Results 81 to 90 of about 125 (118)

Mersenne Prime

2011
Solinas Jérôme A
exaly   +2 more sources

Testing Mersenne Primes with Elliptic Curves

2006
The current primality test in use for Mersenne primes continues to be the Lucas-Lehmer test, invented by Lucas in 1876 and proved by Lehmer in 1935. In this paper, a practical approach to an elliptic curve test of Gross for Mersenne primes, is discussed and analyzed.
Song Y. Yan, Glyn James
openaire   +1 more source

On some geometry of Mersenne primes

Periodica Mathematica Hungarica, 1994
A possible connection between Mersenne primes and certain geometrical structures is implied. Here the authors consider the structures \((\mathbb{Z}_ q,{\mathcal B}_ p^ \#, \in)\) resulting from a planar nearring \((\mathbb{Z}_ q, +, *)\), where \(q= M_ p\) is a Mersenne prime, \(\mathbb{Z}_ q\) denotes the integers modulo \(q\), \(*\) is a ...
Clay, J. R., Yeh, Y.-N.
openaire   +1 more source

Where is the next mersenne prime hiding?

The Mathematical Intelligencer, 1983
Almost identical to the paragraph 3.5 of the author's book reviewed above.
openaire   +2 more sources

Mersenne Primes, Irrationality and Counting Subgroups

Bulletin of the London Mathematical Society, 1997
The author continues his studies on counting congruence subgroups in arithmetic subgroups [see ibid. 26, 255-262 (1994; Zbl 0849.11066)]. In this paper he considers the question of counting subgroups of \(p\)-power index in a group \(G_I\) which is the product of alternating groups \(A_{p^a}\) for \(a\in I\), where \(I\) is some subset of \(\mathbb{N}\)
openaire   +1 more source

Fast Mersenne prime testing on the GPU

Proceedings of the Fourth Workshop on General Purpose Processing on Graphics Processing Units, 2011
The Lucas-Lehmer test for Mersenne primality can be efficiently parallelized for GPU-based computation. The gpuLucas project implements an irrational-base discrete weighted transform approach (IBDWT) using balanced-integers, non-power-of-two transforms, and carry-save radix representations.
openaire   +1 more source

Mersenne composites and cyclotomic primes

The Mathematical Gazette, 2003
One of the long-standing problems of number theory, appealing to professional and recreational mathematicians alike, is the existence of Mersenne primes. These puzzling primes, for example 7, 31, 127 and 8191, are of the form 2 P - 1, where p is itself a prime.
openaire   +1 more source

Merci-A New Mersenne Prime

Science, 1992
openaire   +3 more sources

Efficient arithmetic in (pseudo-)mersenne prime order fields

Advances in Mathematics of Communications, 2022
Palash Sarkar, Kaushik Nath
exaly  

A Remark on the Primeness of Mersenne Numbers

Journal of the London Mathematical Society, 1953
openaire   +1 more source