2 citations · 5 across the 8 of their papers we have counts for
8 papers
Algorithms for Carmichael numbers
Andrew Shallue, Jonathan Webster
Our primary concern is the computational complexity of algorithms that find all Carmichael numbers less than some specified bound . We have three related results. First, we show…
Advances in Tabulating Carmichael Numbers
Andrew Shallue, Jonathan Webster
We report that there are Carmichael numbers less than which is an order of magnitude improvement on Richard Pinch's prior work. We find Carmichael numbers of t…
Fast tabulation of challenge pseudoprimes
Andrew Shallue, Jonathan Webster
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 min…
Average liar count for degree-2 Frobenius pseudoprimes
Andrew Fiori, Andrew Shallue
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 Erdős and Pomeranc…
Counting composites with two strong liars
Eric Bach, Andrew Shallue
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 …
Lifting Automorphisms of Quotients by Central Subgroups
Ben Kane, Andrew Shallue
Given a finitely presented group , we wish to explore the conditions under which automorphisms of quotients can be lifted to automorphisms of . We discover that in the…
Constructing Carmichael numbers through improved subset-product algorithms
W. R. Alford, Jon Grantham, Steven Hayman +1
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. T…
Division algorithms for the fixed weight subset sum problem
Andrew Shallue
Given positive integers , the fixed weight subset sum problem is to find a subset of the that sum to , where the subset has a prescribed number of element…