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pro vyhledávání: '"Shallue, Andrew."'
Autor:
Shallue, Andrew, Webster, Jonathan
We report that there are $49679870$ Carmichael numbers less than $10^{22}$ which is an order of magnitude improvement on Richard Pinch's prior work. We find Carmichael numbers of the form $n = Pqr$ using an algorithm bifurcated by the size of $P$ wit
Externí odkaz:
http://arxiv.org/abs/2401.14495
Autor:
Shallue, Andrew, Webster, Jonathan
Publikováno v:
Open Book Series 2 (2019) 411-423
We provide a new algorithm for tabulating composite numbers which are pseudoprimes to both a Fermat test and a Lucas test. Our algorithm is optimized for parameter choices that minimize the occurrence of pseudoprimes, and for pseudoprimes with a fixe
Externí odkaz:
http://arxiv.org/abs/1806.08697
Autor:
Fiori, Andrew, Shallue, Andrew
Publikováno v:
Math Comp, Vol 89 (321), January 2020, pg 493-514
In this paper we obtain lower and upper bounds on the average number of liars for the Quadratic Frobenius Pseudoprime Test of Grantham, generalizing arguments of Erd\H{o}s and Pomerance, and Monier. These bounds are provided for both Jacobi symbol pl
Externí odkaz:
http://arxiv.org/abs/1707.05002
Autor:
Shallue, Andrew.
Thesis (Ph.D.)--University of Wisconsin--Madison, 2007.
eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (p. 82-85).
eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (p. 82-85).
Autor:
Bach, Eric, Shallue, Andrew
The strong probable primality test is an important practical tool for discovering prime numbers. Its effectiveness derives from the following fact: for any odd composite number $n$, if a base $a$ is chosen at random, the algorithm is unlikely to clai
Externí odkaz:
http://arxiv.org/abs/1308.0880
Autor:
Kane, Ben, Shallue, Andrew
Given a finitely presented group $G$, we wish to explore the conditions under which automorphisms of quotients $G/N$ can be lifted to automorphisms of $G$. We discover that in the case where $N$ is a central subgroup of $G$, the question of lifting c
Externí odkaz:
http://arxiv.org/abs/1304.4632
Publikováno v:
Math. Comp. 83 (2014), no. 286, 899-915
We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations are the product of implementations of two new algori
Externí odkaz:
http://arxiv.org/abs/1203.6664
Autor:
Shallue, Andrew
Given positive integers $a_1,..., a_n, t$, the fixed weight subset sum problem is to find a subset of the $a_i$ that sum to $t$, where the subset has a prescribed number of elements. It is this problem that underlies the security of modern knapsack c
Externí odkaz:
http://arxiv.org/abs/1201.2739
Autor:
Shallue, Andrew1 (AUTHOR), Webster, Jonathan2 (AUTHOR) jewebste@butler.edu
Publikováno v:
Research in Number Theory. 10/10/2022, Vol. 8 Issue 4, p1-11. 11p.
Autor:
BACH, ERIC, SHALLUE, ANDREW
Publikováno v:
Mathematics of Computation, 2015 Nov 01. 84(296), 3069-3089.
Externí odkaz:
https://www.jstor.org/stable/45106656