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• W3034331510 abstract "Let $xge y>0$ be integers. We present an algorithm that will generate an integer $nle x$ at random, with known prime factorization, such that every prime divisor of $n$ is $le y$. Further, asymptotically, $n$ is chosen uniformly from among all integers $le x$ that have no prime divisors $>y$. In particular, if we assume the Extended Riemann Hypothesis, then with probability $1-o(1)$, the average running time of our algorithm is $$ Oleft( frac{ (log x)^3 }{loglog x} right) $$ arithmetic operations. We also present other running times based on differing sets of assumptions and heuristics." @default.
• W3034331510 created "2020-06-19" @default.
• W3034331510 creator A5025020420 @default.
• W3034331510 creator A5057710320 @default.
• W3034331510 date "2020-06-12" @default.
• W3034331510 modified "2023-09-27" @default.
• W3034331510 title "An Algorithm to Generate Random Factored Smooth Integers." @default.
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• W3034331510 hasPublicationYear "2020" @default.
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