2 citations · 5 across the 8 of their papers we have counts for
6 papers · 1 filter
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 …
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…