Results 31 to 40 of about 6,542 (225)
A Simple Algorithm for Prime Factorization and Primality Testing
Journal of Mathematics, 2022 We propose a new simple and faster algorithm to factor numbers based on the nature of the prime numbers contained in such composite numbers. It is well known that every composite number has a unique representation as a product of prime numbers.
Kabenge Hamiss
doaj +1 more source
Lower bounds on the orders of subgroups connected with Agrawal conjecture
Karpatsʹkì Matematičnì Publìkacìï, 2013 Explicit lower bounds are obtained on the multiplicative orders of subgroups of a finite field connected with primality proving algorithm.
R. Popovych
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METHOD OF TESTING LARGE NUMBERS FOR PRIMALITY
Сучасні інформаційні системиThe current stage of scientific and technological development entails ensuring information security across all domains of human activity. Confidential data and wireless channels of remote control systems are particularly sensitive to various types of ...
Vladimir Pevnev +3 more
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Factorization invariants in numerical monoids
, 2016 Nonunique factorization in commutative monoids is often studied using factorization invariants, which assign to each monoid element a quantity determined by the factorization structure. For numerical monoids (co-finite, additive submonoids of the natural
O'Neill, Christopher, Pelayo, Roberto
core +1 more source
On Taking Square Roots without Quadratic Nonresidues over Finite Fields
, 2009 We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and the proof is elementary.
Sze, Tsz-Wo
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Assessing Agricultural Green Total Factor Productivity in Latin America
Agribusiness, EarlyView.ABSTRACT The agricultural sector in Latin America plays a vital role in ensuring food security while impacting the environment. However, there remains a lack of analysis regarding the inputs responsible for pollution within its sub‐technologies. Hence, this article aims to assess agricultural green total factor productivity (TFP) through a novel ...
Tianxiang Li +2 more
wiley +1 more source
Four primality testing algorithms [PDF]
, 2008 In this expository paper we describe four primality tests. The first test is very efficient, but is only capable of proving that a given number is either composite or 'very probably' prime.
Schoof, Rene
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A deterministic version of Pollard's p-1 algorithm
, 2009 In this article we present applications of smooth numbers to the unconditional derandomization of some well-known integer factoring algorithms. We begin with Pollard's $p-1$ algorithm, which finds in random polynomial time the prime divisors $p$ of an ...
Zralek, Bartosz
core +5 more sources
Trust‐region filter algorithms utilizing Hessian information for gray‐box optimization
AIChE Journal, EarlyView.Abstract Optimizing industrial processes often involves gray‐box models that couple algebraic glass‐box equations with black‐box components lacking analytic derivatives. Such systems challenge derivative‐based solvers. The classical trust‐region filter (TRF) algorithm provides a robust framework but requires extensive parameter tuning and numerous ...
Gul Hameed +4 more
wiley +1 more source
Implementing the asymptotically fast version of the elliptic curve primality proving algorithm [PDF]
, 2005 The elliptic curve primality proving (ECPP) algorithm is one of the current fastest practical algorithms for proving the primality of large numbers. Its running time cannot be proven rigorously, but heuristic arguments show that it should run in time O ((
Morain, François
core +3 more sources