Related papers: Four primality testing algorithms
This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical…
A compression algorithm is presented that uses the set of prime numbers. Sequences of numbers are correlated with the prime numbers, and labeled with the integers. The algorithm can be iterated on data sets, generating factors of doubles on…
We calculate the probability that random polynomial matrices over a finite field with certain structures are right prime or left prime, respectively. In particular, we give an asymptotic formula for the probability that finitely many…
A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division.…
Primality generation is the cornerstone of several essential cryptographic systems. The problem has been a subject of deep investigations, but there is still a substantial room for improvements. Typically, the algorithms used have two parts…
The first efficient general primality proving method was proposed in the year 1980 by Adleman, Pomerance and Rumely and it used Jacobi sums. The method was further developed by H. W. Lenstra Jr. and more of his students and the resulting…
We give Deterministic Primality tests for large families of numbers. These tests were inspired in the recent and celebrated Agrawal-Kayal-Saxena (AKS) test. The AKS test has proved polynomial complexity O ((log n)^12) and they expect it to…
Popularity is an approach in mechanism design to find fair structures in a graph, based on the votes of the nodes. Popular matchings are the relaxation of stable matchings: given a graph G=(V,E) with strict preferences on the neighbors of…
Most prime gaps results have been proven using tools from analytic or algebraic number theory in the last few centuries. In this paper, we would like to present some probabilistic way of proving many essential results. A major component of…
Motivated by settings such as medical treatments or aircraft maintenance, we consider a scheduling problem with jobs that consist of two operations, a test and a processing part. The time required to execute the test is known in advance…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the…
In this set of three companion manuscripts/articles, we unveil our new results on primality testing and reveal new primality testing algorithms enabled by those results. The results have been classified (and referred to) as…
The theoretical aspects of four integer factorization algorithms are discussed in details in this note. The focus is on the performances of these algorithms on the subset of hard to factor balanced integers N = pq, p < q < 2p. The running…
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…
Following Stolarsky, we say that a natural number n is flimsy in base b if some positive multiple of n has smaller digit sum in base b than n does; otherwise it is sturdy. We develop algorithmic methods for the study of sturdy and flimsy…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
Factorization is the most fundamental way to determine if a number $n$ is prime or composite. Yet, this approach becomes impracticable when considering large values of $n$, a difficulty that is exploited by cryptographic protocols. We…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
In many simple integral domains, such as $\mathbb{Z}$ or $\mathbb{Z}[i]$, there is a straightforward procedure to determine if an element is prime by simply reducing to a direct check of finitely many potential divisors. Despite the fact…