenne asserted that out of the 56 primes not < 257, there were only 12 primes, viz.:—
openaire +2 more sources