Related papers: A faster pseudo-primality test

This paper proposes the use of the binary primes sequence to strengthen pseudorandom (PN) decimal sequences for cryptography applications. The binary primes sequence is added to the PN decimal sequence (where one can choose from many…

For any fixed $k\geq 2$, we prove that every sufficiently large integer can be expressed as the sum of a $k$th power of a prime and a number with at most $M(k)=6k$ prime factors. For sufficiently large $k$ we also show that one can take…

For a cyclic Kummer extension $K$ of a rational function field $k$ is considered, via class field theory, the extended Hilbert class field $K_H^+$ of $K$ and the corresponding extended genus field $K_g^+$ of $K$ over $k$, along the lines of…

We examine two quantum operations, the Permutation Test and the Circle Test, which test the identity of n quantum states. These operations naturally extend the well-studied Swap Test on two quantum states. We first show the optimality of…

A positive integer $n$ is defined to be cyclic if and only if every group of size $n$ is cyclic. Equivalently, $n$ is cyclic if and only if $n$ is relatively prime to the number of positive integers less than $n$ that are relatively prime…

Let $D(\mu)$ denote a harmonically weighted Dirichlet space on the unit disc $\mathbb D$. We show that outer functions $f\in D(\mu)$ are cyclic in $D(\mu)$, whenever $\log f$ belongs to the Pick-Smirnov class $N^+(D(\mu))$. If $f$ has…

We propose an algorithm determining the primality of numbers $M=Ap^n+w_n$ where $w_n^{p-1}\equiv1\pmod{p^n}$ and $A<p^n$ and give example when $p=7$. $p$ th reciprocity law is involved. The algorithm runs in polynomial time in $\log_2(M)$…

We consider the problem of generating symmetric pseudo-random sign (+/-1) matrices based on the similarity of their spectra to Wigner's semicircular law. Using binary m-sequences (Golomb sequences) of lengths n=2^m-1, we give a simple…

Multivariate meta-analysis of test accuracy studies when tests are evaluated in terms of sensitivity and specificity at more than one threshold represents an effective way to synthesize results by fully exploiting the data, if compared to…

The calculation of many and large Perrin pseudoprimes is a challenge. This is mainly due to their rarity. Perrin pseudoprimes are one of the rarest known pseudoprimes. In order to calculate many such large numbers, one needs not only a fast…

This paper deals with a class of nonparametric two-sample tests for ordered alternatives. The test statistics proposed are based on the number of observations from one sample that precede or exceed a threshold specified by the other sample,…

In this note, we are going to introduce some recurrence divisibility tests for all primes except than 2 and 5.

We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…

This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…

Multiple hypothesis testing is widely used to evaluate scientific studies involving statistical tests. However, for many of these tests, p-values are not available and are thus often approximated using Monte Carlo tests such as permutation…

Given a $k\times n$ integer primitive matrix $\bf{A}$ (i.e., a matrix can be extended to an $n\times n$ unimodular matrix over the integers) with the maximal absolute value of entries $\|\bf{A}\|$ bounded by {an integer} $\lambda$ from…

Suppose $ m,n\geq 2 $ are co prime integers. We prove certain new symmetries of the base $ n $ representation of $ 1/m $, and in particular characterize the subgroup generated by $ n $ inside $ (\mathbb{Z}/m\mathbb{Z})^\times $. As an…

We present an efficient proof scheme for any instance of left-to-right modular exponentiation, used in many computational tests for primality. Specifically, we show that for any $(a,n,r,m)$ the correctness of a computation $a^n\equiv r\pmod…

Online evaluation of machine learning models is typically conducted through A/B experiments. Sequential statistical tests are valuable tools for analysing these experiments, as they enable researchers to stop data collection early without…

We present a new way of testing ordered hypotheses against all alternatives which overpowers the classical approach both in simplicity and statistical power. Our new method tests the constrained likelihood ratio statistic against the…