Zobrazeno 1 - 10
of 3 160
pro vyhledávání: '"Sieve of Eratosthenes"'
Autor:
Hartman, Samuel, Sorenson, Jonathan P.
We present a version of the sieve of Eratosthenes that can factor all integers $\le x$ in $O(x \log\log x)$ arithmetic operations using at most $O(\sqrt{x}/\log\log x)$ bits of space. This is an improved space bound under the condition that the algor
Externí odkaz:
http://arxiv.org/abs/2406.09150
Autor:
Diouf, Madieyna
We have devised an alternative approach to sifting integers in the sieve of Eratosthenes that helps refine the error term. Instead of eliminating all multiples of a prime number $p
Externí odkaz:
http://arxiv.org/abs/2310.08144
Akademický článek
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Autor:
Fan, Steve, Pomerance, Carl
Let $\Phi(x,y)$ denote the number of integers $n\in[1,x]$ free of prime factors $\le y$. We show that but for a few small cases, $\Phi(x,y)<.6x/\log y$ when $y\le\sqrt{x}$.
Comment: 15 pages, 1 figure; to appear in the Journal of Number Theory
Comment: 15 pages, 1 figure; to appear in the Journal of Number Theory
Externí odkaz:
http://arxiv.org/abs/2306.03339
Autor:
Fan, Kai, Pomerance, Carl
Publikováno v:
In Journal of Number Theory January 2024 254:169-183
Autor:
LYNCH, PETER1 Peter.Lynch@ucd.ie
Publikováno v:
Bulletin of the Irish Mathematical Society. Winter2023/2024, Issue 92, p49-53. 5p.
Publikováno v:
Phys. Rev. A 105, L021304 (2022)
We catalog known optical moir\'e lattices and uncover exotic lattice configurations following a geometric analog of the ancient sieve of Eratosthenes algorithm for finding prime numbers. Rich dynamics of Bose-Einstein condensates loaded into these op
Externí odkaz:
http://arxiv.org/abs/2203.02017
Autor:
Grob, George F.
This paper analyzes the emergence and distribution of potential twin primes, pairs of integers that are both relatively prime to the first n primes or to a given set M of primes, and which are the breeding grounds of true twin primes. It describes cy
Externí odkaz:
http://arxiv.org/abs/2107.06950
Autor:
Diab, Ahmed
We make two algorithms that generate all prime numbers up to a given limit, they are a development of sieve of Eratosthenes algorithm, we use two formulas to achieve this development, where all the multiples of prime number 2 are eliminated in the fi
Externí odkaz:
http://arxiv.org/abs/2102.06653
Autor:
Grob, George, Schmitt, Matthias
We describe recurring patterns of numbers that survive each wave of the Sieve of Eratosthenes, including symmetries, uniform subdivisions, and quantifiable, predictive cycles that characterize their distribution across the number line. We generalize
Externí odkaz:
http://arxiv.org/abs/1905.03117