Výsledky vyhledávání - "Wolf, François"

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Semi-primitive roots and irreducible quadratic forms

Autor: Wolf, Marc, Wolf, François

Modulo a prime number, we define semi-primitive roots as the square of primitive roots. We present a method for calculating primitive roots from quadratic residues, including semi-primitive roots. We then present progressions that generate primitive

Externí odkaz: http://arxiv.org/abs/2407.20269

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On the density of primes of the form $X^2+c$

Autor: Wolf, Marc, Wolf, François

We present a method for finding large fixed-size primes of the form $X^2+c$. We study the density of primes on the sets $E_c = \{N(X,c)=X^2+c,\ X \in (2\mathbb{Z}+(c-1))\}$, $c \in \mathbb{N}^*$. We describe an algorithm for generating values of $c$

Externí odkaz: http://arxiv.org/abs/2311.05647

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On the factorization of numbers of the form $X^2+c$

Autor: Wolf, Marc, Wolf, François

Publikováno v: Transactions on Machine Learning and Artificial Intelligence (2022), Volume 10, Issue 4, pages 59 to 77

We study the factorization of the numbers $N = X^2+c$, where $c$ is a fixed constant, and this independently of the value of gcd$(X,c)$. We prove the existence of a family of sequences with arithmetic difference $(U_n, Z_n)$ generating factorizations

Externí odkaz: http://arxiv.org/abs/2208.12579

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On the distribution of consecutive composite odd numbers and twin primes

Autor: Wolf, Marc, Wolf, FranÇOis, Villemin, FranÇOis-Xavier

Publikováno v: Fundamental Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 1, 2019, Pages 1 to 24

We study pairs of consecutive odd numbers through a straightforward indexing. We focus in particular on twin primes and their distribution. With a counting argument, we calculate the limit of an alternating sum that is equal to 1 which means there ar

Externí odkaz: http://arxiv.org/abs/2106.03071

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Primality test and primes enumeration using odd numbers indexation

Autor: Wolf, Marc, Wolf, François

Publikováno v: Transactions on Machine Learning and Artificial Intelligence (2020) vol 8 pages 11 to 41

Odd numbers can be indexed by the map k(n)=(n-3)/2, n belonging to 2N+3. We first propose a basic primality test using this index function that was first introduced in article (8). Input size of operations is reduced which improves computational time

Externí odkaz: http://arxiv.org/abs/2106.01327

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Calculation of extended gcd by normalization

Autor: Wolf, Marc, Wolf, François, Coz, Corentin Le

Publikováno v: SCIREA Journal of Mathematics. Vol. 3, No. 3, 2018, pp. 118 - 131

We propose a new algorithm solving the extended gcd problem, which provides a solution minimizing one of the two coordinates. The algorithm relies on elementary arithmetic properties.
Comment: 9 pages

Externí odkaz: http://arxiv.org/abs/1809.05844

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Representation theorem of composite odd numbers indices

Autor: Marc, Wolf, Wolf, François

We study the composite odd numbers via their indices with a function ranging through all of them. This mapping allows us to demonstrate that the set of these indices are described with two families of finite sequences with arithmetic differences. Com

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od_______166::f7e26dbbc782efcc5bb5864061267054
https://hal.archives-ouvertes.fr/hal-01832624

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