406 citations
- University of Massachusetts AmherstUS13 papers
- National Institute of Astrophysics, Optics and ElectronicsMX12 papers
- University of Colorado BoulderUS10 papers
- University of PennsylvaniaUS10 papers
- National Astronomical Observatory of JapanJP7 papers
- The University of TokyoJP7 papers
- California Institute of TechnologyUS6 papers
- University of EdinburghGB5 papers
- Durham UniversityGB4 papers
- Royal ObservatoryGB4 papers
- UK Astronomy Technology CentreGB4 papers
- Cardiff UniversityGB3 papers
5 papers · 1 filter
On the Solutions of Three Variable Frobenius Related Problems Using Order Reduction Approach
Tian-Xiao He, Peter J. -S. Shiue, Rama Venkat
This paper presents a new approach to determine the number of solutions of three variable Frobenius related problems and to find their solutions by using order reducing methods. He…
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…