Andrew Shallue

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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 algorithms for the subset product problem that exploit the non-uniform distribution of primes p with the property(More)
This article explores the asymptotic complexity of two problems related to the Miller-Rabin-Selfridge primality test. The first problem is to tabulate strong pseudoprimes to a single fixed base <i>a</i>. It is now proven that tabulating up to <i>x</i> requires <i>O</i>(<i>x</i>) arithmetic operations and <i>O</i>(<i>x</i>log&thinsp;<i>x</i>) bits of space.(More)
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