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Tabulating Pseudoprimes and Tabulating Liars

Andrew Shallue
2016 ACM Transactions on Algorithms  
The first problem is to tabulate strong pseudoprimes to a single fixed base a. It is now proven that tabulating up to x requires O(x) arithmetic operations and O(x log x) bits of space.  ...  The second problem is to find all strong liars and witnesses, given a fixed odd composite n.  ...  Any or all of these might apply to the problems of tabulating pseudoprimes and liars.  ... 
doi:10.1145/2957759 fatcat:t6miqebql5eyjbaia3e2jnp5ve

Counting composites with two strong liars [article]

Eric Bach, Andrew Shallue
2013 arXiv   pre-print
If this does happen we call a a liar. In 1986, Erdős and Pomerance computed the normal and average number of liars, over all n ≤ x.  ...  We also provide asymptotic counts for the restricted case in which n has two prime factors, and for the n with exactly two Euler liars.  ...  Our algorithm counts odd n ≤ x with two strong liars by tabulating them.  ... 
arXiv:1308.0880v1 fatcat:3ofkqbo6jjdsfjpkqua423fkvy

Generalizations of Carmichael numbers I [article]

Romeo Meštrović
2013 arXiv   pre-print
Motivated by heuristic arguments, our computations and some old conjectures and results for Carmichael numbers, we propose several conjectures for weak Carmichael numbers and for some other classes of  ...  Motivated by the investigations of Carmichael numbers in the last hundred years, here we establish several related results, notions, examples and computatinoal searches for weak Carmichael numbers and  ...  Any a such that a n−1 ≡ 1(mod n) when n is composite is called a Fermat liar. In this case n is called Fermat pseudoprime to base a.  ... 
arXiv:1305.1867v1 fatcat:nag7ilossra7hdznq7qdjq5gei